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11 September 2013 at 11:02 AM
by - remove spam links

Deleted lines 23-24:

http://asortie.com http://asortie.com http://asortie.com http://asortie.com http://asortie.com http://www.mynet.com

28 July 2013 at 02:00 PM
by - Yes

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http://asortie.com http://asortie.com http://asortie.com http://asortie.com http://asortie.com

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http://asortie.com http://asortie.com http://asortie.com http://asortie.com http://asortie.com http://www.mynet.com

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[

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http://asortie.com http://asortie.com http://asortie.com http://asortie.com http://asortie.com

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The site is running {$Version} and {$WPVersion}.

to:

The site is running {$Version} and {$WPVersion}.

[http://asortie.com/ klasik mobilya] [http://asortie.com/ classic furniture] [http://asortie.com/ istanbul klasik mobilya]

[http://asortie.com/ avangard mobilya] [http://asortie.com/ el yapımı mobilya - handmade furniture]

[http://asortie.com/ klasik mobilya] [http://asortie.com/ classic furniture] [http://asortie.com/ istanbul klasik mobilya]

[http://asortie.com/ avangard mobilya] [http://asortie.com/ el yapımı mobilya - handmade furniture]

02 May 2012 at 06:02 PM
by - fix evil spammer

Changed lines 1-25 from:

No wonder, your home is the world’s coziest place for you

As you are a busy person and you don’t have enough time to do self inspection for getting an estimate

http://sites

'''Receive Estimates from Licensed Contractors Online…'''

To receive estimates from contractors, it’s better to take help from the online world. There are many web directories dedicated to provide information on licensed contractors in your area. You just need to sign up the web directory and need to fill out a simple form that includes the project name, the date you want to start renovation, your name, address, email address and the best time to call you. Once the form is filled, it’s time to click the submit button after reading the terms and conditions.

Now, your 30% work is over. You will receive call from several licensed contractors in your area since you filled the form

It is advised to make a note of everything you want done to the property and discuss these things with contractors to find a well-convincing estimate. Remember, a trustable contractor will discuss many things that you haven’t included in your note, but they are essential to discuss for getting an exact estimate.

http://sites.leadstormmedia.com/uploads/image/iStock_000008013955XSmall.jpg

The contractor will sure to discuss about the demolition work, climate, greenery and the building code. You just wonder about the climate discussion, but there are some home renovations dependent on climate. For example, roofing work and landscaping cannot be done in a bad weather.

Greenery is essential to discuss because some work can be done for creating healthier environment. It may possible that some extra effort, time and money need to meet the building code standard. The contractor will discuss openly about his fees and will not try to keep you in dark. The additional 5% or 10% expenditure will also be discussed due to the fluctuating price of building materials.

Discuss at least 3-5 contractors about your home renovation work. Compare their prices to finalize the one that you find perfect for your home renovation. Invite the contractor to see your home and to start the work as soon as possible.

For more information visit http://www.bizzibid.com/

to:

W;ikipublisher is a TypesettingEngine; that re-purposes Web content for print, with 2 mouse-clicks. It provides a Web-based [[Book(Guide) ]]Production platform.

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be recast as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print. :)

(:keywords collaborative authoring, book production, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those showing [[(PmWiki/wiki )trails]], [[PmWiki/page lists]] or [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document.

:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how. Look at the [[example book -> http://www.wikipublisher.org/books/GNUZealand2009/Transcripts]].

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

(:typeset-trail toc=on colorlinks=on marginshift=on:)

The site is running {$Version} and {$WPVersion}.

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be recast as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print. :)

(:keywords collaborative authoring, book production, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those showing [[(PmWiki/wiki )trails]], [[PmWiki/page lists]] or [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document.

:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how. Look at the [[example book -> http://www.wikipublisher.org/books/GNUZealand2009/Transcripts]].

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

(:typeset-trail toc=on colorlinks=on marginshift=on:)

The site is running {$Version} and {$WPVersion}.

01 May 2012 at 12:54 AM
by - No wonder, your home is the world’s coziest place for you. It is your home where you find freedom to

Changed lines 1-22 from:

:Turn Web pages into beautiful print:Wikipublisher is an extension

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with

(:keywords collaborative authoring, book production, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page

:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how. Look at the [[example book -> http://www

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

(:typeset-trail toc=on colorlinks=on marginshift=on:)

The site is running {$Version} and {$WPVersion}

to:

!! How To Receive Home Improvement Estimates From Licensed Contractors Online

No wonder, your home is the world’s coziest place for you. It is your home where you find freedom to live life in your own way. Though, to make your home remains the coziest place, it’s essential to think about its renovation. A time comes when your home roof starts leaking, walls, doors and windows get faded, and the drawing room desperately needs a huge change. Though, renovating a home is a time consuming and expensive affair. You need to estimate both the time and cost of the renovation work.

As you are a busy person and you don’t have enough time to do self inspection for getting an estimate, in this case all you need to take help from a licensed contractor in your area. Remember, a licensed contractor is the one whom you can trust for your estimates. They are expert in this field and have up to date knowledge about current rates of materials required for home renovation.

http://sites.leadstormmedia.com/uploads/image/iStock_000006824056XSmall.jpg

'''Receive Estimates from Licensed Contractors Online…'''

To receive estimates from contractors, it’s better to take help from the online world. There are many web directories dedicated to provide information on licensed contractors in your area. You just need to sign up the web directory and need to fill out a simple form that includes the project name, the date you want to start renovation, your name, address, email address and the best time to call you. Once the form is filled, it’s time to click the submit button after reading the terms and conditions.

Now, your 30% work is over. You will receive call from several licensed contractors in your area since you filled the form. They will discuss their estimates and you will be able to hire the one that suits to your budget and needs.

It is advised to make a note of everything you want done to the property and discuss these things with contractors to find a well-convincing estimate. Remember, a trustable contractor will discuss many things that you haven’t included in your note, but they are essential to discuss for getting an exact estimate.

http://sites.leadstormmedia.com/uploads/image/iStock_000008013955XSmall.jpg

The contractor will sure to discuss about the demolition work, climate, greenery and the building code. You just wonder about the climate discussion, but there are some home renovations dependent on climate. For example, roofing work and landscaping cannot be done in a bad weather.

Greenery is essential to discuss because some work can be done for creating healthier environment. It may possible that some extra effort, time and money need to meet the building code standard. The contractor will discuss openly about his fees and will not try to keep you in dark. The additional 5% or 10% expenditure will also be discussed due to the fluctuating price of building materials.

Discuss at least 3-5 contractors about your home renovation work. Compare their prices to finalize the one that you find perfect for your home renovation. Invite the contractor to see your home and to start the work as soon as possible.

For more information visit http://www.bizzibid.com/

No wonder, your home is the world’s coziest place for you. It is your home where you find freedom to live life in your own way. Though, to make your home remains the coziest place, it’s essential to think about its renovation. A time comes when your home roof starts leaking, walls, doors and windows get faded, and the drawing room desperately needs a huge change. Though, renovating a home is a time consuming and expensive affair. You need to estimate both the time and cost of the renovation work.

As you are a busy person and you don’t have enough time to do self inspection for getting an estimate, in this case all you need to take help from a licensed contractor in your area. Remember, a licensed contractor is the one whom you can trust for your estimates. They are expert in this field and have up to date knowledge about current rates of materials required for home renovation.

http://sites.leadstormmedia.com/uploads/image/iStock_000006824056XSmall.jpg

'''Receive Estimates from Licensed Contractors Online…'''

To receive estimates from contractors, it’s better to take help from the online world. There are many web directories dedicated to provide information on licensed contractors in your area. You just need to sign up the web directory and need to fill out a simple form that includes the project name, the date you want to start renovation, your name, address, email address and the best time to call you. Once the form is filled, it’s time to click the submit button after reading the terms and conditions.

Now, your 30% work is over. You will receive call from several licensed contractors in your area since you filled the form. They will discuss their estimates and you will be able to hire the one that suits to your budget and needs.

It is advised to make a note of everything you want done to the property and discuss these things with contractors to find a well-convincing estimate. Remember, a trustable contractor will discuss many things that you haven’t included in your note, but they are essential to discuss for getting an exact estimate.

http://sites.leadstormmedia.com/uploads/image/iStock_000008013955XSmall.jpg

The contractor will sure to discuss about the demolition work, climate, greenery and the building code. You just wonder about the climate discussion, but there are some home renovations dependent on climate. For example, roofing work and landscaping cannot be done in a bad weather.

Greenery is essential to discuss because some work can be done for creating healthier environment. It may possible that some extra effort, time and money need to meet the building code standard. The contractor will discuss openly about his fees and will not try to keep you in dark. The additional 5% or 10% expenditure will also be discussed due to the fluctuating price of building materials.

Discuss at least 3-5 contractors about your home renovation work. Compare their prices to finalize the one that you find perfect for your home renovation. Invite the contractor to see your home and to start the work as soon as possible.

For more information visit http://www.bizzibid.com/

06 September 2010 at 08:32 AM
by - reference book production group

Changed lines 1-2 from:

W;ikipublisher is a TypesettingEngine; that re-purposes Web content for print, with 2 mouse-clicks.

to:

W;ikipublisher is a TypesettingEngine; that re-purposes Web content for print, with 2 mouse-clicks. It provides a Web-based [[Book(Guide) ]]Production platform.

Changed lines 5-7 from:

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

to:

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print. :)

(:keywords collaborative authoring, book production, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

(:keywords collaborative authoring, book production, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

14 April 2010 at 02:53 PM
by - add marginshift option and example book

Changed line 13 from:

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

to:

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how. Look at the [[example book -> http://www.wikipublisher.org/books/GNUZealand2009/Transcripts]].

14 April 2010 at 02:48 PM
by - add marginshift option

Changed line 20 from:

(:typeset-trail toc=on colorlinks=on:)

to:

(:typeset-trail toc=on colorlinks=on marginshift=on:)

Changed lines 1-76 from:

Definiens 1.2.1 is a comprehensive image analysis platform for multi-dimensional image analysis

The client software is role-based and supports the needs and skills of different users in an organization. The server software, known as the Definiens eCognition® Life Server, is a processing environment that allows the batch processing of jobs and is hugely scalable, capable of handling tens, hundreds or many thousands of images in a single job.

Figure 1: Definiens multi-dimensional image analysis software.

!!Client Software

!!!Developer XD

Definiens Developer XD is a powerful and completely integrated environment designed for image analysis specialists to develop, test

Definiens Developer XD incorporates the latest generation of Definiens Cognition Network Technology®, enabling the creation

is an intuitive end-user tool used to configure and execute image analysis applications. It provides support for fully automated or semi-automated workflows and guides users through the application they are running. incorporates all the required tools for users to import, view and visualize multidimensional images

!!!Definiens Viewer

Definiens Viewer is a free product that enables managers and other users to review the results of multidimensional image analysis.

!!Server Software

!!!Definiens eCognition® Life Server

The Definiens eCognition® Life Server provides a processing environment for

Supported connectors and drivers are described in a separate document, Supported Connectors and File Drivers.

!!!Definiens Administration Console

The Definiens Administration Console provides system administrators with a web-based interface that simplifies the management of the Definiens eCognition® Server environment.

!!!Definiens Data Management

Definiens Data Management offers an open, enterprise-ready and cost-effective solution for managing the huge volume of data generated by image analysis projects. The data is managed using standard relational database technologies and can be used with all Definiens products.

!!Integration Software

!!!Application Software

Definiens applications are designed to address a range of specific image analysis problems. Each application is used from the Definiens client. Batch processing is handled by the Definiens eCognition® Life Server.

Available applications are:

*Definiens TissueMap: Used for automated analysis of slides and tissue microarrays.

*Definiens TissueMap TMA: Used for automated analysis of tissue microarrays.

*Definiens Cellenger: Used for high-content analysis in cell-based studies.

!!!!Definiens Software Development Kit (SDK)

The Definiens Software Development Kit (SDK) enables the integration of the Definiens products within any business process using any data source or target, and allows the core analysis capabilities of the Definiens eCognition® Life Server to be extended.

!!!!Definiens TissueMap

The Definiens TissueMap application automates the challenging task of image analysis, supporting research scientists to discover, validate and measure new drug targets and disease-specific biomarkers. Definiens TissueMap enables research scientists to examine whole tissue section slides and tissue microarrays in many different ways. It can do the following:

*Analyze xenografts including the detection of viable and necrotic regions

*Detect nuclear markers, including proliferation markers such as Ki67/MIB1, PCNA, BrdU, steroid hormone receptor markers such as estrogen (ER), progesterone (PR) and apoptosis markers

*Detect cytoplasmic markers – regions of IHC-stained cells using cytoceratin stains like AE1/3, CK5, CK15, CK8, CK14

*Detect and quantify the amount and intensity of stains in membranes, for example detection of membrane resident hormone-receptors such as Her2neu and EFGR

*Classify positive nuclei based on the intensity of IHC stain

!!!!Definiens Cellenger

The Definiens Cellenger application is designed to address all the needs of high-content analysis for automated cell-based experiments. Definiens Cellenger is the first truly open, platform-independent high-content analysis software that is independent of image acquisition devices. It has the flexibility to design your image analysis processes without the usual constraints of canned image analysis routines. You can configure your own specific analysis solutions using the modules provided with the Definiens Cellenger library.

!!!!Applications and Product Line Compatibility

The following table summarizes the compatibility of Definiens applications with Definiens product lines.

||!Application||!Definiens||!Definiens Enterprise Image Intelligence™ Suite||

||Definiens Cellenger 2.3||Yes||Yes||

||Definiens TissueMap 2.0||Yes||Yes||

The Definiens platform is underpinned by our revolutionary Definiens Cognition Network Technology®, which extracts intelligence from image data by emulating human cognitive processes

to:

W;ikipublisher is a TypesettingEngine; that re-purposes Web content for print, with 2 mouse-clicks.

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be recast as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those showing [[(PmWiki/wiki )trails]], [[PmWiki/page lists]] or [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document.

:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

(:typeset-trail toc=on colorlinks=on:)

The site is running {$Version} and {$WPVersion}.

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be recast as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those showing [[(PmWiki/wiki )trails]], [[PmWiki/page lists]] or [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document.

:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

(:typeset-trail toc=on colorlinks=on:)

The site is running {$Version} and {$WPVersion}.

Changed lines 1-22 from:

:Turn Web pages into beautiful print:Wikipublisher is an extension

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those showing [[(PmWiki/wiki )trails]], [[PmWiki/page lists]] or [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document.

:Choose the print style:Readers can customise

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

(:typeset-trail toc=on colorlinks=on:)

The site is running {$Version} and {$WPVersion}

to:

!!Definiens Developer XD

Definiens 1.2.1 is a comprehensive image analysis platform for multi-dimensional image analysis. It contains all the client and server software needed to extract intelligence from any digital image in a fully automated or semi-automated way.

The client software is role-based and supports the needs and skills of different users in an organization. The server software, known as the Definiens eCognition® Life Server, is a processing environment that allows the batch processing of jobs and is hugely scalable, capable of handling tens, hundreds or many thousands of images in a single job.

Figure 1: Definiens multi-dimensional image analysis software.

!!Client Software

!!!Developer XD

Definiens Developer XD is a powerful and completely integrated environment designed for image analysis specialists to develop, test and package new image analysis applications. Definiens Developer XD can be used as a standalone tool or in combination with the Definiens eCognition® Life Server.

Definiens Developer XD incorporates the latest generation of Definiens Cognition Network Technology®, enabling the creation of new solutions for multidimensional image analysis applications. It incorporates a new programming paradigm, high-performance analysis for complex multidimensional data and sophisticated viewing, visualization and registration capabilities.

is an intuitive end-user tool used to configure and execute image analysis applications. It provides support for fully automated or semi-automated workflows and guides users through the application they are running. incorporates all the required tools for users to import, view and visualize multidimensional images and results.

!!!Definiens Viewer

Definiens Viewer is a free product that enables managers and other users to review the results of multidimensional image analysis.

!!Server Software

!!!Definiens eCognition® Life Server

The Definiens eCognition® Life Server provides a processing environment for the batch execution of image analysis using a high-performance grid computing environment. The Definiens eCognition® Life Server includes specific components designed to meet the needs of the multidimensional image analysis required for cell, tissue and non-invasive imaging in life sciences and healthcare.

Supported connectors and drivers are described in a separate document, Supported Connectors and File Drivers.

!!!Definiens Administration Console

The Definiens Administration Console provides system administrators with a web-based interface that simplifies the management of the Definiens eCognition® Server environment.

!!!Definiens Data Management

Definiens Data Management offers an open, enterprise-ready and cost-effective solution for managing the huge volume of data generated by image analysis projects. The data is managed using standard relational database technologies and can be used with all Definiens products.

!!Integration Software

!!!Application Software

Definiens applications are designed to address a range of specific image analysis problems. Each application is used from the Definiens client. Batch processing is handled by the Definiens eCognition® Life Server.

Available applications are:

*Definiens TissueMap: Used for automated analysis of slides and tissue microarrays.

*Definiens TissueMap TMA: Used for automated analysis of tissue microarrays.

*Definiens Cellenger: Used for high-content analysis in cell-based studies.

!!!!Definiens Software Development Kit (SDK)

The Definiens Software Development Kit (SDK) enables the integration of the Definiens products within any business process using any data source or target, and allows the core analysis capabilities of the Definiens eCognition® Life Server to be extended.

!!!!Definiens TissueMap

The Definiens TissueMap application automates the challenging task of image analysis, supporting research scientists to discover, validate and measure new drug targets and disease-specific biomarkers. Definiens TissueMap enables research scientists to examine whole tissue section slides and tissue microarrays in many different ways. It can do the following:

*Analyze xenografts including the detection of viable and necrotic regions

*Detect nuclear markers, including proliferation markers such as Ki67/MIB1, PCNA, BrdU, steroid hormone receptor markers such as estrogen (ER), progesterone (PR) and apoptosis markers

*Detect cytoplasmic markers – regions of IHC-stained cells using cytoceratin stains like AE1/3, CK5, CK15, CK8, CK14

*Detect and quantify the amount and intensity of stains in membranes, for example detection of membrane resident hormone-receptors such as Her2neu and EFGR

*Classify positive nuclei based on the intensity of IHC stain

!!!!Definiens Cellenger

The Definiens Cellenger application is designed to address all the needs of high-content analysis for automated cell-based experiments. Definiens Cellenger is the first truly open, platform-independent high-content analysis software that is independent of image acquisition devices. It has the flexibility to design your image analysis processes without the usual constraints of canned image analysis routines. You can configure your own specific analysis solutions using the modules provided with the Definiens Cellenger library.

!!!!Applications and Product Line Compatibility

The following table summarizes the compatibility of Definiens applications with Definiens product lines.

||!Application||!Definiens||!Definiens Enterprise Image Intelligence™ Suite||

||Definiens Cellenger 2.3||Yes||Yes||

||Definiens TissueMap 2.0||Yes||Yes||

The Definiens platform is underpinned by our revolutionary Definiens Cognition Network Technology®, which extracts intelligence from image data by emulating human cognitive processes.

Definiens 1.2.1 is a comprehensive image analysis platform for multi-dimensional image analysis. It contains all the client and server software needed to extract intelligence from any digital image in a fully automated or semi-automated way.

The client software is role-based and supports the needs and skills of different users in an organization. The server software, known as the Definiens eCognition® Life Server, is a processing environment that allows the batch processing of jobs and is hugely scalable, capable of handling tens, hundreds or many thousands of images in a single job.

Figure 1: Definiens multi-dimensional image analysis software.

!!Client Software

!!!Developer XD

Definiens Developer XD is a powerful and completely integrated environment designed for image analysis specialists to develop, test and package new image analysis applications. Definiens Developer XD can be used as a standalone tool or in combination with the Definiens eCognition® Life Server.

Definiens Developer XD incorporates the latest generation of Definiens Cognition Network Technology®, enabling the creation of new solutions for multidimensional image analysis applications. It incorporates a new programming paradigm, high-performance analysis for complex multidimensional data and sophisticated viewing, visualization and registration capabilities.

is an intuitive end-user tool used to configure and execute image analysis applications. It provides support for fully automated or semi-automated workflows and guides users through the application they are running. incorporates all the required tools for users to import, view and visualize multidimensional images and results.

!!!Definiens Viewer

Definiens Viewer is a free product that enables managers and other users to review the results of multidimensional image analysis.

!!Server Software

!!!Definiens eCognition® Life Server

The Definiens eCognition® Life Server provides a processing environment for the batch execution of image analysis using a high-performance grid computing environment. The Definiens eCognition® Life Server includes specific components designed to meet the needs of the multidimensional image analysis required for cell, tissue and non-invasive imaging in life sciences and healthcare.

Supported connectors and drivers are described in a separate document, Supported Connectors and File Drivers.

!!!Definiens Administration Console

The Definiens Administration Console provides system administrators with a web-based interface that simplifies the management of the Definiens eCognition® Server environment.

!!!Definiens Data Management

Definiens Data Management offers an open, enterprise-ready and cost-effective solution for managing the huge volume of data generated by image analysis projects. The data is managed using standard relational database technologies and can be used with all Definiens products.

!!Integration Software

!!!Application Software

Definiens applications are designed to address a range of specific image analysis problems. Each application is used from the Definiens client. Batch processing is handled by the Definiens eCognition® Life Server.

Available applications are:

*Definiens TissueMap: Used for automated analysis of slides and tissue microarrays.

*Definiens TissueMap TMA: Used for automated analysis of tissue microarrays.

*Definiens Cellenger: Used for high-content analysis in cell-based studies.

!!!!Definiens Software Development Kit (SDK)

The Definiens Software Development Kit (SDK) enables the integration of the Definiens products within any business process using any data source or target, and allows the core analysis capabilities of the Definiens eCognition® Life Server to be extended.

!!!!Definiens TissueMap

The Definiens TissueMap application automates the challenging task of image analysis, supporting research scientists to discover, validate and measure new drug targets and disease-specific biomarkers. Definiens TissueMap enables research scientists to examine whole tissue section slides and tissue microarrays in many different ways. It can do the following:

*Analyze xenografts including the detection of viable and necrotic regions

*Detect nuclear markers, including proliferation markers such as Ki67/MIB1, PCNA, BrdU, steroid hormone receptor markers such as estrogen (ER), progesterone (PR) and apoptosis markers

*Detect cytoplasmic markers – regions of IHC-stained cells using cytoceratin stains like AE1/3, CK5, CK15, CK8, CK14

*Detect and quantify the amount and intensity of stains in membranes, for example detection of membrane resident hormone-receptors such as Her2neu and EFGR

*Classify positive nuclei based on the intensity of IHC stain

!!!!Definiens Cellenger

The Definiens Cellenger application is designed to address all the needs of high-content analysis for automated cell-based experiments. Definiens Cellenger is the first truly open, platform-independent high-content analysis software that is independent of image acquisition devices. It has the flexibility to design your image analysis processes without the usual constraints of canned image analysis routines. You can configure your own specific analysis solutions using the modules provided with the Definiens Cellenger library.

!!!!Applications and Product Line Compatibility

The following table summarizes the compatibility of Definiens applications with Definiens product lines.

||!Application||!Definiens||!Definiens Enterprise Image Intelligence™ Suite||

||Definiens Cellenger 2.3||Yes||Yes||

||Definiens TissueMap 2.0||Yes||Yes||

The Definiens platform is underpinned by our revolutionary Definiens Cognition Network Technology®, which extracts intelligence from image data by emulating human cognitive processes.

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* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

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:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

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(:cellnr:)Molecular Devices MetaXpress Plate with Timepoint

(:cell:)Molecular Devices MetaXpress, Molecular Devices ImageXpress

(:cell:).tif

(:cell:)Yes

(:cell:)Yes

(:cell:)Yes

(:cell:)X

(:cell:)X

(:cell:)

(:cellnr:)Zeiss Mirax Slide IO

(:cell:)

(:cell:).ini

(:cell:)Yes

(:cell:)Yes

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(:cell:)X

(:tableend:)

(:table border=0:)

(:cellnr width=22%:)'''Import Template (Connector)'''

(:cell width=18%:)'''Image Reader'''

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(:cell width=8%:)'''File Based'''

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(:cell width=8%:)'''Linux'''

(:cell width=8%:)'''Life Portal'''

(:cell width=8%:)'''Cell Portal'''

(:cell width=8%:)'''Tissue Portal'''

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(:cell:)

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(:cellnr:)Bacus WebSlide

(:cell:)

(:cell:).ini

(:cell:)Yes

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(:cell:)Opera I

(:cell:).tif

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(:cellnr:)Generic One Scene per Folder

(:cell:)Generic Instruments

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(:cell:)X

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(:cellnr:)Molecular Devices MetaXpress Plate with Timepoint

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(:cell:)

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Changed lines 1-391 from:

Position features refer to the position of an image object relative to the entire scene. These features are of special interest when working with geographically referenced data, as an image object can be described by its geographic position. Position features refer

!!Distance

%gray%''Object Features > Position > Distance''

!!!Distance to Line

%gray%''Object Features > Position > Distance > Distance to Line''

The distance between the center of gravity of

!!!!Editable Parameters

To set, right-click the Distance to Line feature, select Edit Feature and adapt the co-ordinates of the two points:

*First Co-ordinate {$ (X) $}

*First Co-ordinate {$ (Y) $}

*Second Co-ordinate {$ (X) $}

*Second Co-ordinate {$ (Y) $}

Figure 110: Distance between an image object and

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Distance to Scene Border

%gray%''Object Features > Position > Distance > Distance to Scene Border''

The distance of an image object slice (a 2D piece of the image object in a slice) to the nearest border of the scene within

!!!!Parameters

* {$ \mathrm {min} \ x $}is

* {$ \mathrm {max} \ x $}is the maximum distance from the scene border at {$ x $}-axis

* {$ \mathrm {min} \ y $}is the minimum distance from the scene border at {$ y $}

*

* {$ (sx,sy) $}is the scene size

!!!!Expression

%left%{$ \mathrm{min} \{\mathrm{min} \ x, sx-\mathrm{max} \ x, \mathrm{min} \ y, sy-\mathrm{max} \ y\}

Figure 111: Examples of the distance between an image object and the nearest scene border

!!!!Feature Value Range

%left%{$ [0, \mathrm {max} \ {sx-1, sy-1}] $}

!!!T Distance to First Frame (Pxl)

%gray%''Object Features > Position > Distance > T Distance to First Frame (Pxl)''

The distance of an image object to the first frame of the scene.

!!!T Distance to Last Frame

%gray%''Object Features > Position > Distance > T Distance to Last Frame''

The distance of an image object to the last frame of the scene.

!!!X Distance to Scene Left Border

%gray%''Object Features > Position > Distance > X Distance to Scene Left Border''

Horizontal distance of an image object slice (a 2D piece of the image object in a slice) to the left border of the scene within the current slice.

!!!!Parameters

* {$ sx $} is the scene size at the {$ x $}-axis

* {$ min \ x $}is the minimum distance from the scene border at {$ x $}-axis

!!!!Expression

%left%{$ \displaystyle \underset {(x,y)\in P_v} {\mathrm{min}}\mathrm{x} $}

Figure 112: X-distance between the image object and the left border.

!!!!Feature Value Range

%left%{$ [0, sx-1] $}

!!!X Distance to Scene Right Border

%gray%''Object Features > Position > Distance > X Distance to Scene Right Border''

Horizontal distance of an image object slice (a 2D piece of the image object in a slice) to the right border of the scene within the current slice.

!!!!Parameters

* {$ sx $} is the scene size at the {$ x $}-axis

* {$ max \ x $}is the maximum distance from the scene border at {$ x $}-axis

!!!!Expression

%left%{$ \mathrm{sx} - \underset {(x,y)\in P_v} {\mathrm{max}}\mathrm{x} $}

Figure 113: X-distance to the image object right border.

!!!!Feature Value Range

%left%{$ [0, sx-1] $}

!!!Y Distance to Scene Bottom Border

%gray%''Object Features > Position > Distance > Y Distance to Scene Bottom Border''

Vertical distance of an image object slice (a 2D piece of the image object in a slice) to the bottom border of the scene within the current slice.

!!!!Parameters

* {$ sy $} is the scene size

* {$ min \ y $}is the minimum distance from the scene border at {$ y $}-axis

!!!!Expression

%left%{$ \underset {(x,y)\in P_v} {\mathrm{min}}\mathrm{y} $}

Figure 114: Y-distance between the image object and the bottom border.

!!!!Feature Value Range

%left%{$ [0, sy-1] $}

!!!Y Distance to Scene Top Border

%gray%''Object Features > Position > Distance > Y Distance to Scene Top Border''

Vertical distance of an image object slice (a 2D piece of the image object in a slice) to the top border of the scene within the current slice.

!!!!Parameters

* {$ sy $} is the scene size

* {$ max \ y $}is the maximum distance from the scene border at {$ y $}-axis

!!!!Expression

%left%{$ \mathrm{sy} - \underset {(x,y)\in P_v} {\mathrm{max}}\mathrm{y} $}

Figure 115: Y-distance between the image object and the top border of the scene.

!!!!Feature Value Range

%left%{$ [0, sy-1] $}

!!!Z Distance to First Slice (Pxl)

%gray%''Object Features > Position > Distance > Z Distance to First Slice (Pxl)''

Distance of an image object to the first slice of the scene.

!!!Z Distance to Last Slice (Pxl)

%gray%''Object Features > Position > Distance > Z Distance to Last Slice (Pxl)''

Distance of an image object to the last slice of the scene.

!!Co-ordinate

%gray%''Object Features > Position > Co-ordinate''

!!!Is at Active Pixel

%gray%''Object Features > Position > Co-ordinate > Is at Active Pixel''

This feature returns 1 if the current active pixel is within the image object, otherwise 0.

!!!Time (Pxl)

%gray%''Object Features > Position > Co-ordinate > Time''

T-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

!!!!Parameters

* {$ \bar t_v $} is the {$ t $}-center of an image object {$ v $}

* {$ \bar x_v $} is the {$ x $}-center of an image object {$ v $} in an internal map with {$ \bar x_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}x_{\mathrm{map}} $}

* {$ sx_{\mathrm {frame}}$} is the extent in {$ x $}of each slice and frame

!!!!Expression

%left%{$ \bar t_v = \mathrm{floor} \bigg( \frac {\bar x_v (\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) $}

!!!!Feature Value Range

%left%{$ [0.5, {\mathrm {number \ of \ frames \ in \ map}} - 0.5] $}

!!!Time Max (Pxl)

%gray%''Object Features > Position > Co-ordinate > Time Max (Pxl)''

Maximum {$t$}-position of an image object derived from its bounding box. The calculation is based on the maximum {$t$}-position of the image object in the internal map.

!!!!Parameters

*{$ t_{\mathrm {max}}(v) $} is the maximum {$t$}-position of an image object {$v$}

*{$ x_{\mathrm {max}}(v, {\mathrm map}) $} is the maximum {$x$}-position of an image object {$v$} in an internal map

*{$ sx_{frame}$} is the extent in {$x$} of each slice and frame

!!!!Expression

%left%{$ \bar t_v = \mathrm{floor} \bigg( \frac {\bar x_v (\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) $}

!!!!Feature Value Range

%left%{$ [1, {\mathrm {number \ of \ frames \ in \ map}} ] $}

!!!Time Min (Pxl)

%gray%''Object Features > Position > Co-ordinate > Time Min (Pxl)''

Minimum {$ t $}-position of an image object derived from its bounding box. The calculation is based on the minimum {$ t $}-position of the image object in the internal map.

!!!!Parameters

* {$ t_{\mathrm {min}}(v) $} is the minimum {$ t $}-position of an image object {$v$}

* {$ x_{\mathrm {min}}(v, {\mathrm map}) $} is the minimum {$ x $}-position of an image object {$ t $} in an internal map

* {$ sx_{\mathrm {frame}} $} is the extent in {$ x $} of each slice and frame

!!!!Expression

%left%{$ t_{min} (v) = \mathrm{floor} \bigg( \frac {x_{min} (v,\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) $}

!!!!Feature Value Range

%left%{$ [0.5, {\mathrm {number \ of \ frames \ in \ map}} - 1] $}

!!!X Center

%gray%''Object Features > Position > Co-ordinate > X Center''

X-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

!!!!Parameters

*{$ \bar x_v $} is the {$x$}-center of an image object {$v$}

*{$ \bar x_v {(\mathrm {map}}) $} is the {$ x $} -center of an image object {$ v $} in an internal map with {$ \bar x_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}x_{\mathrm{map}} $}

*{$ \#P_v $} is the total number of pixels contained in {$ P_v $}

*{$ (x_{\mathrm {map}}, y_{\mathrm {map}}) $}are the co-ordinates in an internal map

* {$ sx_{\mathrm {slice}} $} is the extent in {$ x $} of each slice and frame

!!!!Expression

%left%{$ \bar x_v = \bar x_v \mathrm{(map)}- \mathrm{floor} \bigg( \frac {\bar x_v (\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) \times sx_{\mathrm{frame}} $}

!!!!Feature Value Range

%left%{$ [{\mathrm {scene \ extent \ in \ }} x , 0.5] $}

!!!X Max.

%gray%''Object Features > Position > Co-ordinate > X Max''

Maximum {$ x $}-position of an image object derived from its bounding box. The calculation is based on the maximum {$ x $}-position of the image object in the internal map.

!!!!Parameters

* {$ x_{\mathrm {max}}(v) $} is the minimum {$ x $}-position of an image object {$ v $}

* {$ x_{\mathrm {max}}(v, {\mathrm {map})} $} is the maximum {$ x $}-position of an image object {$ t $} in an internal map

* {$ sx_{\mathrm {frame}} $} is the extent in {$ x $} of each slice and frame

!!!!Expression

%left%{$ x_{max} (v) = x_{max} (v,\mathrm{map})- \mathrm{floor} \bigg( \frac {\bar x_{\mathrm{max}} (\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) \times sx_{\mathrm{frame}} $}

Figure 116: Maximum value of the x-coordinate at the image object border.

!!!!Feature Value Range

%left%{$ [1, {\mathrm {scene \ extent \ in \ }} x] $}

!!!X Min.

%gray%''Object Features > Position > Co-ordinate > X Min''

Minimum x-position of an image object derived from its bounding box. The calculation is based on the minimum x-position of the image object in the internal map.

!!!!Parameters

*{$ t_{\mathrm {max}}(v) $} is the minimum {$x$}-position of an image object {$v$}

*{$ x_{\mathrm {min}}(v, {\mathrm {map})} $} is the minimum {$x$}-position of an image object {$v$} in an internal map

*{$ sx_{\mathrm {frame}}$} is the extent in {$x$} of each slice and frame

!!!!Expression

%left%{$ x_{min} (v) = x_{min} (v, \mathrm{map})- \mathrm{floor} \bigg( \frac {x_{min} (v,\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) \times sx_{\mathrm{frame}} $}

Figure 117: Minimum value of the x-coordinate at the image object border.

!!!!Feature Value Range

%left%{$ [ {\mathrm {scene \ extent \ in \ }} x - 1] $}

!!!Y Center

%gray%''Object Features > Position > Co-ordinate > Y Center''

Y-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

!!!!Parameters

*{$ \bar y_v $} is the {$y$}-center of an image object {$v$}

*{$ \bar y_v {(\mathrm {map})} $} is the {$ y $} -center of an image object {$ v $} in an internal map with {$ \bar y_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}y_{\mathrm{map}} $}

*{$ \#P_v $} is the total number of pixels contained in {$ P_v $}

*{$ (x_{\mathrm {map}}, y_{\mathrm {map})} $}are the co-ordinates in an internal map

* {$ sy_{\mathrm {slice}} $} is the extent in {$ x $} of each slice and frame

!!!!Expression

%left% {$ \bar y_v = \bar y_v (\mathrm{map})- \mathrm{floor} \bigg( \frac {\bar y_v (\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) \times sy_{\mathrm{slice}} $}

Figure 118: Center of gravity of an image object.

!!!!Feature Value Range

%left%{$ [0.5, {\mathrm {scene \ extent \ in \ }} x - 0.5] $}

!!!Y Max.

%gray%''Object Features > Position > Co-ordinate > Y Max''

Maximum y-position of an image object derived from its bounding box. The calculation is based on the maximum y-position of the image object in the internal map.

!!!!Parameters

*{$ y_{\mathrm {max}}(v) $} is the maximum {$y$}-position of an image object {$v$}

*{$ y_{\mathrm {max}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

!!!!Expression

%left%{$ y_{\mathrm{max}} (v) = \bar y_{max} (v,\mathrm{map})- \mathrm{floor} \bigg( \frac {y_{\mathrm{max}} (v,\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) \times sy_{\mathrm{slice}} $}

Figure 119: Maximum value of the y-coordinate at the image object border.

!!!!Feature Value Range

%left%{$ [1, {\mathrm {scene \ extent \ in \ }} y] $}

!!!Y Min.

%gray%''Object Features > Position > Co-ordinate > Y Min''

Minimum y-position of an image object derived from its bounding box. The calculation is based on the minimum y-position of the image object in the internal map.

!!!!Parameters

*{$ y_{\mathrm {min}}(v) $} is the minimum {$y$}-position of an image object {$v$}

*{$ y_{\mathrm {min}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

!!!!Expression

%left%{$ y_{\mathrm{min}} (v) = \bar y_{min} (v,\mathrm{map})- \mathrm{floor} \bigg( \frac {y_{\mathrm{min}} (v,\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) \times sy_{\mathrm{slice}} $}

Figure 120: Minimum value of the y-coordinate at the image object border.

!!!!Feature Value Range

%left%{$ [0, {\mathrm {scene \ extent \ in \ }} y - 1] $}

!!!Z Center

%gray%''Object Features > Position > Co-ordinate > Z Center''

{$Z$}-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

!!!!Parameters

*{$ \bar z_v $} is the {$z$}-center of an image object {$v$}

*{$ \bar y_v {(\mathrm {map})} $} is the {$ y $} -center of an image object {$ v $} in an internal map with {$ \bar y_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}y_{\mathrm{map}} $}

* {$ sy_{\mathrm {slice}} $} is the extent in {$ y $} of each slice and frame

!!!!Expression

%left%{$ \bar z_v = \mathrm{floor} \bigg( \frac {\bar y_v (\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) $}

!!!!Feature Value Range

%left%{$ [0.5, {\mathrm {number \ of \ slices \ in \ map }} - 0.5] $}

!!!Z Max

%gray%''Object Features > Position > Co-ordinate > Z Max''

Maximum {$ z $}-position of an image object derived from its bounding box. The calculation is based on the maximum {$ z $}-position of the image object in the internal map.

!!!!Parameters

*{$ z_{\mathrm {max}}(v) $} is the maximum {$z$}-position of an image object {$v$}

*{$ y_{\mathrm {max}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

!!!!Expression

%left%{$ z_{\mathrm{max}} (v)= \mathrm{floor} \bigg( \frac {y_{\mathrm{max}} (v,\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) $}

!!!!Feature Value Range

%left%{$ [1, {\mathrm {number \ of \ slices \ in \ map }} ] $}

!!!Z Min

%gray%''Object Features > Position > Co-ordinate > Z Min''

Minimum {$ z $}-position of an image object derived from its bounding box. The calculation is based on the minimum {$ z $}-position of the image object in the internal map.

!!!!Parameters

*{$ z_{\mathrm {min}}(v) $} is the maximum {$z$}-position of an image object {$v$}

*{$ y_{\mathrm {min}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

!!!!Expression

%left%{$ z_{\mathrm{min}} (v)= \mathrm{floor} \bigg( \frac {y_{\mathrm{min}} (v,\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) $}

!!!!Feature Value Range

%left%{$ [0, {\mathrm {number \ of \ slices \ in \ map }} -1] $}

!!Is Object in Region

%gray%''Object Features > Position > Is Object in Region''

The Is Object In Region feature checks if an image object is located in a given region. If this is true, the feature value is 1 (= true), otherwise it is 0 (= false).

!!!Editable Parameters

* Region

!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

to:

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be recast as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those showing [[(PmWiki/wiki )trails]], [[PmWiki/page lists]] or [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document.

:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

(:typeset-trail toc=on colorlinks=on:)

The site is running {$Version} and {$WPVersion}.

Changed lines 1-23 from:

%gray%''Object Features > ~~Geometry~~''

~~Geometry~~ features ~~are based on an image~~ object~~'s shape, calculated from ~~the ~~pixels that form it. Because images are raster-based, geometry features may be rotation variant: after~~ image ~~objects are rotated, different feature values may arise~~.

!!Extent

%gray%''Object Features > Geometry > Extent''

!!~~!Area~~

%gray%''Object Features > ~~Geometry~~ > ~~Extent > Area~~''

~~The number of pixels forming an image object. If unit information is A_vailable,~~ the ~~number~~ of ~~pixels can be converted into a measurement.~~

In scenes that provide no unit information, the area of a single pixel is 1 and the area is simply the number of pixels that form it. If the image data provides unit information, the ~~area can be multiplied using the appropriate factor.~~

!!!!Parameters

*{$ A_v $} is the ~~area of image object ~~{$ ~~v~~ $}

*{$ ~~\# P_v ~~$} ~~is the total number of pixels contained in {~~$ ~~P_v $} ~~

*{$ u $} is the pixel size in co-ordinate system units.~~ If the unit is a pixel, then {$ u=1. $}~~

!!!!Expression

%left%{$ \displaystyle A_v= \#P_v \times u^2 $}

!!Extent

%gray%''Object Features > Geometry > Extent''

In scenes that provide no unit information, the area of a single pixel is 1 and the area is simply the number of pixels that form it. If the image data provides unit information

!!!!Parameters

*{$ A_v $} is

*

*{$ u $} is the pixel size in co-ordinate system units

!!!!Expression

%left%{$ \displaystyle A_v= \#P_v \times u^2 $}

to:

%gray%''Object Features > Position''

Position features refer to the position of an image object relative to the entire scene. These features are of special interest when working with geographically referenced data, as an image object can be described by its geographic position. Position features refer to the pixel co-ordinate definition.

!!Distance

%gray%''Object Features > Position > Distance''

!!!Distance to Line

%gray%''Object Features > Position > Distance > Distance to Line''

The distance between the center of gravity of a two-dimensional image object and a given line. The line is defined manually by entering two points that are a part of this line. Note that the line has neither a start nor an end.

!!!!Editable Parameters

To set, right-click the Distance to Line feature, select Edit Feature and adapt the co-ordinates of the two points:

*First Co-ordinate {$ (X) $}

*First Co-ordinate {$ (Y) $}

*Second Co-ordinate {$ (X) $}

*Second Co-ordinate {$ (Y) $}

Figure 110: Distance between an image object and a line.

Position features refer to the position of an image object relative to the entire scene. These features are of special interest when working with geographically referenced data, as an image object can be described by its geographic position. Position features refer to the pixel co-ordinate definition.

!!Distance

%gray%''Object Features > Position > Distance''

!!!Distance to Line

%gray%''Object Features > Position > Distance > Distance to Line''

The distance between the center of gravity of a two-dimensional image object and a given line. The line is defined manually by entering two points that are a part of this line. Note that the line has neither a start nor an end.

!!!!Editable Parameters

To set, right-click the Distance to Line feature, select Edit Feature and adapt the co-ordinates of the two points:

*First Co-ordinate {$ (X) $}

*First Co-ordinate {$ (Y) $}

*Second Co-ordinate {$ (X) $}

*Second Co-ordinate {$ (Y) $}

Figure 110: Distance between an image object and a line.

Changed lines 23-30 from:

%left%{$ \displaystyle ~~ ~~[0, \~~mathrm~~ ~~{scene \ size}] $}~~

!!!Border Length [for 2D Image Objects]

%gray%''Object Features > Geometry > Extent > Border Length''

The border length of an image object is defined as the sum of edges of the image object shared with other image objects, or situated on the edge of the entire scene.~~ For a torus `- and other image objects with holes `- the border length is the sum of the inner and outer borders.~~

!!!Border Length [for 2D Image Objects]

%gray%''Object Features > Geometry > Extent > Border Length''

The border length of an image object is defined as the sum of edges of the image object shared with other image objects, or situated on the edge of the entire scene

to:

%left%{$ \displaystyle [0, \infty] $}

!!!Distance to Scene Border

%gray%''Object Features > Position > Distance > Distance to Scene Border''

The distance of an image object slice (a 2D piece of the image object in a slice) to the nearest border of the scene within the current slice. (The Z-direction is ignored.)

!!!Distance to Scene Border

%gray%''Object Features > Position > Distance > Distance to Scene Border''

The distance of an image object slice (a 2D piece of the image object in a slice) to the nearest border of the scene within the current slice. (The Z-direction is ignored.)

Changed lines 32-35 from:

*{$ ~~b_v $~~} ~~is the border length of image object~~

*{$ b_o $} is the length of outer border

*{$ ~~b_i ~~$~~} is the length of inner~~ border

*{$ b_o $} is the length of outer border

*{

to:

* {$ \mathrm {min} \ x $}is the minimum distance from the scene border at {$ x $}-axis

* {$ \mathrm {max} \ x $}is the maximum distance from the scene border at {$ x $}-axis

* {$ \mathrm {min} \ y $}is the minimum distance from the scene border at {$ y $}-axis

* {$ \mathrm {max} \ y $}is the maximum distance from the scene border at {$ y $}-axis

* {$ (sx,sy) $}is the scene size

* {$ \mathrm {max} \ x $}is the maximum distance from the scene border at {$ x $}-axis

* {$ \mathrm {min} \ y $}is the minimum distance from the scene border at {$ y $}-axis

* {$ \mathrm {max} \ y $}is the maximum distance from the scene border at {$ y $}-axis

* {$ (sx,sy) $}is the scene size

Changed lines 39-44 from:

%left%{$ \~~displaystyle b_v = b_o+b_i $~~}

Figure 84: Border length of an image object {$ ~~v $} or between two objects v, u.~~

Figure 85: Innerand ~~outer border length of a torus image object~~.

Figure 84: Border length of an image object {

Figure 85: Inner

to:

%left%{$ \mathrm{min} \{\mathrm{min} \ x, sx-\mathrm{max} \ x, \mathrm{min} \ y, sy-\mathrm{max} \ y\} $}

Figure 111: Examples of the distance between an image object and the nearest scene border.

Figure 111: Examples of the distance between an image object and the nearest scene border.

Changed lines 44-52 from:

%left%{$ ~~\displaystyle ~~[0, \~~infty] $~~}

!!!Border Length [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > ~~Border Length''~~

The border length of a 3D image object is the sumof ~~border lengths of all image object slices, multiplied by ~~the ~~spatial distance between them~~.

Image object slices are 2D pieces of the image object in each slice. The border length of an image object ~~slice is defined as~~ the ~~sum of edges shared with other image object pieces, or are situated on the edge of the entire slice. For a torus and other image objects with holes~~ the ~~border length sums the inner and outer~~ border.

!!!Border Length [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent

The border length of a 3D image object is the sum

Image object slices are 2D pieces of the image object in each slice. The border length

to:

%left%{$ [0, \mathrm {max} \ {sx-1, sy-1}] $}

!!!T Distance to First Frame (Pxl)

%gray%''Object Features > Position > Distance > T Distance to First Frame (Pxl)''

The distance of an image object to the first frame of the scene.

!!!T Distance to Last Frame

%gray%''Object Features > Position > Distance > T Distance to Last Frame''

The distance of an image object to the last frame of the scene.

!!!X Distance to Scene Left Border

%gray%''Object Features > Position > Distance > X Distance to Scene Left Border''

Horizontal distance of an image object slice (a 2D piece of the image object in a slice) to the left border of the scene within the current slice.

!!!T Distance to First Frame (Pxl)

%gray%''Object Features > Position > Distance > T Distance to First Frame (Pxl)''

The distance of an image object to the first frame of the scene.

!!!T Distance to Last Frame

%gray%''Object Features > Position > Distance > T Distance to Last Frame''

The distance of an image object to the last frame of the scene.

!!!X Distance to Scene Left Border

%gray%''Object Features > Position > Distance > X Distance to Scene Left Border''

Horizontal distance of an image object slice (a 2D piece of the image object in a slice) to the left border of the scene within the current slice.

Changed lines 64-70 from:

* {$ ~~b_v~~ $} is the ~~border length of image object ~~{$ ~~v~~ $}

* {$ ~~b_v (~~\~~mathrm {slice})~~ $}~~ ~~is the ~~border length of image object slice ~~

* {$ ~~b_v(z)~~ $}~~ is the border length of image object in z~~-~~direction ~~

* {$ u_{\mathrm {slices}} $} is the spatial distance between slices in the co-ordinate system unit

* {$ b_o $} is the length of the outer border

* {$ b_i $} is the length of the inner border

*

* {$ u_{\mathrm {slices}} $} is the spatial distance between slices in the co-ordinate system unit

* {$ b_o $} is the length of the outer border

* {$ b_i $} is the length of the inner border

to:

* {$ sx $} is the scene size at the {$ x $}-axis

* {$ min \ x $}is the minimum distance from the scene border at {$ x $}-axis

* {$ min \ x $}is the minimum distance from the scene border at {$ x $}-axis

Changed lines 68-74 from:

Figure 86: Border length of an image object {$ v $} or between two objects v, u.

Figure 87: Inner and outer border length of a torus image object

to:

%left%{$ \displaystyle \underset {(x,y)\in P_v} {\mathrm{min}}\mathrm{x} $}

Figure 112: X-distance between the image object and the left border.

Figure 112: X-distance between the image object and the left border.

Changed lines 73-80 from:

%left%{$ ~~\displaystyle ~~[0, ~~\infty~~] $}

!!!~~Length [for 2D Image Objects]~~

%gray%''Object Features > ~~Geometry~~ > ~~Extent~~ > ~~Length''~~

The length of a 2D image object is calculated using the length-to-width ratio.

!!!

The length of a 2D image object is calculated using the length-to-width ratio

to:

%left%{$ [0, sx-1] $}

!!!X Distance to Scene Right Border

%gray%''Object Features > Position > Distance > X Distance to Scene Right Border''

Horizontal distance of an image object slice (a 2D piece of the image object in a slice) to the right border of the scene within the current slice.

!!!X Distance to Scene Right Border

%gray%''Object Features > Position > Distance > X Distance to Scene Right Border''

Horizontal distance of an image object slice (a 2D piece of the image object in a slice) to the right border of the scene within the current slice.

Changed lines 82-84 from:

*{$ ~~\# P_v ~~$} is the ~~total number of pixels contained in ~~{$ ~~P_v~~ $}

*{$ \~~gamma_v ~~$}~~ ~~is the ~~length-width ratio of an image object ~~{$ ~~v~~ $}

to:

* {$ sx $} is the scene size at the {$ x $}-axis

* {$ max \ x $}is the maximum distance from the scene border at {$ x $}-axis

* {$ max \ x $}is the maximum distance from the scene border at {$ x $}-axis

Changed lines 88-89 from:

%left%{$ \~~displaystyle~~ \~~sqrt~~ {\~~#~~ P_v \~~cdot \gamma_v~~}~~ $~~}

to:

%left%{$ \mathrm{sx} - \underset {(x,y)\in P_v} {\mathrm{max}}\mathrm{x} $}

Figure 113: X-distance to the image object right border.

Figure 113: X-distance to the image object right border.

Changed lines 93-110 from:

!!!

The length of an image object is the largest of three eigenvalues of a rectangular 3D space that is defined by the same volume, and same proportions

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length/Thickness

%gray%''Object Features > Geometry > Extent > Length/Thickness''

The length-to-thickness ratio of an image object

to:

%left%{$ [0, sx-1] $}

!!!Y Distance to Scene Bottom Border

%gray%''Object Features > Position > Distance > Y Distance to Scene Bottom Border''

Vertical distance of an image object slice (a 2D piece of the image object in a slice) to the bottom border of the scene within the current slice.

!!!Y Distance to Scene Bottom Border

%gray%''Object Features > Position > Distance > Y Distance to Scene Bottom Border''

Vertical distance of an image object slice (a 2D piece of the image object in a slice) to the bottom border of the scene within the current slice.

Changed lines 101-103 from:

*~~Length of the image object~~

*Thickness ofthe ~~image object~~

*Thickness of

to:

* {$ sy $} is the scene size

* {$ min \ y $}is the minimum distance from the scene border at {$ y $}-axis

* {$ min \ y $}is the minimum distance from the scene border at {$ y $}-axis

Changed lines 106-107 from:

%left%{$ \~~displaystyle \frac ~~{\~~mathrm {Length~~}~~}~~{\mathrm~~ ~~{~~Thickness~~}} $}

to:

%left%{$ \underset {(x,y)\in P_v} {\mathrm{min}}\mathrm{y} $}

Figure 114: Y-distance between the image object and the bottom border.

Figure 114: Y-distance between the image object and the bottom border.

Changed lines 111-129 from:

!!!

The length-

1. The ratio of length to width is identical

%left%{$ \displaystyle \gamma_v^{EV} = \frac {\lambda_1 (v)} {\lambda_2(v)} $}

2. The ratio of length to width can also be approximated using the bounding box:

%left%{$ \displaystyle \gamma_v^{BB} = \frac {\big(k_v^{bb'} \big)^2} {\#P_v} $}

Both calculations are compared; the smaller of both results is returned as the feature value

to:

%left%{$ [0, sy-1] $}

!!!Y Distance to Scene Top Border

%gray%''Object Features > Position > Distance > Y Distance to Scene Top Border''

Vertical distance of an image object slice (a 2D piece of the image object in a slice) to the top border of the scene within the current slice.

!!!Y Distance to Scene Top Border

%gray%''Object Features > Position > Distance > Y Distance to Scene Top Border''

Vertical distance of an image object slice (a 2D piece of the image object in a slice) to the top border of the scene within the current slice.

Changed lines 119-136 from:

* {$ ~~\# P_v ~~$} is the ~~Size of a set of pixels of an image object {$ v $}~~

* {$ \lambda_1 \lambda_2$~~} are eigenvalues~~

* {$~~ \gamma_v^ {\mathrm {EV~~}~~} $} is the ratio length of {$ v $} of the eigenvalues~~

* {$ \gamma_v^ {\mathrm {BB}} $} is the ratio length of {$ v $} of the bounding box

* {$ \gamma_v $} is the length-~~width ratio of an image object {$ v $}~~

* {$ k_v^ {\mathrm {BB'}} $}

* {$ h_v^ {\mathrm {BB'}} $}

* {$ a $} is the bounding box fill rate

* {$ \#Pxl $}

* {$ h $}

* {$ w $} is the image layer weight

*{$ k_v^{bb^1} = \sqrt{ {(k_v^{bb'})^2} + (1-a)(h_v^{bb'})^2} $}

*{$ a = \frac {\#P_v}{k_v^{bb'} - h_v^{bb'}} $}

*{$ k\cdot h = \# P_v \Rightarrow k=\frac {\# P_v} {w}, h = \frac {\# P_v} {k} \Rightarrow \frac {k} {w} = \frac {k^2} {\# P_{xl}} = \frac {\# P_{xl}} {w^2} $}

* {$ \lambda_1 \lambda_2

* {

* {$ \gamma_v^ {\mathrm {BB}} $} is the ratio length of {$ v $} of the bounding box

* {$ \gamma_v $} is the length

* {$ k_v^ {\mathrm {BB'}} $}

* {$ h_v^ {\mathrm {BB'}} $}

* {$ a $} is the bounding box fill rate

* {$ \#Pxl $}

* {$ h $}

* {$ w $} is the image layer weight

*{$ k_v^{bb^1} = \sqrt{ {(k_v^{bb'})^2} + (1-a)(h_v^{bb'})^2} $}

*{$ a = \frac {\#P_v}{k_v^{bb'} - h_v^{bb'}} $}

*{$ k\cdot h = \# P_v \Rightarrow k=\frac {\# P_v} {w}, h = \frac {\# P_v} {k} \Rightarrow \frac {k} {w} = \frac {k^2} {\# P_{xl}} = \frac {\# P_{xl}} {w^2} $}

to:

* {$ sy $} is the scene size

* {$ max \ y $}is the maximum distance from the scene border at {$ y $}-axis

* {$ max \ y $}is the maximum distance from the scene border at {$ y $}-axis

Changed lines 124-125 from:

%left%{$ \~~displaystyle~~ \~~gamma_v = \mathrm~~{~~min} \gamma~~_v~~^{EV~~}~~, \mathrm~~{max}~~ ~~\~~gamma_v^~~{~~BB~~} $}

to:

%left%{$ \mathrm{sy} - \underset {(x,y)\in P_v} {\mathrm{max}}\mathrm{y} $}

Figure 115: Y-distance between the image object and the top border of the scene.

Figure 115: Y-distance between the image object and the top border of the scene.

Changed lines 129-136 from:

%left%{$ ~~\displaystyle ~~[0, ~~\infty~~] $}

!!!~~Length/Width [for 3D Image Objects]~~

%gray%''Object Features > ~~Geometry~~ > ~~Extent~~ > ~~Length/Width''~~

The length-to~~-width ratio of an image~~ object.

!!!

The length-

to:

%left%{$ [0, sy-1] $}

!!!Z Distance to First Slice (Pxl)

%gray%''Object Features > Position > Distance > Z Distance to First Slice (Pxl)''

Distance of an image object to the first slice of the scene.

!!!Z Distance to Last Slice (Pxl)

%gray%''Object Features > Position > Distance > Z Distance to Last Slice (Pxl)''

Distance of an image object to the last slice of the scene.

!!Co-ordinate

%gray%''Object Features > Position > Co-ordinate''

!!!Is at Active Pixel

%gray%''Object Features > Position > Co-ordinate > Is at Active Pixel''

This feature returns 1 if the current active pixel is within the image object, otherwise 0.

!!!Time (Pxl)

%gray%''Object Features > Position > Co-ordinate > Time''

T-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

!!!Z Distance to First Slice (Pxl)

%gray%''Object Features > Position > Distance > Z Distance to First Slice (Pxl)''

Distance of an image object to the first slice of the scene.

!!!Z Distance to Last Slice (Pxl)

%gray%''Object Features > Position > Distance > Z Distance to Last Slice (Pxl)''

Distance of an image object to the last slice of the scene.

!!Co-ordinate

%gray%''Object Features > Position > Co-ordinate''

!!!Is at Active Pixel

%gray%''Object Features > Position > Co-ordinate > Is at Active Pixel''

This feature returns 1 if the current active pixel is within the image object, otherwise 0.

!!!Time (Pxl)

%gray%''Object Features > Position > Co-ordinate > Time''

T-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

Changed lines 157-159 from:

*~~Length of the image object~~

*Width of the ~~image~~ object

*Width of

to:

* {$ \bar t_v $} is the {$ t $}-center of an image object {$ v $}

* {$ \bar x_v $} is the {$ x $}-center of an image object {$ v $} in an internal map with {$ \bar x_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}x_{\mathrm{map}} $}

* {$ sx_{\mathrm {frame}}$} is the extent in {$ x $}of each slice and frame

* {$ \bar x_v $} is the {$ x $}-center of an image object {$ v $} in an internal map with {$ \bar x_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}x_{\mathrm{map}} $}

* {$ sx_{\mathrm {frame}}$} is the extent in {$ x $}of each slice and frame

Changed lines 163-164 from:

%left%{$ \~~displaystyle \frac~~ {\~~mathrm~~ {~~Length}}{~~\~~mathrm ~~{~~Width~~}} $}

to:

%left%{$ \bar t_v = \mathrm{floor} \bigg( \frac {\bar x_v (\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) $}

Changed lines 166-173 from:

%left%{$ ~~\displaystyle ~~[0, \~~infty] $}~~

!!!Number of ~~Pixels~~

%gray%''Object Features > Geometry > Extent > Number of Pixels''

The number of pixels forming an image object. Unit information is not taken into account.

!!!Number

%gray%''Object Features > Geometry > Extent > Number of Pixels''

The number of pixels forming an image object. Unit information is not taken into account

to:

%left%{$ [0.5, {\mathrm {number \ of \ frames \ in \ map}} - 0.5] $}

!!!Time Max (Pxl)

%gray%''Object Features > Position > Co-ordinate > Time Max (Pxl)''

Maximum {$t$}-position of an image object derived from its bounding box. The calculation is based on the maximum {$t$}-position of the image object in the internal map.

!!!Time Max (Pxl)

%gray%''Object Features > Position > Co-ordinate > Time Max (Pxl)''

Maximum {$t$}-position of an image object derived from its bounding box. The calculation is based on the maximum {$t$}-position of the image object in the internal map.

Changed lines 175-176 from:

*~~ ~~{$ \~~# P_~~v $} is the ~~total number of pixels contained in ~~{$~~ P_v~~ $}

to:

*{$ t_{\mathrm {max}}(v) $} is the maximum {$t$}-position of an image object {$v$}

*{$ x_{\mathrm {max}}(v, {\mathrm map}) $} is the maximum {$x$}-position of an image object {$v$} in an internal map

*{$ sx_{frame}$} is the extent in {$x$} of each slice and frame

!!!!Expression

%left%{$ \bar t_v = \mathrm{floor} \bigg( \frac {\bar x_v (\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) $}

*{$ x_{\mathrm {max}}(v, {\mathrm map}) $} is the maximum {$x$}-position of an image object {$v$} in an internal map

*{$ sx_{frame}$} is the extent in {$x$} of each slice and frame

!!!!Expression

%left%{$ \bar t_v = \mathrm{floor} \bigg( \frac {\bar x_v (\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) $}

Changed lines 185-193 from:

%gray%''Object Features > Geometry

The thickness of an image object is the smallest

to:

%left%{$ [1, {\mathrm {number \ of \ frames \ in \ map}} ] $}

!!!Time Min (Pxl)

%gray%''Object Features > Position > Co-ordinate > Time Min (Pxl)''

Minimum {$ t $}-position of an image object derived from its bounding box. The calculation is based on the minimum {$ t $}-position of the image object in the internal map.

!!!!Parameters

* {$ t_{\mathrm {min}}(v) $} is the minimum {$ t $}-position of an image object {$v$}

* {$ x_{\mathrm {min}}(v, {\mathrm map}) $} is the minimum {$ x $}-position of an image object {$ t $} in an internal map

* {$ sx_{\mathrm {frame}} $} is the extent in {$ x $} of each slice and frame

!!!!Expression

%left%{$ t_{min} (v) = \mathrm{floor} \bigg( \frac {x_{min} (v,\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) $}

!!!Time Min (Pxl)

%gray%''Object Features > Position > Co-ordinate > Time Min (Pxl)''

Minimum {$ t $}-position of an image object derived from its bounding box. The calculation is based on the minimum {$ t $}-position of the image object in the internal map.

!!!!Parameters

* {$ t_{\mathrm {min}}(v) $} is the minimum {$ t $}-position of an image object {$v$}

* {$ x_{\mathrm {min}}(v, {\mathrm map}) $} is the minimum {$ x $}-position of an image object {$ t $} in an internal map

* {$ sx_{\mathrm {frame}} $} is the extent in {$ x $} of each slice and frame

!!!!Expression

%left%{$ t_{min} (v) = \mathrm{floor} \bigg( \frac {x_{min} (v,\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) $}

Changed lines 203-211 from:

!!!Volume

%gray%''Object Features > Geometry > Extent > Volume''

The number of voxels forming an image object rescaled by using unit information for{$ x $}and{$ y $}co-ordinates and distance information between slices

to:

%left%{$ [0.5, {\mathrm {number \ of \ frames \ in \ map}} - 1] $}

!!!X Center

%gray%''Object Features > Position > Co-ordinate > X Center''

X-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

!!!X Center

%gray%''Object Features > Position > Co-ordinate > X Center''

X-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

Changed lines 211-215 from:

*~~ ~~{$ ~~V~~_v $} is the ~~volume of image object ~~{$~~ v ~~$}

~~* {$ \# P_v $} is the total number of voxels contained in ~~{$ ~~P_v ~~$~~}~~

* {$ u$} ~~is the size of a slice pixel~~ in ~~the co-ordinate system unit~~

* {$ ~~u_{~~\~~mathrm ~~{~~slices~~}~~} $~~} ~~is the spatial distance between slices in~~ the ~~co-ordinate system unit~~

* {$ u

*

to:

*{$ \bar x_v $} is the {$x$}-center of an image object {$v$}

*{$ \bar x_v {(\mathrm {map}}) $} is the {$ x $} -center of an image object {$ v $} in an internal map with {$ \bar x_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}x_{\mathrm{map}} $}

*{$ \#P_v $} is the total number of pixels contained in {$ P_v $}

*{$ (x_{\mathrm {map}}, y_{\mathrm {map}}) $}are the co-ordinates in an internal map

* {$ sx_{\mathrm {slice}} $} is the extent in {$ x $} of each slice and frame

*{$ \bar x_v {(\mathrm {map}}) $} is the {$ x $} -center of an image object {$ v $} in an internal map with {$ \bar x_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}x_{\mathrm{map}} $}

*{$ \#P_v $} is the total number of pixels contained in {$ P_v $}

*{$ (x_{\mathrm {map}}, y_{\mathrm {map}}) $}are the co-ordinates in an internal map

* {$ sx_{\mathrm {slice}} $} is the extent in {$ x $} of each slice and frame

Changed lines 218-219 from:

%left%{$ \~~displaystyle V~~_v = \~~# P~~_v \~~times u^2 ~~\~~times u_~~{\~~mathrm~~ {~~slices}}~~ $}

to:

%left%{$ \bar x_v = \bar x_v \mathrm{(map)}- \mathrm{floor} \bigg( \frac {\bar x_v (\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) \times sx_{\mathrm{frame}} $}

Changed lines 222-229 from:

%left%{$ \~~displaystyle~~ ~~[0, ~~\~~mathrm {scene~~ \ ~~size}] $~~}

!!!Width [for 2D Image Objects]

%gray%''Object Features > ~~Geometry~~ > ~~Extent~~ > ~~Width~~''

~~The width of an image object is calculated using the length-to-width ratio~~.

!!!Width [for 2D Image Objects]

to:

%left%{$ [{\mathrm {scene \ extent \ in \ }} x , 0.5] $}

!!!X Max.

%gray%''Object Features > Position > Co-ordinate > X Max''

Maximum {$ x $}-position of an image object derived from its bounding box. The calculation is based on the maximum {$ x $}-position of the image object in the internal map.

!!!X Max.

%gray%''Object Features > Position > Co-ordinate > X Max''

Maximum {$ x $}-position of an image object derived from its bounding box. The calculation is based on the maximum {$ x $}-position of the image object in the internal map.

Changed lines 232-234 from:

* {$ \~~# P_~~v $} is the ~~total number of pixels contained in {$ P_v~~ $~~}~~

* {$ \gamma_v$} ~~is the length/width ratio of an image object ~~{~~$ v $~~}

* {$ \gamma_v

to:

* {$ x_{\mathrm {max}}(v) $} is the minimum {$ x $}-position of an image object {$ v $}

* {$ x_{\mathrm {max}}(v, {\mathrm {map})} $} is the maximum {$ x $}-position of an image object {$ t $} in an internal map

* {$ sx_{\mathrm {frame}} $} is the extent in {$ x $} of each slice and frame

* {$ x_{\mathrm {max}}(v, {\mathrm {map})} $} is the maximum {$ x $}-position of an image object {$ t $} in an internal map

* {$ sx_{\mathrm {frame}} $} is the extent in {$ x $} of each slice and frame

Changed lines 238-239 from:

%left%{$ ~~\displaystyle~~ ~~\frac ~~{~~\# P_~~v} ~~{~~\~~gamma _v} $~~}

to:

%left%{$ x_{max} (v) = x_{max} (v,\mathrm{map})- \mathrm{floor} \bigg( \frac {\bar x_{\mathrm{max}} (\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) \times sx_{\mathrm{frame}} $}

Figure 116: Maximum value of the x-coordinate at the image object border.

Figure 116: Maximum value of the x-coordinate at the image object border.

Changed lines 243-250 from:

%left%{$ ~~\displaystyle ~~[~~0~~, \~~infty] $}~~

!!!Width [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > Width''

The width of an image object is the mid-~~point~~ of ~~three eigenvalues of a rectangular 3D space with the same volume as~~ the ~~image object and~~ the ~~same proportions of eigenvalues as the image object. The width of an image object can be smaller or equal to the mid-point of dimensions of~~ the ~~smallest rectangular 3D space enclosing the image~~ object.

!!!Width [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > Width''

The width of an image object is the mid

to:

%left%{$ [1, {\mathrm {scene \ extent \ in \ }} x] $}

!!!X Min.

%gray%''Object Features > Position > Co-ordinate > X Min''

Minimum x-position of an image object derived from its bounding box. The calculation is based on the minimum x-position of the image object in the internal map.

!!!!Parameters

*{$ t_{\mathrm {max}}(v) $} is the minimum {$x$}-position of an image object {$v$}

*{$ x_{\mathrm {min}}(v, {\mathrm {map})} $} is the minimum {$x$}-position of an image object {$v$} in an internal map

*{$ sx_{\mathrm {frame}}$} is the extent in {$x$} of each slice and frame

!!!!Expression

%left%{$ x_{min} (v) = x_{min} (v, \mathrm{map})- \mathrm{floor} \bigg( \frac {x_{min} (v,\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) \times sx_{\mathrm{frame}} $}

Figure 117: Minimum value of the x-coordinate at the image object border.

!!!X Min.

%gray%''Object Features > Position > Co-ordinate > X Min''

Minimum x-position of an image object derived from its bounding box. The calculation is based on the minimum x-position of the image object in the internal map.

!!!!Parameters

*{$ t_{\mathrm {max}}(v) $} is the minimum {$x$}-position of an image object {$v$}

*{$ x_{\mathrm {min}}(v, {\mathrm {map})} $} is the minimum {$x$}-position of an image object {$v$} in an internal map

*{$ sx_{\mathrm {frame}}$} is the extent in {$x$} of each slice and frame

!!!!Expression

%left%{$ x_{min} (v) = x_{min} (v, \mathrm{map})- \mathrm{floor} \bigg( \frac {x_{min} (v,\mathrm{map})} {sx_{\mathrm{frame}}}\bigg) \times sx_{\mathrm{frame}} $}

Figure 117: Minimum value of the x-coordinate at the image object border.

Changed lines 263-280 from:

%left%{$ ~~\displaystyle~~ ~~[0,~~ \~~infty] $~~}

!!Shape

%gray%''Object Features > Geometry > Shape''

!!!Asymmetry [for 2D Image Objects]

%gray%''Object Features > ~~Geometry > Shape > Asymmetry~~''

~~The Asymmetry feature describes the relative length of an image object, compared to a regular polygon. An ellipse is approximated around a given image object, which can be expressed by the ratio of the lengths of its minor and the major axes. The feature value increases with this asymmetry.~~

(:div class=frame:)

->'''NOTE:'''We recommend that you use the Length/Width ratio because it is more accurate.

(:divend:)

!!Shape

%gray%''Object Features > Geometry > Shape

!!!Asymmetry [for 2D Image Objects]

%gray%''Object Features

(:div class=frame:)

->'''NOTE:'''We recommend that you use the Length/Width ratio because it is more accurate.

(:divend:)

to:

%left%{$ [ {\mathrm {scene \ extent \ in \ }} x - 1] $}

!!!Y Center

%gray%''Object Features > Position > Co-ordinate > Y Center''

Y-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

!!!Y Center

%gray%''Object Features > Position > Co-ordinate > Y Center''

Y-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

Changed lines 271-273 from:

*~~Var X is the variance of X~~

*Var Y is the variance of Y

*Var Y is the variance of Y

to:

*{$ \bar y_v $} is the {$y$}-center of an image object {$v$}

*{$ \bar y_v {(\mathrm {map})} $} is the {$ y $} -center of an image object {$ v $} in an internal map with {$ \bar y_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}y_{\mathrm{map}} $}

*{$ \#P_v $} is the total number of pixels contained in {$ P_v $}

*{$ (x_{\mathrm {map}}, y_{\mathrm {map})} $}are the co-ordinates in an internal map

* {$ sy_{\mathrm {slice}} $} is the extent in {$ x $} of each slice and frame

*{$ \bar y_v {(\mathrm {map})} $} is the {$ y $} -center of an image object {$ v $} in an internal map with {$ \bar y_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}y_{\mathrm{map}} $}

*{$ \#P_v $} is the total number of pixels contained in {$ P_v $}

*{$ (x_{\mathrm {map}}, y_{\mathrm {map})} $}are the co-ordinates in an internal map

* {$ sy_{\mathrm {slice}} $} is the extent in {$ x $} of each slice and frame

Changed lines 279-280 from:

%left%{$ \~~displaystyle ~~ \~~frac{2 \sqrt~~ {~~\frac {1~~}{~~4~~} ~~(~~\~~mathrm{Var}X + ~~\~~mathrm~~{~~Var}Y)^2 +~~(\mathrm{~~Var~~}~~XY~~)~~^2 - \mathrm~~{~~Var~~}~~X ~~\~~cdot~~ \~~mathrm~~{~~Var~~}~~Y~~}}~~{\textrm{Var}X + \mathrm{Var}Y} $}~~

to:

%left% {$ \bar y_v = \bar y_v (\mathrm{map})- \mathrm{floor} \bigg( \frac {\bar y_v (\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) \times sy_{\mathrm{slice}} $}

Figure 118: Center of gravity of an image object.

Figure 118: Center of gravity of an image object.

Changed lines 284-291 from:

%left%{$ ~~\displaystyle ~~[0, ~~1] $}~~

!!!Asymmetry [for 3D Image Objects]

%gray%''Object Features > Geometry >Shape > Asymmetry''

The Asymmetry feature describes the relative length of an image object, in the same manner as 2D image objects. The ~~asymmetry~~ is ~~calculated from~~ the ~~ratio between~~ the ~~smallest and largest eigenvalues of the image object~~.

!!!Asymmetry [for 3D Image Objects]

%gray%''Object Features > Geometry >Shape > Asymmetry''

The Asymmetry feature describes the relative length of an image object, in the same manner as 2D image objects.

to:

%left%{$ [0.5, {\mathrm {scene \ extent \ in \ }} x - 0.5] $}

!!!Y Max.

%gray%''Object Features > Position > Co-ordinate > Y Max''

Maximum y-position of an image object derived from its bounding box. The calculation is based on the maximum y-position of the image object in the internal map.

!!!Y Max.

%gray%''Object Features > Position > Co-ordinate > Y Max''

Maximum y-position of an image object derived from its bounding box. The calculation is based on the maximum y-position of the image object in the internal map.

Changed lines 293-295 from:

*{$ ~~\lambda~~_{\mathrm {~~min~~}} $} is the ~~minimal eigenvalue ~~

*{$~~ \lambda_{\mathrm {max}} $} is the maximal eigenvalue~~

*

to:

*{$ y_{\mathrm {max}}(v) $} is the maximum {$y$}-position of an image object {$v$}

*{$ y_{\mathrm {max}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

*{$ y_{\mathrm {max}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

Changed lines 299-302 from:

%left%{$ \~~displaystyle~~ ~~1-~~ \~~sqrt \frac ~~{\~~lambda_~~{~~\mathrm{min~~}~~}} {~~\~~lambda_~~{~~\mathrm{max~~}~~}} $}~~

Figure 88: Asymmetry based on maximal and minimal eigenvalues.

Figure 88: Asymmetry based on maximal and minimal eigenvalues

to:

%left%{$ y_{\mathrm{max}} (v) = \bar y_{max} (v,\mathrm{map})- \mathrm{floor} \bigg( \frac {y_{\mathrm{max}} (v,\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) \times sy_{\mathrm{slice}} $}

Figure 119: Maximum value of the y-coordinate at the image object border.

Figure 119: Maximum value of the y-coordinate at the image object border.

Changed lines 304-311 from:

%left%{$ ~~\displaystyle ~~[~~0~~, ~~1] $}~~

!!!Border Index

%gray%''Object Features > Geometry >Shape > Border Index''

The Border Index feature describes how jagged an image object is; the more jagged, the higher its ~~border index~~. ~~This feature~~ is ~~similar to~~ the ~~Shape Index feature, but ~~the ~~Border Index feature uses a rectangular approximation instead of a square. The smallest rectangle enclosing the image object is created and the border index is calculated as the ratio between the border lengths of the image object and the smallest enclosing rectangle~~.

!!!Border Index

%gray%''Object Features > Geometry >Shape > Border Index''

The Border Index feature describes how jagged an image object is; the more jagged, the higher

to:

%left%{$ [1, {\mathrm {scene \ extent \ in \ }} y] $}

!!!Y Min.

%gray%''Object Features > Position > Co-ordinate > Y Min''

Minimum y-position of an image object derived from its bounding box. The calculation is based on the minimum y-position of the image object in the internal map.

!!!Y Min.

%gray%''Object Features > Position > Co-ordinate > Y Min''

Minimum y-position of an image object derived from its bounding box. The calculation is based on the minimum y-position of the image object in the internal map.

Changed lines 313-316 from:

*{$ ~~b~~_~~v $~~} is the ~~image object border length~~

*{$~~ l_v ~~$} ~~is the length of an image object ~~{$~~ ~~v~~ ~~$}

*{$~~w~~_~~v $~~} ~~is the width of an image object ~~{$~~ v ~~$}

*

*{$

to:

*{$ y_{\mathrm {min}}(v) $} is the minimum {$y$}-position of an image object {$v$}

*{$ y_{\mathrm {min}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

*{$ y_{\mathrm {min}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

Changed lines 319-322 from:

%left%{$ \~~displaystyle~~ \~~frac {b~~_~~v}~~{~~2~~(~~l_~~v ~~+ w_v)} $} [[<<]]~~

Figure 89: Border index of an image object{~~$ v $~~}.

Figure 89: Border index of an image object

to:

%left%{$ y_{\mathrm{min}} (v) = \bar y_{min} (v,\mathrm{map})- \mathrm{floor} \bigg( \frac {y_{\mathrm{min}} (v,\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) \times sy_{\mathrm{slice}} $}

Figure 120: Minimum value of the y-coordinate at the image object border.

Figure 120: Minimum value of the y-coordinate at the image object border.

Changed lines 324-331 from:

%left%{$ ~~\displaystyle ~~[0, \~~infty] $}; 1 = ideal.~~

!!!Compactness [for 2D Image Objects]

%gray%''Object Features > Geometry > ~~Shape~~ > ~~Compactness''~~

The Compactness feature describes how compact an image object is. It is similar to Border Index, but is based on area. However, the ~~more compact an image object is, the smaller its border appears. The compactness of an image object is the product of the length and the width, divided by the number of pixels~~.

!!!Compactness [for 2D Image Objects

%gray%''Object Features > Geometry

The Compactness feature describes how compact an image object is. It is similar to Border Index, but is based on area. However,

to:

%left%{$ [0, {\mathrm {scene \ extent \ in \ }} y - 1] $}

!!!Z Center

%gray%''Object Features > Position > Co-ordinate > Z Center''

{$Z$}-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

!!!Z Center

%gray%''Object Features > Position > Co-ordinate > Z Center''

{$Z$}-position of the center of an image object. The calculation is based on the center of gravity (geometric center) of the image object in the internal map.

Changed lines 333-336 from:

*{$ ~~l~~_v $} is the ~~length of an image object ~~{$~~ v ~~$}

~~*{$ w_v $} is the width of an image object ~~{$~~ ~~v~~ ~~$}

*~~ ~~{$ \~~# P~~_v ~~$} is the total number of pixels contained in {$ P_v ~~$}

*

to:

*{$ \bar z_v $} is the {$z$}-center of an image object {$v$}

*{$ \bar y_v {(\mathrm {map})} $} is the {$ y $} -center of an image object {$ v $} in an internal map with {$ \bar y_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}y_{\mathrm{map}} $}

* {$ sy_{\mathrm {slice}} $} is the extent in {$ y $} of each slice and frame

*{$ \bar y_v {(\mathrm {map})} $} is the {$ y $} -center of an image object {$ v $} in an internal map with {$ \bar y_v (\mathrm{map})= \frac{1}{\# P_v} \times \sum_{(x_{\mathrm{\mathrm{map}}},y_{\mathrm{map}})\in P_v}y_{\mathrm{map}} $}

* {$ sy_{\mathrm {slice}} $} is the extent in {$ y $} of each slice and frame

Changed lines 339-342 from:

%left%{$ \~~displaystyle ~~ \~~frac ~~{~~2~~\~~lambda_1~~ \~~times 2~~\~~lambda_2 \times 2~~\~~lambda_3}~~{~~V_v~~} ~~$~~}

Figure 90: Compactness of an image object {$~~ v $~~}~~.~~

Figure 90: Compactness of an image object {

to:

%left%{$ \bar z_v = \mathrm{floor} \bigg( \frac {\bar y_v (\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) $}

Changed lines 342-351 from:

%left%{$ ~~\displaystyle ~~[0, \~~infty] $}; 1 = ideal.~~

!!!Compactness [for 3D Image Objects]

%gray%''Object Features > Geometry >Shape > Compactness''

Compactness describes how compact a 3D image object is. Appropriately scaled eigenvectors of an image object~~'s covariance matrix provide a rough figure of the object's extent in three dimensions. ~~

A figure for the ~~compactness of a 3D image object is calculated by a scaled product of its three eigenvalues {$ (2 \times \lambda_1, 2 \times \lambda_2, 2 \times \lambda_3) $} divided by the number of its pixel/voxel. We include a factor of 2 with each eigenvalue, since {$ \lambda_i \times $} eigenvectors represent otherwise half axes of an ellipsoid defined by its covariance matrix. The chosen approach therefore provides an estimate of a cuboid occupied by the object~~.

!!!Compactness [for 3D Image Objects]

%gray%''Object Features > Geometry >Shape > Compactness

Compactness describes how compact a 3D image object is. Appropriately scaled eigenvectors

A figure for

to:

%left%{$ [0.5, {\mathrm {number \ of \ slices \ in \ map }} - 0.5] $}

!!!Z Max

%gray%''Object Features > Position > Co-ordinate > Z Max''

Maximum {$ z $}-position of an image object derived from its bounding box. The calculation is based on the maximum {$ z $}-position of the image object in the internal map.

!!!Z Max

%gray%''Object Features > Position > Co-ordinate > Z Max''

Maximum {$ z $}-position of an image object derived from its bounding box. The calculation is based on the maximum {$ z $}-position of the image object in the internal map.

Changed lines 351-355 from:

*{$ ~~\lambda~~_~~1 $~~} is ~~eigenvalue 1~~ of ~~a 3D ~~image object {$~~ ~~v~~ ~~$}~~ ~~

*{$ ~~\lambda~~_~~2 $~~} ~~is the eigenvalue 2 of a 3D image object ~~{$~~ v ~~$}

*{$ \lambda_3 $} is eigenvalue 3 of a 3D image object{$ ~~v $} ~~

*{$ V_v $} ~~is the volume of image object {$ v $} ~~

*{$ \lambda_3 $} is eigenvalue 3 of a 3D image object

*{$ V_v

to:

*{$ z_{\mathrm {max}}(v) $} is the maximum {$z$}-position of an image object {$v$}

*{$ y_{\mathrm {max}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

*{$ y_{\mathrm {max}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

Changed lines 357-360 from:

%left%{$ \~~displaystyle~~ \~~frac ~~{~~2~~\~~lambda_1~~ \~~times 2\lambda~~_~~2 ~~\~~times 2~~\~~lambda_3}~~{~~V_v~~} ~~$~~}

Figure 91: Compactness of an image object {$~~ v $~~}~~.~~

Figure 91: Compactness of an image object {

to:

%left%{$ z_{\mathrm{max}} (v)= \mathrm{floor} \bigg( \frac {y_{\mathrm{max}} (v,\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) $}

Changed lines 360-368 from:

%left%{$ ~~\displaystyle ~~[~~0~~, \~~infty] $}; 1 = ideal.~~

!!!Density [for 2D Image Objects]

%gray%''Object Features > Geometry > ~~Shape~~ > ~~Density''~~

The Density feature describes the distribution in spaceof ~~the pixels of an image object. In Definiens Developer XD 1.2.5 the most "dense" shape is a square;~~ the ~~more an ~~object ~~is shaped like a filament, the lower its density.~~

The density is calculated by the number of pixels forming the image object divided by its approximated radius, based on the covariance matrix.

!!!Density [for 2D Image Objects

%gray%''Object Features > Geometry

The Density feature describes the distribution in space

The density is calculated by the number of pixels forming the image object divided by its approximated radius, based on the covariance matrix.

to:

%left%{$ [1, {\mathrm {number \ of \ slices \ in \ map }} ] $}

!!!Z Min

%gray%''Object Features > Position > Co-ordinate > Z Min''

Minimum {$ z $}-position of an image object derived from its bounding box. The calculation is based on the minimum {$ z $}-position of the image object in the internal map.

!!!Z Min

%gray%''Object Features > Position > Co-ordinate > Z Min''

Minimum {$ z $}-position of an image object derived from its bounding box. The calculation is based on the minimum {$ z $}-position of the image object in the internal map.

Changed lines 369-371 from:

*~~ ~~{$ \~~sqrt~~ {~~\#P_v~~}~~ $~~} is the ~~diameter~~ of ~~a square~~ object ~~with ~~{$~~ \# P_~~v~~ ~~$}~~ pixels~~

*~~ ~~{$ \~~sqrt~~ {~~VarX + VarY~~}~~ $~~} ~~is the diameter of~~ the ~~ellipse~~

to:

*{$ z_{\mathrm {min}}(v) $} is the maximum {$z$}-position of an image object {$v$}

*{$ y_{\mathrm {min}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

*{$ y_{\mathrm {min}}(v, {\mathrm {map})} $} is the minimum {$y$}-position of an image object {$v$} in an internal map

*{$ sy_{\mathrm {slice}}$} is the extent in {$y$} of each slice and frame

Changed lines 376-377 from:

%left%{$ \~~displaystyle~~ \~~frac ~~{\~~sqrt {~~\~~# P~~_~~v}}~~{~~1+ ~~\~~sqrt ~~{~~VarX+VarY~~}} $}

to:

%left%{$ z_{\mathrm{min}} (v)= \mathrm{floor} \bigg( \frac {y_{\mathrm{min}} (v,\mathrm{map})} {sy_{\mathrm{slice}}}\bigg) $}

Changed lines 379-1168 from:

%left%{$ ~~\displaystyle ~~[0, {\mathrm {~~depending~~ \ ~~on~~ \ ~~shape~~ \ ~~of~~ \ ~~image \ object~~}}~~]~~ $}

!!~~!Density [for 3D Image Objects]~~

%gray%''Object Features > ~~Geometry~~ > ~~Shape > Density~~''

~~Using the same principle as Density [for 2D Image Objects], the most "dense" shape for ~~a ~~3D object is a cube. The more filament-shaped an image object is, the lower its density. The value is calculated by dividing the edge of the volume of a fitted cuboid by the radius of a fitted sphere.~~

!!!!Parameters

*{$ V_v $} is the volume of image object {$ v $}

*{$ \sqrt[3]{V_v} $} is the edge of the volume fitted cuboid

*{$ \sqrt {\mathrm{Var}(X) + \mathrm{Var}(Y) + \mathrm{Var}(Z)} $} is the radius of the fitted sphere

!!!!Expression

%left%{$ \displaystyle \frac {\sqrt[3]{V_v}} {\sqrt {\mathrm{Var}(X) + \mathrm{Var}(Y) + \mathrm{Var}(Z)}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ image \ object}}] $}

!!!Elliptic Fit [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit''

The Elliptic Fit feature describes how well an image object fits into an ellipse of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on an ellipse with the same area as the selected image object. The proportions of the ellipse are equal to the length to the width of the image object. The area of the image object outside the ellipse is compared with the area inside the ellipse that is not filled by the image object.

!!!!Parameters

*{$ \varepsilon_v(x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

*{$ P_v $} is the set of pixels of an image object {$ v $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \varphi =2 \cdot \frac {\#\big \{(x,y)\epsilon P_v:\varepsilon_v(x,y)\leq 1\big \}}{\# P_v}-1 $}

Figure 92: Elliptic fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}; 1 = complete fitting, 0 = <50% fit.

!!!Elliptic Fit [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit''

The Elliptic Fit feature describes how well an image object fits into an ellipsoid of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on an ellipsoid with the same volume as the considered image object. The proportions of the ellipsoid are equal to the proportions of the length, width and thickness of the image object. The volume of the image object outside the ellipsoid is compared with the volume inside the ellipsoid that is not filled out with the image object.

!!!!Parameters

*{$ \varepsilon_v(x,y,z) $} is the elliptic distance at a pixel {$ {(x,y,z)} $}

*{$ P_v $} is the set of pixels of an image object {$ v $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \varphi =2 \cdot \frac {\#\big \{(x,y,z)\epsilon P_v:\varepsilon_v(x,y,z)\leq 1\big \}}{\# P_v}-1 $}

Figure 93: Elliptic fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0,1] $}; 1 = complete fitting, whereas 0 = < 50% voxels.

!!!Main Direction [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit > Main Direction''

The Main Direction feature of an image object is defined as the direction of the eigenvector belonging to the larger of the two eigenvalues, derived from the covariance matrix of the spatial distribution of the image object.

!!!!Parameters

* {$ Var X $} is the variance of {$ X $}

* {$ Var Y $} is the variance of {$ Y $}

* {$ \lambda_1 $} is the eigenvalue

!!!!Expression

%left%{$ \displaystyle \frac {180^{\circ}}{\pi}\mathrm{tan}^{-1}(\mathrm{Var}XY,\lambda_1-\mathrm{Var}Y) + {90^{\circ}} $}

Figure 94: The main direction is based on direction of the larger eigenvector.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 180] $}

!!!Main Direction [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Main Direction''

The Main Direction feature of a three-dimensional image object is computed as follows:

#For each (2D) image object slice, the centers of gravities are calculated.

#The co-ordinates of all centers of gravities a reused to calculate a line of best fit, according to the Weighted Least Square method.

#The angle a between the resulting line of best fit and the z-axis is returned as feature value.

Figure 95: The line of best fit (blue) calculated from centers of gravity of image object slices (light blue).

!!!!Feature Value Range

%left%{$ \displaystyle [0, 90] $}

!!!Radius of Largest Enclosed Ellipse [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Largest Enclosed Ellipse''

The Radius of Largest Enclosed Ellipse feature describes how similar an image object is to an ellipse. The calculation uses an ellipse with the same area as the object and based on the covariance matrix. This ellipse is scaled down until it is totally enclosed by the image object. The ratio of the radius of this largest enclosed ellipse to the radius of the original ellipse is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o) $}, where {$ (x_o,y_o) = min \ \varepsilon_v (x,y), (x,y) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Largest Enclosed Ellipse [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Largest Enclosed Ellipse''

The Radius of Largest Enclosed Ellipse feature describes how much the shape of an image object is similar to an ellipsoid.

The calculation is based on an ellipsoid with the same volume as the object and based on the covariance matrix. This ellipsoid is scaled down until it is totally enclosed by the image object. The ratio of the radius of this largest enclosed ellipsoid to the radius of the original ellipsoid is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y,z) $} is the elliptic distance at a pixel {$ (x,y,z) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o,z_o) $}, where {$ (x_o,y_o,z_o) = min \ \varepsilon_v (x,y,z), (x,y,z) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Smallest Enclosing Ellipse [for 2D Image Objects]

%gray%''Object Features > Geometry >Shape > Radius of Smallest Enclosing Ellipse''

The Radius of Smallest Enclosing Ellipse feature describes how much the shape of an image object is similar to an ellipse.

The calculation is based on an ellipse with the same area as the image object and based on the covariance matrix. This ellipse is enlarged until it encloses the image object in total. The ratio of the radius of this smallest enclosing ellipse to the radius of the original ellipse is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o) $}, where {$ (x_o,y_o) = max \ \varepsilon_v (x,y), (x,y) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Smallest Enclosing Ellipse [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Smallest Enclosing Ellipse''

The Radius of Smallest Enclosing Ellipse feature describes how much the shape of an image object is similar to an ellipsoid.

The calculation is based on an ellipsoid with the same volume as the image object and based on the covariance matrix. This ellipsoid is enlarged until it encloses the image object in total. The ratio of the radius of this smallest enclosing ellipsoid to the radius of the original ellipsoid is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y,z) $} is the elliptic distance at a pixel {$ (x,y,z) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o,z_o) $}, where {$ (x_o,y_o,z_o) = max \ \varepsilon_v (x,y,z), (x,y,z) \in \sigma P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Rectangular Fit [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Rectangular Fit''

The Rectangular Fit feature describes how well an image object fits into a rectangle of similar size and proportions. While 0 indicates no fit, 1 indicates for a complete fitting image object.

The calculation is based on a rectangle with the same area as the image object. The proportions of the rectangle are equal to the proportions of the length to width of the image object. The area of the image object outside the rectangle is compared with the area inside the rectangle.

!!!!Parameters

*{$ \rho_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \frac {\big \{\#(x,y)\epsilon P_v:\rho _v(x,y)\leq 1\big \}}{\#P_v} $}

Figure 96: Rectangular fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}; where 1 is a perfect rectangle.

!!!Rectangular Fit [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Rectangular Fit''

The Rectangular Fit feature describes how well an image object fits into a cuboid of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on a cuboid with the same volume as the considered image object. The proportions of the cuboid are equal to the proportions of the length to width to thickness of the image object. The volume of the image object outside the rectangle is compared with the volume inside the cuboid that is not filled out with the image object.

!!!!Parameters

*{$ \rho_v(x,y,z) $} is the rectangular distance at a pixel {$ (x,y,z) $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \frac {\big \{\#(x,y,z)\epsilon P_v:\rho _v(x,y,z)\leq 1\big \}}{\#P_v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $} ; 1 = complete fitting, whereas 0 = 0% fits inside the rectangular approximation.

!!!Roundness [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Roundness''

The Roundness feature describes how similar an image object is to an ellipse. It is calculated by the difference of the enclosing ellipse and the enclosed ellipse. The radius of the largest enclosed ellipse is subtracted from the radius of the smallest enclosing ellipse.

!!!!Parameters

*{$ \varepsilon_v^\mathrm{max} $} is the radius of the smallest enclosing ellipse

*{$ \varepsilon_v^\mathrm{min} $} is the radius of the largest enclosed ellipse

!!!!Expression

%left%{$ \displaystyle \varepsilon_v^\mathrm{max} - \varepsilon_v^\mathrm{min} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 0 = ideal.

!!!Roundness [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Roundness''

The Roundness feature describes how much the shape of an image object is similar to an ellipsoid. The more the shape of an image object is similar to an ellipsoid, the lower its roundness.

It is calculated by the difference of the enclosing ellipsoid and the enclosed ellipsoid. The radius of the largest enclosed ellipsoid is subtracted from the radius of the smallest enclosing ellipsoid.

!!!!Parameters

*{$ \varepsilon_v^\mathrm{max} $} is the radius of the smallest enclosing ellipsoid

*{$ \varepsilon_v^\mathrm{min} $} is the radius of the largest enclosed ellipsoid

!!!!Expression

%left%{$ \displaystyle \varepsilon_v^\mathrm{max} - \varepsilon_v^\mathrm{min} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 0 = ideal.

!!!Main Direction [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit > Main Direction''

The Main Direction feature of an image object is defined as the direction of the eigenvector belonging to the larger of the two eigenvalues, derived from the covariance matrix of the spatial distribution of the image object.

!!!!Parameters

* {$ VarX $} is the variance of {$ X $}

* {$ VarY $} is the variance of {$ Y $}

* {$ \lambda_1 $} is the eigenvalue

!!!!Expression

%left%{$ \displaystyle \frac {180^{\circ}}{\pi}\mathrm{tan}^{-1}(\mathrm{Var}XY,\lambda_1-\mathrm{Var}Y) + {90^{\circ}} $}

Equation 1: The main direction is based on the direction of the larger eigenvector

!!!!Feature Value Range

%left%{$ \displaystyle [0,180] $}

!!!Main Direction [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Main Direction''

The Main Direction feature of a three-dimensional image object is computed as follows:

#For each (2D) image object slice, the centers of gravities are calculated.

#The co-ordinates of all centers of gravities a reused to calculate a line of best fit, according to the Weighted Least Square method.

#The angle a between the resulting line of best fit and the {$ z $}-axis is returned as feature value.

Figure 97: The line of best fit (blue) calculated from centers of gravity of image object slices (light blue).

!!!!Feature Value Range

%left%{$ \displaystyle [0,90] $}

!!!Shape Index [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Shape Index''

The Shape index describes the smoothness of an image object border. The smoother the border of an image object is, the lower its shape index. It is calculated from the Border Length feature of the image object divided by four times the square root of its area.

!!!!Parameters

*{$ b_v $} is the image object border length

*{$ \sqrt[4] {\#P_v} $} is the border of square with area {$ \# P_v $}

!!!!Expression

%left%{$ \displaystyle \frac {b_v}{\sqrt[4]{\# P_v}} $}

Figure 98: Shape index of an image object {$ v $}

!!!!Feature Value Range

%left%{$ \displaystyle [1, \infty] $}; 1 = ideal.

!!!Shape Index [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Shape Index''

The Shape Index describes the smoothness of the surface of an image object. The smoother the surface of an image object is, the lower its shape index. It is calculated from the Border Length feature of the image object divided by four times the square root of its area.

!!!!Parameters

*{$ b_v $} is the image object border length

*{$ V_v $} is the volume of image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \frac {b_v}{V_v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [1, \infty] $}; 1 = ideal.

!!To Superobject

%gray%''Object Features > Geometry > To Superobject''

Use the To Superobject feature to describe an image object by its shape and relationship to one of its superobjects, where appropriate. Editing the feature distance determines which superobject is referred to. When working with thematic layers these features can be of interest.

!!!Rel. Area to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Area to Superobject''

The area of an image object divided by the area of its superobject. If the feature value is 1, the image object is identical to its superobject. Use this feature to describe an image object in terms of the amount of area it shares with its superobject.

!!!!Parameters

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ \# P_{Uv(d)} $} is the the size of the superobject of {$ v $} in the image object level of the level distance {$ d $}

!!!!Expression

%left%{$ \displaystyle \frac {\# P_v}{\# P_{Uv(d)}} $}

!!!!Conditions

If {$ U_v(d) = \varnothing \therefore $} the formula is undefined.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. Rad. Position to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Rad. Position to Superobject''

This value is calculated by dividing the distance between the center of a selected image object and the center of its superobject, by the distance of the center of the most distant image object (which has the same superobject). Use this feature to describe an image object by its position relative to the center of its superobject.

!!!!Parameters

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ \#P_{Uv( d)} $} is the the size of the superobject of an image object {$ v $}

*{$ d_g( v,Uv( d)) $} is the distance of {$ v $} to the center of gravity of the superobject {$ U_v( d) $}

!!!!Expression

Figure 99: Relative radial position to superobject.

%left%{$ \displaystyle \frac {d_g \big( v,U_v(d) \big)}{\underset {u\in S_{U{v(d)^{( d)}}}} {\mathrm{max}} d_g \big( u,U_v (d)\big)} $}

!!!!Conditions

If {$ U_v(d) = \varnothing \therefore $} the formula is undefined.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. Inner Border to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Inner Border to Superobject''

This feature is calculated by dividing the sum of the border shared with other image objects, which have the same superobject, by the total border of the image object. If the relative inner border to the superobject is 1, the image object of concern is not situated on the border of its superobject. Use this feature to describe how much of an image object is situated at the edge of its superobject.

!!!!Parameters

*{$ N_u(v) $} are neighbors of {$ v $} that exist within the superobject {$ N_u(v): \{ u \in N_v:U_u(d) - U_v(d) \} $}

*{$ b_v $} is the image object border length

!!!!Expression

%left%{$ \displaystyle \frac {\sum_ { u \in N_U( v) } b( v,m)}{b_v} $}

Figure 100: Relative inner border of an image object {$ v $} to superobject {$ u $}.

!!!!Conditions

If the feature range is 0 then {$ v=U_v(d) $}

If the feature range is 1 then {$ v $} is an inner object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Distance to Superobject Center

%gray%''Object Features > Geometry > To Superobject > Distance to Superobject Center''

The distance of an image object's center to the center of its superobject. This might not be the shortest distance between the two points, since the way to the center of the superobject must be within the borders of the superobject.

!!!!Expression

%left%{$ \displaystyle d_g( v,U_v(d)) $} is the distance of {$ v $} to the center of gravity of the superobject {$ U_v(d) $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, sx \times sy] $}

!!!Elliptic Distance to Superobject Center

%gray%''Object Features > Geometry > To Superobject > Elliptic Distance to Superobject Center''

Distance of objects to the center of the superobject.

!!!!Expression

%left%{$ \displaystyle d_e( v,U_v(d)) $}

Figure 101: Distance between the distance from the superobject's center to the center of a sub-objectt.

!!!!Feature Value Range

Typically {$ [0, 5] $}

!!!Is End of Superobject

%gray%''Object Features > Geometry > To Superobject > Is End of Superobject''

This feature is true for two image objects {$ a $} and {$ b $} if following conditions are true:

*{$ a $} and {$ b $} are sub-objects of the same superobject.

*{$ a $} is the image object with the maximum distance to the superobject.

*{$ b $} is the image object with the maximum distance to {$ a $}.

!!!!Editable Parameter

*Level Distance

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Is Center of Superobject

%gray%''Object Features > Geometry > To Superobject > Is Center of Superobject''

This feature is true if the image object is the center of its superobject.

!!!!Editable Parameter

*Level Distance

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. X Position to Superobject

%gray%''Object Features > Geometry > To Superobject Rel. X Position to Superobject''

This feature returns the relative{$ x $}position of an image object with regard to its superobject, based on the centers of gravity of both objects.

!!!!Editable Parameters

*Level Distance `- the upward distance of image object levels in the image object hierarchy between the image object and the superobject.

!!!!Expression

%left%{$ \displaystyle \Delta x = x_{CG} $} of current image object {$ - x_{CG} $} of superobject (where {$ x_{CG} $} is the center of gravity)

!!!!Feature Value Range

%left%{$ \displaystyle - \frac {\mathrm{scene \ width}}{2} + \frac {\mathrm{scene \ width}}{2} $}

!!!Rel. Y Position to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Y Position to Superobject''

This feature returns the relative{$ y $}position of an image object with regard to its superobject, based on the centers of gravity of both objects.

!!!!Editable Parameter

*Level Distance: Upward distance of image object levels in the image object hierarchy between the image object and the superobject.

!!!!Expression

%left%{$ \displaystyle \Delta y = y_{CG} $} of current image object {$ - y_{CG} $} of superobject (where {$ y_{CG} $} is the center of gravity)

!!!!Feature Value Range

%left%{$ \displaystyle - \frac {\mathrm{scene \ height}}{2} + \frac {\mathrm{scene \ height}}{2} $}

!!Based on Polygons

%gray%''Object Features > Geometry > Based on Polygons''

The polygon features provided by Definiens Developer XD 1.2.5 are based on the vectorization of the pixels that form an image object.

Figure 102: Raster image object (black area) with its polygon object (red lines) after vectorization.

!!!Edges Longer Than

%gray%''Object Features > Geometry > Based on Polygons > Edges Longer Than''

!!!!Editable Parameters

*Minimum Length

!!!Number of Right Angles With Edges Longer Than

%gray%''Object Features > Geometry > Based on Polygons > Number of Right Angles with Edges Longer Than''

The number of right angles that have at least one side edge longer than a given threshold.

!!!!Editable Parameters

*Minimum length

Figure 103: A polygon with one rectangular angle.

!!!Area (Excluding Inner Polygons)

%gray%''Object Features > Geometry > Based on Polygons > Area (Excluding Inner Polygons)''

The Area (Excluding Inner Polygons) feature calculates the area of a polygon based on Green's Theorem in a plane. In contrast to the Area (Including Inner Polygons) feature, the feature value does not include the areas of any existing inner polygons.

!!!!Parameters

*{$ (x_i, y_i), i = 0, \dots , n, $} with {$ x_o = x_n $} and {$ y_o = y_n $} as the given points

*{$ a_i = x_iy_{i+1} - x_{i+1}y_i $}

!!!!Expression

%left%{$ \displaystyle \frac {1}{2}\sum_{i=0}^{n-1} a_i $}

Figure 104: A polygon with an inner polygon that is not included in the feature value.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {scene \ size}}] $}

!!!Area (Including Inner Polygons)

%gray%''Object Features > Geometry > Based on Polygons > Area (Including Inner Polygons)''

The Area (Excluding Inner Polygons) feature calculates the area of a polygon based on Green's Theorem in a plane. Different to the Area (Excluding Inner Polygons) feature, the feature value includes the areas of any existing inner polygons (for instance the single polygon formed in the center of a donut-shaped object).

Figure 105: A polygon with an inner polygon that is included in the feature value.

!!!Average Length of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > average Length of Edges (Polygon)''

The average length of all edges in a polygon.

!!!!Parameters

*{$ X_i $} is the length of edge {$ i $}

*{$ n $} is the total number of edges

!!!!Expression

%left%{$ \displaystyle \mathrm{Average} = \frac {\displaystyle \sum_{i=1}^{n} X_{i}} {n} $}

!!!Compactness (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Compactness (Polygon)''

The ratio of the area of a polygon to the area of a circle with the same perimeter.

!!!!Parameters

*Area

*Perimeter

!!!!Expression

%left%{$ \displaystyle \frac {4 \times \pi \times \mathrm{Area}} {\mathrm{Perimeter}^2} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {1 \ for \ a \ circle}}] $}

!!!Length of Longest Edge (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Length of Longest Edge (Polygon)''

The length of the longest edge of a polygon.

!!!Number of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Number of Edges (Polygon)''

The number of edges of a polygon.

!!!Number of Inner Objects (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Number of Inner Objects (Polygon)''

The number of inner polygons that are completely surrounded by a selected outer polygon.

!!!Perimeter (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Perimeter (Polygon)''

The sum of the lengths of all the edges of a polygon.

!!!Polygon Self-Intersection (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Polygon Self-Intersection (Polygon)''

The Polygon Self-Intersection (Polygon) feature allows the identification of a rare arrangement of image objects, leading to a polygon self-intersection when exported as a polygon vector file.

This feature enables you to identify the affected image objects and take measures To avoid this self-intersection. All image objects with a value of 1 will cause a polygon self-intersection when exported to a shapefile.

Figure 106: This type of image object leads to a self-intersection at the circled point.

To avoid the self-intersection, the enclosed image object needs to be merged with the enclosing image object.

(:div class=frame:)

->'''TIP: '''Use the Image Object Fusion algorithm to remove polygon intersections. To do so, set the domain to all image objects with a value larger than 0 for the polygon intersection feature. In the algorithm parameter, set the Fitting Function Threshold to Polygon Self-Intersection (Polygon) feature to zero and in the Weighted Sum group, set Target Value Factor to 1. This will merge all image objects with a value of 1 for the Polygon Self-Intersection (Polygon) feature, so that the resulting image object will not include a self-intersection.

(:divend:)

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Std. Dev. of Length of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Stddev of Length of Edges (Polygon)''

The Std. Dev. of Length of Edges (Polygon) feature measures how the lengths of edges deviate from their mean value.

!!!!Parameters

*{$ x_i $} is the length of edge {$ i $}

*{$ \bar X $} is the mean value of all lengths

*{$ n $} is the total number of edges

!!!!Expression

%left%{$ \displaystyle \sqrt \frac {\displaystyle \sum_{i=1}^{n} {(x_i-\bar x)^2}} {n} $}

!!Based on Skeletons

%gray%''Object Features > Geometry > Based on Skeletons''

For the better understanding of the following descriptions, the skeleton is structured in a main line and subordinate branches. A node is a mid-point of the triangles created by the Delaunay triangulation.

!!!Number of Segments of Order

%gray%''Object Features > Geometry > Based on Skeletons > Number of Segments of Order''

The number of line segments of branches of an object that are of a given order. Note that only segments that do not belong to a lower order are counted

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Branches of Order

%gray%''Object Features > Geometry > Based on Skeletons > Number of Branches of Order''

The number of branches of an object that are of a given order.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Average Length of Branches of Order

%gray%''Object Features > Geometry > Based on Skeletons > average Length of Branches of Order''

The average length of branches of an object that are of a given order. The length of the branch of the selected order is measured from the intersect point of the whole branch and the main line to the end of the branch.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Branches of Length

%gray%''Object Features > Geometry > Based on Skeletons > Number of Branches of Length''

The number of branches of an object that are of a special length up to a selected order. All ends of branches are counted up to the selected order.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

*Minimum length

*Maximum length

!!!!Feature Value Range

[0; depending on shape of objects]

!!!Average Branch Length

%gray%''Object Features > Geometry > Based on Skeletons > Average Branch Length''

The average length of all branches of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Avrg. Area Represented by Segments

%gray%''Object Features > Geometry > Based on Skeletons > Avrg. Area Represented by Segments''

The average area of all triangles created by a Delaunay triangulation.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Curvature/Length (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Curvature/Length (only main line)''

The length-to-curvature ratio of the main line of an object. The curvature is the sum of all changes in direction of the main line. Changes in direction are expressed by the acute angle a in which sections of the main line, built by the connection between the nodes, cross each other.

Figure 107: The main line (green) connects the mid-points of triagles (black and blue) created by a Delaunay triangulation of the objects' shape (not depicted).

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Degree of Skeleton Branching

%gray%''Object Features > Geometry > Based on Skeletons > Degree of Skeleton Branching''

The highest order of branching in an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length of Main Line (No Cycles)

%gray%''Object Features > Geometry > Based on Skeletons > Length of Main Line (No Cycles)''

The sum of all distances between the nodes of the main line of an object. If an object contains an island polygon `- a polygon derived from the inner borders of an image object `- it is ignored and the main line may cross it (no cycles). This is different to the Length of Main Line (regarding cycles) feature where the main line goes around the island polygon. This feature does not visualize skeletons.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length of Main Line (Regarding Cycles)

%gray%''Object Features > Geometry > Based on Skeletons > Length of Main Line (regarding cycles)''

The sum of all distances between the nodes of the main line of an object. If an object contains an island polygon `- a polygon derived from the inner borders of an image object `- the main line is calculated so as not to cross it (Regarding Cycles).

In contrast to the Length of Main Line (No Cycles) feature, the skeletons are visualized.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length/Width (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons >Length/Width (Only Main Line)''

The length-to-width ratio of the main line of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Maximum Branch Length

%gray%''Object Features > Geometry > Based on Skeletons > Maximum Branch Length''

The length of the longest branch of an object. It is measured from the intersect point of the branch and the main line to the end of the branch.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Segments

%gray%''Object Features > Geometry > Based on Skeletons > Number of Segments''

The number of all segments of the main line and the branches of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Stddev Curvature (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Stddev Curvature (Only Main Line)''

The standard deviation of the curvature is the result of the standard deviation of the changes in direction of the main line. Changes in direction are expressed by the acute angle in which sections of the mainline, built by the connection between the nodes, cross each other.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Stddev of Area Represented by Segments

%gray%''Object Features > Geometry > Based on Skeletons > Stddev. of Area Represented by Segments''

The standard deviation of all triangles created by the Delaunay triangulation.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Width (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Width (Only Main Line)''

The width of an object based on the height of triangles created by a Delaunay triangulation. It is calculated by the average height{$ h $}of all triangles crossed by the main line.

Figure 108: Height {$ h $} of an triangle that is crossed by the main line.

An exception is triangles where the height {$ h $} does not cross one of the sides of the triangle. In this case, the nearest side {$ s $} is used to define the height.

Figure 109: Height of an triangle that is crossed by the main line. In this case the side {$ s $} defines the height.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!

!!!!Parameters

*{$ V_v $} is the volume of image object {$ v $}

*{$ \sqrt[3]{V_v} $} is the edge of the volume fitted cuboid

*{$ \sqrt {\mathrm{Var}(X) + \mathrm{Var}(Y) + \mathrm{Var}(Z)} $} is the radius of the fitted sphere

!!!!Expression

%left%{$ \displaystyle \frac {\sqrt[3]{V_v}} {\sqrt {\mathrm{Var}(X) + \mathrm{Var}(Y) + \mathrm{Var}(Z)}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ image \ object}}] $}

!!!Elliptic Fit [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit''

The Elliptic Fit feature describes how well an image object fits into an ellipse of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on an ellipse with the same area as the selected image object. The proportions of the ellipse are equal to the length to the width of the image object. The area of the image object outside the ellipse is compared with the area inside the ellipse that is not filled by the image object.

!!!!Parameters

*{$ \varepsilon_v(x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

*{$ P_v $} is the set of pixels of an image object {$ v $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \varphi =2 \cdot \frac {\#\big \{(x,y)\epsilon P_v:\varepsilon_v(x,y)\leq 1\big \}}{\# P_v}-1 $}

Figure 92: Elliptic fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}; 1 = complete fitting, 0 = <50% fit.

!!!Elliptic Fit [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit''

The Elliptic Fit feature describes how well an image object fits into an ellipsoid of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on an ellipsoid with the same volume as the considered image object. The proportions of the ellipsoid are equal to the proportions of the length, width and thickness of the image object. The volume of the image object outside the ellipsoid is compared with the volume inside the ellipsoid that is not filled out with the image object.

!!!!Parameters

*{$ \varepsilon_v(x,y,z) $} is the elliptic distance at a pixel {$ {(x,y,z)} $}

*{$ P_v $} is the set of pixels of an image object {$ v $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \varphi =2 \cdot \frac {\#\big \{(x,y,z)\epsilon P_v:\varepsilon_v(x,y,z)\leq 1\big \}}{\# P_v}-1 $}

Figure 93: Elliptic fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0,1] $}; 1 = complete fitting, whereas 0 = < 50% voxels.

!!!Main Direction [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit > Main Direction''

The Main Direction feature of an image object is defined as the direction of the eigenvector belonging to the larger of the two eigenvalues, derived from the covariance matrix of the spatial distribution of the image object.

!!!!Parameters

* {$ Var X $} is the variance of {$ X $}

* {$ Var Y $} is the variance of {$ Y $}

* {$ \lambda_1 $} is the eigenvalue

!!!!Expression

%left%{$ \displaystyle \frac {180^{\circ}}{\pi}\mathrm{tan}^{-1}(\mathrm{Var}XY,\lambda_1-\mathrm{Var}Y) + {90^{\circ}} $}

Figure 94: The main direction is based on direction of the larger eigenvector.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 180] $}

!!!Main Direction [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Main Direction''

The Main Direction feature of a three-dimensional image object is computed as follows:

#For each (2D) image object slice, the centers of gravities are calculated.

#The co-ordinates of all centers of gravities a reused to calculate a line of best fit, according to the Weighted Least Square method.

#The angle a between the resulting line of best fit and the z-axis is returned as feature value.

Figure 95: The line of best fit (blue) calculated from centers of gravity of image object slices (light blue).

!!!!Feature Value Range

%left%{$ \displaystyle [0, 90] $}

!!!Radius of Largest Enclosed Ellipse [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Largest Enclosed Ellipse''

The Radius of Largest Enclosed Ellipse feature describes how similar an image object is to an ellipse. The calculation uses an ellipse with the same area as the object and based on the covariance matrix. This ellipse is scaled down until it is totally enclosed by the image object. The ratio of the radius of this largest enclosed ellipse to the radius of the original ellipse is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o) $}, where {$ (x_o,y_o) = min \ \varepsilon_v (x,y), (x,y) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Largest Enclosed Ellipse [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Largest Enclosed Ellipse''

The Radius of Largest Enclosed Ellipse feature describes how much the shape of an image object is similar to an ellipsoid.

The calculation is based on an ellipsoid with the same volume as the object and based on the covariance matrix. This ellipsoid is scaled down until it is totally enclosed by the image object. The ratio of the radius of this largest enclosed ellipsoid to the radius of the original ellipsoid is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y,z) $} is the elliptic distance at a pixel {$ (x,y,z) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o,z_o) $}, where {$ (x_o,y_o,z_o) = min \ \varepsilon_v (x,y,z), (x,y,z) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Smallest Enclosing Ellipse [for 2D Image Objects]

%gray%''Object Features > Geometry >Shape > Radius of Smallest Enclosing Ellipse''

The Radius of Smallest Enclosing Ellipse feature describes how much the shape of an image object is similar to an ellipse.

The calculation is based on an ellipse with the same area as the image object and based on the covariance matrix. This ellipse is enlarged until it encloses the image object in total. The ratio of the radius of this smallest enclosing ellipse to the radius of the original ellipse is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o) $}, where {$ (x_o,y_o) = max \ \varepsilon_v (x,y), (x,y) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Smallest Enclosing Ellipse [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Smallest Enclosing Ellipse''

The Radius of Smallest Enclosing Ellipse feature describes how much the shape of an image object is similar to an ellipsoid.

The calculation is based on an ellipsoid with the same volume as the image object and based on the covariance matrix. This ellipsoid is enlarged until it encloses the image object in total. The ratio of the radius of this smallest enclosing ellipsoid to the radius of the original ellipsoid is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y,z) $} is the elliptic distance at a pixel {$ (x,y,z) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o,z_o) $}, where {$ (x_o,y_o,z_o) = max \ \varepsilon_v (x,y,z), (x,y,z) \in \sigma P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Rectangular Fit [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Rectangular Fit''

The Rectangular Fit feature describes how well an image object fits into a rectangle of similar size and proportions. While 0 indicates no fit, 1 indicates for a complete fitting image object.

The calculation is based on a rectangle with the same area as the image object. The proportions of the rectangle are equal to the proportions of the length to width of the image object. The area of the image object outside the rectangle is compared with the area inside the rectangle.

!!!!Parameters

*{$ \rho_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \frac {\big \{\#(x,y)\epsilon P_v:\rho _v(x,y)\leq 1\big \}}{\#P_v} $}

Figure 96: Rectangular fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}; where 1 is a perfect rectangle.

!!!Rectangular Fit [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Rectangular Fit''

The Rectangular Fit feature describes how well an image object fits into a cuboid of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on a cuboid with the same volume as the considered image object. The proportions of the cuboid are equal to the proportions of the length to width to thickness of the image object. The volume of the image object outside the rectangle is compared with the volume inside the cuboid that is not filled out with the image object.

!!!!Parameters

*{$ \rho_v(x,y,z) $} is the rectangular distance at a pixel {$ (x,y,z) $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \frac {\big \{\#(x,y,z)\epsilon P_v:\rho _v(x,y,z)\leq 1\big \}}{\#P_v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $} ; 1 = complete fitting, whereas 0 = 0% fits inside the rectangular approximation.

!!!Roundness [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Roundness''

The Roundness feature describes how similar an image object is to an ellipse. It is calculated by the difference of the enclosing ellipse and the enclosed ellipse. The radius of the largest enclosed ellipse is subtracted from the radius of the smallest enclosing ellipse.

!!!!Parameters

*{$ \varepsilon_v^\mathrm{max} $} is the radius of the smallest enclosing ellipse

*{$ \varepsilon_v^\mathrm{min} $} is the radius of the largest enclosed ellipse

!!!!Expression

%left%{$ \displaystyle \varepsilon_v^\mathrm{max} - \varepsilon_v^\mathrm{min} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 0 = ideal.

!!!Roundness [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Roundness''

The Roundness feature describes how much the shape of an image object is similar to an ellipsoid. The more the shape of an image object is similar to an ellipsoid, the lower its roundness.

It is calculated by the difference of the enclosing ellipsoid and the enclosed ellipsoid. The radius of the largest enclosed ellipsoid is subtracted from the radius of the smallest enclosing ellipsoid.

!!!!Parameters

*{$ \varepsilon_v^\mathrm{max} $} is the radius of the smallest enclosing ellipsoid

*{$ \varepsilon_v^\mathrm{min} $} is the radius of the largest enclosed ellipsoid

!!!!Expression

%left%{$ \displaystyle \varepsilon_v^\mathrm{max} - \varepsilon_v^\mathrm{min} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 0 = ideal.

!!!Main Direction [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit > Main Direction''

The Main Direction feature of an image object is defined as the direction of the eigenvector belonging to the larger of the two eigenvalues, derived from the covariance matrix of the spatial distribution of the image object.

!!!!Parameters

* {$ VarX $} is the variance of {$ X $}

* {$ VarY $} is the variance of {$ Y $}

* {$ \lambda_1 $} is the eigenvalue

!!!!Expression

%left%{$ \displaystyle \frac {180^{\circ}}{\pi}\mathrm{tan}^{-1}(\mathrm{Var}XY,\lambda_1-\mathrm{Var}Y) + {90^{\circ}} $}

Equation 1: The main direction is based on the direction of the larger eigenvector

!!!!Feature Value Range

%left%{$ \displaystyle [0,180] $}

!!!Main Direction [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Main Direction''

The Main Direction feature of a three-dimensional image object is computed as follows:

#For each (2D) image object slice, the centers of gravities are calculated.

#The co-ordinates of all centers of gravities a reused to calculate a line of best fit, according to the Weighted Least Square method.

#The angle a between the resulting line of best fit and the {$ z $}-axis is returned as feature value.

Figure 97: The line of best fit (blue) calculated from centers of gravity of image object slices (light blue).

!!!!Feature Value Range

%left%{$ \displaystyle [0,90] $}

!!!Shape Index [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Shape Index''

The Shape index describes the smoothness of an image object border. The smoother the border of an image object is, the lower its shape index. It is calculated from the Border Length feature of the image object divided by four times the square root of its area.

!!!!Parameters

*{$ b_v $} is the image object border length

*{$ \sqrt[4] {\#P_v} $} is the border of square with area {$ \# P_v $}

!!!!Expression

%left%{$ \displaystyle \frac {b_v}{\sqrt[4]{\# P_v}} $}

Figure 98: Shape index of an image object {$ v $}

!!!!Feature Value Range

%left%{$ \displaystyle [1, \infty] $}; 1 = ideal.

!!!Shape Index [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Shape Index''

The Shape Index describes the smoothness of the surface of an image object. The smoother the surface of an image object is, the lower its shape index. It is calculated from the Border Length feature of the image object divided by four times the square root of its area.

!!!!Parameters

*{$ b_v $} is the image object border length

*{$ V_v $} is the volume of image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \frac {b_v}{V_v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [1, \infty] $}; 1 = ideal.

!!To Superobject

%gray%''Object Features > Geometry > To Superobject''

Use the To Superobject feature to describe an image object by its shape and relationship to one of its superobjects, where appropriate. Editing the feature distance determines which superobject is referred to. When working with thematic layers these features can be of interest.

!!!Rel. Area to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Area to Superobject''

The area of an image object divided by the area of its superobject. If the feature value is 1, the image object is identical to its superobject. Use this feature to describe an image object in terms of the amount of area it shares with its superobject.

!!!!Parameters

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ \# P_{Uv(d)} $} is the the size of the superobject of {$ v $} in the image object level of the level distance {$ d $}

!!!!Expression

%left%{$ \displaystyle \frac {\# P_v}{\# P_{Uv(d)}} $}

!!!!Conditions

If {$ U_v(d) = \varnothing \therefore $} the formula is undefined.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. Rad. Position to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Rad. Position to Superobject''

This value is calculated by dividing the distance between the center of a selected image object and the center of its superobject, by the distance of the center of the most distant image object (which has the same superobject). Use this feature to describe an image object by its position relative to the center of its superobject.

!!!!Parameters

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ \#P_{Uv( d)} $} is the the size of the superobject of an image object {$ v $}

*{$ d_g( v,Uv( d)) $} is the distance of {$ v $} to the center of gravity of the superobject {$ U_v( d) $}

!!!!Expression

Figure 99: Relative radial position to superobject.

%left%{$ \displaystyle \frac {d_g \big( v,U_v(d) \big)}{\underset {u\in S_{U{v(d)^{( d)}}}} {\mathrm{max}} d_g \big( u,U_v (d)\big)} $}

!!!!Conditions

If {$ U_v(d) = \varnothing \therefore $} the formula is undefined.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. Inner Border to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Inner Border to Superobject''

This feature is calculated by dividing the sum of the border shared with other image objects, which have the same superobject, by the total border of the image object. If the relative inner border to the superobject is 1, the image object of concern is not situated on the border of its superobject. Use this feature to describe how much of an image object is situated at the edge of its superobject.

!!!!Parameters

*{$ N_u(v) $} are neighbors of {$ v $} that exist within the superobject {$ N_u(v): \{ u \in N_v:U_u(d) - U_v(d) \} $}

*{$ b_v $} is the image object border length

!!!!Expression

%left%{$ \displaystyle \frac {\sum_ { u \in N_U( v) } b( v,m)}{b_v} $}

Figure 100: Relative inner border of an image object {$ v $} to superobject {$ u $}.

!!!!Conditions

If the feature range is 0 then {$ v=U_v(d) $}

If the feature range is 1 then {$ v $} is an inner object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Distance to Superobject Center

%gray%''Object Features > Geometry > To Superobject > Distance to Superobject Center''

The distance of an image object's center to the center of its superobject. This might not be the shortest distance between the two points, since the way to the center of the superobject must be within the borders of the superobject.

!!!!Expression

%left%{$ \displaystyle d_g( v,U_v(d)) $} is the distance of {$ v $} to the center of gravity of the superobject {$ U_v(d) $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, sx \times sy] $}

!!!Elliptic Distance to Superobject Center

%gray%''Object Features > Geometry > To Superobject > Elliptic Distance to Superobject Center''

Distance of objects to the center of the superobject.

!!!!Expression

%left%{$ \displaystyle d_e( v,U_v(d)) $}

Figure 101: Distance between the distance from the superobject's center to the center of a sub-objectt.

!!!!Feature Value Range

Typically {$ [0, 5] $}

!!!Is End of Superobject

%gray%''Object Features > Geometry > To Superobject > Is End of Superobject''

This feature is true for two image objects {$ a $} and {$ b $} if following conditions are true:

*{$ a $} and {$ b $} are sub-objects of the same superobject.

*{$ a $} is the image object with the maximum distance to the superobject.

*{$ b $} is the image object with the maximum distance to {$ a $}.

!!!!Editable Parameter

*Level Distance

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Is Center of Superobject

%gray%''Object Features > Geometry > To Superobject > Is Center of Superobject''

This feature is true if the image object is the center of its superobject.

!!!!Editable Parameter

*Level Distance

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. X Position to Superobject

%gray%''Object Features > Geometry > To Superobject Rel. X Position to Superobject''

This feature returns the relative{$ x $}position of an image object with regard to its superobject, based on the centers of gravity of both objects.

!!!!Editable Parameters

*Level Distance `- the upward distance of image object levels in the image object hierarchy between the image object and the superobject.

!!!!Expression

%left%{$ \displaystyle \Delta x = x_{CG} $} of current image object {$ - x_{CG} $} of superobject (where {$ x_{CG} $} is the center of gravity)

!!!!Feature Value Range

%left%{$ \displaystyle - \frac {\mathrm{scene \ width}}{2} + \frac {\mathrm{scene \ width}}{2} $}

!!!Rel. Y Position to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Y Position to Superobject''

This feature returns the relative{$ y $}position of an image object with regard to its superobject, based on the centers of gravity of both objects.

!!!!Editable Parameter

*Level Distance: Upward distance of image object levels in the image object hierarchy between the image object and the superobject.

!!!!Expression

%left%{$ \displaystyle \Delta y = y_{CG} $} of current image object {$ - y_{CG} $} of superobject (where {$ y_{CG} $} is the center of gravity)

!!!!Feature Value Range

%left%{$ \displaystyle - \frac {\mathrm{scene \ height}}{2} + \frac {\mathrm{scene \ height}}{2} $}

!!Based on Polygons

%gray%''Object Features > Geometry > Based on Polygons''

The polygon features provided by Definiens Developer XD 1.2.5 are based on the vectorization of the pixels that form an image object.

Figure 102: Raster image object (black area) with its polygon object (red lines) after vectorization.

!!!Edges Longer Than

%gray%''Object Features > Geometry > Based on Polygons > Edges Longer Than''

!!!!Editable Parameters

*Minimum Length

!!!Number of Right Angles With Edges Longer Than

%gray%''Object Features > Geometry > Based on Polygons > Number of Right Angles with Edges Longer Than''

The number of right angles that have at least one side edge longer than a given threshold.

!!!!Editable Parameters

*Minimum length

Figure 103: A polygon with one rectangular angle.

!!!Area (Excluding Inner Polygons)

%gray%''Object Features > Geometry > Based on Polygons > Area (Excluding Inner Polygons)''

The Area (Excluding Inner Polygons) feature calculates the area of a polygon based on Green's Theorem in a plane. In contrast to the Area (Including Inner Polygons) feature, the feature value does not include the areas of any existing inner polygons.

!!!!Parameters

*{$ (x_i, y_i), i = 0, \dots , n, $} with {$ x_o = x_n $} and {$ y_o = y_n $} as the given points

*{$ a_i = x_iy_{i+1} - x_{i+1}y_i $}

!!!!Expression

%left%{$ \displaystyle \frac {1}{2}\sum_{i=0}^{n-1} a_i $}

Figure 104: A polygon with an inner polygon that is not included in the feature value.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {scene \ size}}] $}

!!!Area (Including Inner Polygons)

%gray%''Object Features > Geometry > Based on Polygons > Area (Including Inner Polygons)''

The Area (Excluding Inner Polygons) feature calculates the area of a polygon based on Green's Theorem in a plane. Different to the Area (Excluding Inner Polygons) feature, the feature value includes the areas of any existing inner polygons (for instance the single polygon formed in the center of a donut-shaped object).

Figure 105: A polygon with an inner polygon that is included in the feature value.

!!!Average Length of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > average Length of Edges (Polygon)''

The average length of all edges in a polygon.

!!!!Parameters

*{$ X_i $} is the length of edge {$ i $}

*{$ n $} is the total number of edges

!!!!Expression

%left%{$ \displaystyle \mathrm{Average} = \frac {\displaystyle \sum_{i=1}^{n} X_{i}} {n} $}

!!!Compactness (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Compactness (Polygon)''

The ratio of the area of a polygon to the area of a circle with the same perimeter.

!!!!Parameters

*Area

*Perimeter

!!!!Expression

%left%{$ \displaystyle \frac {4 \times \pi \times \mathrm{Area}} {\mathrm{Perimeter}^2} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {1 \ for \ a \ circle}}] $}

!!!Length of Longest Edge (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Length of Longest Edge (Polygon)''

The length of the longest edge of a polygon.

!!!Number of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Number of Edges (Polygon)''

The number of edges of a polygon.

!!!Number of Inner Objects (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Number of Inner Objects (Polygon)''

The number of inner polygons that are completely surrounded by a selected outer polygon.

!!!Perimeter (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Perimeter (Polygon)''

The sum of the lengths of all the edges of a polygon.

!!!Polygon Self-Intersection (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Polygon Self-Intersection (Polygon)''

The Polygon Self-Intersection (Polygon) feature allows the identification of a rare arrangement of image objects, leading to a polygon self-intersection when exported as a polygon vector file.

This feature enables you to identify the affected image objects and take measures To avoid this self-intersection. All image objects with a value of 1 will cause a polygon self-intersection when exported to a shapefile.

Figure 106: This type of image object leads to a self-intersection at the circled point.

To avoid the self-intersection, the enclosed image object needs to be merged with the enclosing image object.

(:div class=frame:)

->'''TIP: '''Use the Image Object Fusion algorithm to remove polygon intersections. To do so, set the domain to all image objects with a value larger than 0 for the polygon intersection feature. In the algorithm parameter, set the Fitting Function Threshold to Polygon Self-Intersection (Polygon) feature to zero and in the Weighted Sum group, set Target Value Factor to 1. This will merge all image objects with a value of 1 for the Polygon Self-Intersection (Polygon) feature, so that the resulting image object will not include a self-intersection.

(:divend:)

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Std. Dev. of Length of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Stddev of Length of Edges (Polygon)''

The Std. Dev. of Length of Edges (Polygon) feature measures how the lengths of edges deviate from their mean value.

!!!!Parameters

*{$ x_i $} is the length of edge {$ i $}

*{$ \bar X $} is the mean value of all lengths

*{$ n $} is the total number of edges

!!!!Expression

%left%{$ \displaystyle \sqrt \frac {\displaystyle \sum_{i=1}^{n} {(x_i-\bar x)^2}} {n} $}

!!Based on Skeletons

%gray%''Object Features > Geometry > Based on Skeletons''

For the better understanding of the following descriptions, the skeleton is structured in a main line and subordinate branches. A node is a mid-point of the triangles created by the Delaunay triangulation.

!!!Number of Segments of Order

%gray%''Object Features > Geometry > Based on Skeletons > Number of Segments of Order''

The number of line segments of branches of an object that are of a given order. Note that only segments that do not belong to a lower order are counted

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Branches of Order

%gray%''Object Features > Geometry > Based on Skeletons > Number of Branches of Order''

The number of branches of an object that are of a given order.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Average Length of Branches of Order

%gray%''Object Features > Geometry > Based on Skeletons > average Length of Branches of Order''

The average length of branches of an object that are of a given order. The length of the branch of the selected order is measured from the intersect point of the whole branch and the main line to the end of the branch.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Branches of Length

%gray%''Object Features > Geometry > Based on Skeletons > Number of Branches of Length''

The number of branches of an object that are of a special length up to a selected order. All ends of branches are counted up to the selected order.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

*Minimum length

*Maximum length

!!!!Feature Value Range

[0; depending on shape of objects]

!!!Average Branch Length

%gray%''Object Features > Geometry > Based on Skeletons > Average Branch Length''

The average length of all branches of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Avrg. Area Represented by Segments

%gray%''Object Features > Geometry > Based on Skeletons > Avrg. Area Represented by Segments''

The average area of all triangles created by a Delaunay triangulation.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Curvature/Length (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Curvature/Length (only main line)''

The length-to-curvature ratio of the main line of an object. The curvature is the sum of all changes in direction of the main line. Changes in direction are expressed by the acute angle a in which sections of the main line, built by the connection between the nodes, cross each other.

Figure 107: The main line (green) connects the mid-points of triagles (black and blue) created by a Delaunay triangulation of the objects' shape (not depicted).

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Degree of Skeleton Branching

%gray%''Object Features > Geometry > Based on Skeletons > Degree of Skeleton Branching''

The highest order of branching in an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length of Main Line (No Cycles)

%gray%''Object Features > Geometry > Based on Skeletons > Length of Main Line (No Cycles)''

The sum of all distances between the nodes of the main line of an object. If an object contains an island polygon `- a polygon derived from the inner borders of an image object `- it is ignored and the main line may cross it (no cycles). This is different to the Length of Main Line (regarding cycles) feature where the main line goes around the island polygon. This feature does not visualize skeletons.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length of Main Line (Regarding Cycles)

%gray%''Object Features > Geometry > Based on Skeletons > Length of Main Line (regarding cycles)''

The sum of all distances between the nodes of the main line of an object. If an object contains an island polygon `- a polygon derived from the inner borders of an image object `- the main line is calculated so as not to cross it (Regarding Cycles).

In contrast to the Length of Main Line (No Cycles) feature, the skeletons are visualized.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length/Width (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons >Length/Width (Only Main Line)''

The length-to-width ratio of the main line of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Maximum Branch Length

%gray%''Object Features > Geometry > Based on Skeletons > Maximum Branch Length''

The length of the longest branch of an object. It is measured from the intersect point of the branch and the main line to the end of the branch.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Segments

%gray%''Object Features > Geometry > Based on Skeletons > Number of Segments''

The number of all segments of the main line and the branches of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Stddev Curvature (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Stddev Curvature (Only Main Line)''

The standard deviation of the curvature is the result of the standard deviation of the changes in direction of the main line. Changes in direction are expressed by the acute angle in which sections of the mainline, built by the connection between the nodes, cross each other.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Stddev of Area Represented by Segments

%gray%''Object Features > Geometry > Based on Skeletons > Stddev. of Area Represented by Segments''

The standard deviation of all triangles created by the Delaunay triangulation.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Width (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Width (Only Main Line)''

The width of an object based on the height of triangles created by a Delaunay triangulation. It is calculated by the average height{$ h $}of all triangles crossed by the main line.

Figure 108: Height {$ h $} of an triangle that is crossed by the main line.

An exception is triangles where the height {$ h $} does not cross one of the sides of the triangle. In this case, the nearest side {$ s $} is used to define the height.

Figure 109: Height of an triangle that is crossed by the main line. In this case the side {$ s $} defines the height.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}

to:

%left%{$ [0, {\mathrm {number \ of \ slices \ in \ map }} -1] $}

!!Is Object in Region

%gray%''Object Features > Position > Is Object in Region''

The Is Object In Region feature checks if an image object is located in a given region. If this is true, the feature value is 1 (= true), otherwise it is 0 (= false).

!!!Editable Parameters

* Region

!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!Is Object in Region

%gray%''Object Features > Position > Is Object in Region''

The Is Object In Region feature checks if an image object is located in a given region. If this is true, the feature value is 1 (= true), otherwise it is 0 (= false).

!!!Editable Parameters

* Region

!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

Changed lines 1-22 from:

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those showing

:Choose the print style:Readers can customise the look of the printed output

=<{

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

(:typeset-trail toc=on colorlinks=on:)

The site is running {$Version}

to:

%gray%''Object Features > Geometry''

Geometry features are based on an image object's shape, calculated from the pixels that form it. Because images are raster-based, geometry features may be rotation variant: after image objects are rotated, different feature values may arise.

!!Extent

%gray%''Object Features > Geometry > Extent''

!!!Area

%gray%''Object Features > Geometry > Extent > Area''

The number of pixels forming an image object. If unit information is A_vailable, the number of pixels can be converted into a measurement.

In scenes that provide no unit information, the area of a single pixel is 1 and the area is simply the number of pixels that form it. If the image data provides unit information, the area can be multiplied using the appropriate factor.

!!!!Parameters

*{$ A_v $} is the area of image object {$ v $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ u $} is the pixel size in co-ordinate system units. If the unit is a pixel, then {$ u=1. $}

!!!!Expression

%left%{$ \displaystyle A_v= \#P_v \times u^2 $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \mathrm {scene \ size}] $}

!!!Border Length [for 2D Image Objects]

%gray%''Object Features > Geometry > Extent > Border Length''

The border length of an image object is defined as the sum of edges of the image object shared with other image objects, or situated on the edge of the entire scene. For a torus `- and other image objects with holes `- the border length is the sum of the inner and outer borders.

!!!!Parameters

*{$ b_v $} is the border length of image object

*{$ b_o $} is the length of outer border

*{$ b_i $} is the length of inner border

!!!!Expression

%left%{$ \displaystyle b_v = b_o+b_i $}

Figure 84: Border length of an image object {$ v $} or between two objects v, u.

Figure 85: Inner and outer border length of a torus image object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Border Length [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > Border Length''

The border length of a 3D image object is the sum of border lengths of all image object slices, multiplied by the spatial distance between them.

Image object slices are 2D pieces of the image object in each slice. The border length of an image object slice is defined as the sum of edges shared with other image object pieces, or are situated on the edge of the entire slice. For a torus and other image objects with holes the border length sums the inner and outer border.

!!!!Parameters

* {$ b_v $} is the border length of image object {$ v $}

* {$ b_v (\mathrm {slice}) $} is the border length of image object slice

* {$ b_v(z) $} is the border length of image object in z-direction

* {$ u_{\mathrm {slices}} $} is the spatial distance between slices in the co-ordinate system unit

* {$ b_o $} is the length of the outer border

* {$ b_i $} is the length of the inner border

!!!!Expression

%left%{$ \displaystyle b_v = \Bigg(\sum_{n=1}^{\# (\mathrm {slices})} b_v (\mathrm {slice}) \Bigg) \times u_{\mathrm {slices}} + b_v (z) $}

Figure 86: Border length of an image object {$ v $} or between two objects v, u.

Figure 87: Inner and outer border length of a torus image object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length [for 2D Image Objects]

%gray%''Object Features > Geometry > Extent > Length''

The length of a 2D image object is calculated using the length-to-width ratio.

!!!!Parameters

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ \gamma_v $} is the length-width ratio of an image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \sqrt {\# P_v \cdot \gamma_v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > Length''

The length of an image object is the largest of three eigenvalues of a rectangular 3D space that is defined by the same volume, and same proportions of eigenvalues, as the image object. The length of an image object can be smaller or equal than the largest of dimensions of the smallest rectangular 3D space enclosing the image object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length/Thickness

%gray%''Object Features > Geometry > Extent > Length/Thickness''

The length-to-thickness ratio of an image object.

!!!!Parameters

*Length of the image object

*Thickness of the image object

!!!!Expression

%left%{$ \displaystyle \frac {\mathrm {Length}}{\mathrm {Thickness}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length/Width [for 2D Image Objects]

%gray%''Object Features > Geometry > Extent > Length/Width''

The length-to-width ratio of an image object. There are two methods to approximate this:

1. The ratio of length to width is identical to the ratio of the eigenvalues of the covariance matrix, with the larger eigenvalue being the numerator of the fraction:

%left%{$ \displaystyle \gamma_v^{EV} = \frac {\lambda_1 (v)} {\lambda_2(v)} $}

2. The ratio of length to width can also be approximated using the bounding box:

%left%{$ \displaystyle \gamma_v^{BB} = \frac {\big(k_v^{bb'} \big)^2} {\#P_v} $}

Both calculations are compared; the smaller of both results is returned as the feature value.

!!!!Parameters

* {$ \# P_v $} is the Size of a set of pixels of an image object {$ v $}

* {$ \lambda_1 \lambda_2 $} are eigenvalues

* {$ \gamma_v^ {\mathrm {EV}} $} is the ratio length of {$ v $} of the eigenvalues

* {$ \gamma_v^ {\mathrm {BB}} $} is the ratio length of {$ v $} of the bounding box

* {$ \gamma_v $} is the length-width ratio of an image object {$ v $}

* {$ k_v^ {\mathrm {BB'}} $}

* {$ h_v^ {\mathrm {BB'}} $}

* {$ a $} is the bounding box fill rate

* {$ \#Pxl $}

* {$ h $}

* {$ w $} is the image layer weight

*{$ k_v^{bb^1} = \sqrt{ {(k_v^{bb'})^2} + (1-a)(h_v^{bb'})^2} $}

*{$ a = \frac {\#P_v}{k_v^{bb'} - h_v^{bb'}} $}

*{$ k\cdot h = \# P_v \Rightarrow k=\frac {\# P_v} {w}, h = \frac {\# P_v} {k} \Rightarrow \frac {k} {w} = \frac {k^2} {\# P_{xl}} = \frac {\# P_{xl}} {w^2} $}

!!!!Expression

%left%{$ \displaystyle \gamma_v = \mathrm{min} \gamma_v^{EV}, \mathrm{max} \gamma_v^{BB} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length/Width [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > Length/Width''

The length-to-width ratio of an image object.

!!!!Parameters

*Length of the image object

*Width of the image object

!!!!Expression

%left%{$ \displaystyle \frac {\mathrm {Length}}{\mathrm {Width}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Number of Pixels

%gray%''Object Features > Geometry > Extent > Number of Pixels''

The number of pixels forming an image object. Unit information is not taken into account.

!!!!Parameters

* {$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \mathrm {scene \ size}] $}

!!!Thickness

%gray%''Object Features > Geometry > Extent > Thickness''

The thickness of an image object is the smallest of three eigenvalues of a rectangular 3D space with the same volume as the image object and the same proportions of eigenvalues as the image object. The thickness of an image object can be smaller or equal to the smallest of dimensions of the smallest rectangular 3D space enclosing the image object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Volume

%gray%''Object Features > Geometry > Extent > Volume''

The number of voxels forming an image object rescaled by using unit information for{$ x $}and{$ y $}co-ordinates and distance information between slices.

!!!!Parameters

* {$ V_v $} is the volume of image object {$ v $}

* {$ \# P_v $} is the total number of voxels contained in {$ P_v $}

* {$ u $} is the size of a slice pixel in the co-ordinate system unit

* {$ u_{\mathrm {slices}} $} is the spatial distance between slices in the co-ordinate system unit

!!!!Expression

%left%{$ \displaystyle V_v = \# P_v \times u^2 \times u_{\mathrm {slices}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \mathrm {scene \ size}] $}

!!!Width [for 2D Image Objects]

%gray%''Object Features > Geometry > Extent > Width''

The width of an image object is calculated using the length-to-width ratio.

!!!!Parameters

* {$ \# P_v $} is the total number of pixels contained in {$ P_v $}

* {$ \gamma_v $} is the length/width ratio of an image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \frac {\# P_v} {\gamma _v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Width [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > Width''

The width of an image object is the mid-point of three eigenvalues of a rectangular 3D space with the same volume as the image object and the same proportions of eigenvalues as the image object. The width of an image object can be smaller or equal to the mid-point of dimensions of the smallest rectangular 3D space enclosing the image object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!Shape

%gray%''Object Features > Geometry > Shape''

!!!Asymmetry [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Asymmetry''

The Asymmetry feature describes the relative length of an image object, compared to a regular polygon. An ellipse is approximated around a given image object, which can be expressed by the ratio of the lengths of its minor and the major axes. The feature value increases with this asymmetry.

(:div class=frame:)

->'''NOTE:'''We recommend that you use the Length/Width ratio because it is more accurate.

(:divend:)

!!!!Parameters

*Var X is the variance of X

*Var Y is the variance of Y

!!!!Expression

%left%{$ \displaystyle \frac{2 \sqrt {\frac {1}{4} (\mathrm{Var}X + \mathrm{Var}Y)^2 +(\mathrm{Var}XY)^2 - \mathrm{Var}X \cdot \mathrm{Var}Y}}{\textrm{Var}X + \mathrm{Var}Y} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Asymmetry [for 3D Image Objects]

%gray%''Object Features > Geometry >Shape > Asymmetry''

The Asymmetry feature describes the relative length of an image object, in the same manner as 2D image objects. The asymmetry is calculated from the ratio between the smallest and largest eigenvalues of the image object.

!!!!Parameters

*{$ \lambda_{\mathrm {min}} $} is the minimal eigenvalue

*{$ \lambda_{\mathrm {max}} $} is the maximal eigenvalue

!!!!Expression

%left%{$ \displaystyle 1- \sqrt \frac {\lambda_{\mathrm{min}}} {\lambda_{\mathrm{max}}} $}

Figure 88: Asymmetry based on maximal and minimal eigenvalues.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Border Index

%gray%''Object Features > Geometry >Shape > Border Index''

The Border Index feature describes how jagged an image object is; the more jagged, the higher its border index. This feature is similar to the Shape Index feature, but the Border Index feature uses a rectangular approximation instead of a square. The smallest rectangle enclosing the image object is created and the border index is calculated as the ratio between the border lengths of the image object and the smallest enclosing rectangle.

!!!!Parameters

*{$ b_v $} is the image object border length

*{$ l_v $} is the length of an image object {$ v $}

*{$ w_v $} is the width of an image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \frac {b_v}{2(l_v + w_v)} $} [[<<]]

Figure 89: Border index of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 1 = ideal.

!!!Compactness [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Compactness''

The Compactness feature describes how compact an image object is. It is similar to Border Index, but is based on area. However, the more compact an image object is, the smaller its border appears. The compactness of an image object is the product of the length and the width, divided by the number of pixels.

!!!!Parameters

*{$ l_v $} is the length of an image object {$ v $}

*{$ w_v $} is the width of an image object {$ v $}

* {$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \frac {2\lambda_1 \times 2\lambda_2 \times 2\lambda_3}{V_v} $}

Figure 90: Compactness of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 1 = ideal.

!!!Compactness [for 3D Image Objects]

%gray%''Object Features > Geometry >Shape > Compactness''

Compactness describes how compact a 3D image object is. Appropriately scaled eigenvectors of an image object's covariance matrix provide a rough figure of the object's extent in three dimensions.

A figure for the compactness of a 3D image object is calculated by a scaled product of its three eigenvalues {$ (2 \times \lambda_1, 2 \times \lambda_2, 2 \times \lambda_3) $} divided by the number of its pixel/voxel. We include a factor of 2 with each eigenvalue, since {$ \lambda_i \times $} eigenvectors represent otherwise half axes of an ellipsoid defined by its covariance matrix. The chosen approach therefore provides an estimate of a cuboid occupied by the object.

!!!!Parameters

*{$ \lambda_1 $} is eigenvalue 1 of a 3D image object {$ v $}

*{$ \lambda_2 $} is the eigenvalue 2 of a 3D image object {$ v $}

*{$ \lambda_3 $} is eigenvalue 3 of a 3D image object {$ v $}

*{$ V_v $} is the volume of image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \frac {2\lambda_1 \times 2\lambda_2 \times 2\lambda_3}{V_v} $}

Figure 91: Compactness of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 1 = ideal.

!!!Density [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Density''

The Density feature describes the distribution in space of the pixels of an image object. In Definiens Developer XD 1.2.5 the most "dense" shape is a square; the more an object is shaped like a filament, the lower its density.

The density is calculated by the number of pixels forming the image object divided by its approximated radius, based on the covariance matrix.

!!!!Parameters

* {$ \sqrt {\#P_v} $} is the diameter of a square object with {$ \# P_v $} pixels

* {$ \sqrt {VarX + VarY} $} is the diameter of the ellipse

!!!!Expression

%left%{$ \displaystyle \frac {\sqrt {\# P_v}}{1+ \sqrt {VarX+VarY}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ image \ object}}] $}

!!!Density [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Density''

Using the same principle as Density [for 2D Image Objects], the most "dense" shape for a 3D object is a cube. The more filament-shaped an image object is, the lower its density. The value is calculated by dividing the edge of the volume of a fitted cuboid by the radius of a fitted sphere.

!!!!Parameters

*{$ V_v $} is the volume of image object {$ v $}

*{$ \sqrt[3]{V_v} $} is the edge of the volume fitted cuboid

*{$ \sqrt {\mathrm{Var}(X) + \mathrm{Var}(Y) + \mathrm{Var}(Z)} $} is the radius of the fitted sphere

!!!!Expression

%left%{$ \displaystyle \frac {\sqrt[3]{V_v}} {\sqrt {\mathrm{Var}(X) + \mathrm{Var}(Y) + \mathrm{Var}(Z)}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ image \ object}}] $}

!!!Elliptic Fit [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit''

The Elliptic Fit feature describes how well an image object fits into an ellipse of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on an ellipse with the same area as the selected image object. The proportions of the ellipse are equal to the length to the width of the image object. The area of the image object outside the ellipse is compared with the area inside the ellipse that is not filled by the image object.

!!!!Parameters

*{$ \varepsilon_v(x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

*{$ P_v $} is the set of pixels of an image object {$ v $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \varphi =2 \cdot \frac {\#\big \{(x,y)\epsilon P_v:\varepsilon_v(x,y)\leq 1\big \}}{\# P_v}-1 $}

Figure 92: Elliptic fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}; 1 = complete fitting, 0 = <50% fit.

!!!Elliptic Fit [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit''

The Elliptic Fit feature describes how well an image object fits into an ellipsoid of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on an ellipsoid with the same volume as the considered image object. The proportions of the ellipsoid are equal to the proportions of the length, width and thickness of the image object. The volume of the image object outside the ellipsoid is compared with the volume inside the ellipsoid that is not filled out with the image object.

!!!!Parameters

*{$ \varepsilon_v(x,y,z) $} is the elliptic distance at a pixel {$ {(x,y,z)} $}

*{$ P_v $} is the set of pixels of an image object {$ v $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \varphi =2 \cdot \frac {\#\big \{(x,y,z)\epsilon P_v:\varepsilon_v(x,y,z)\leq 1\big \}}{\# P_v}-1 $}

Figure 93: Elliptic fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0,1] $}; 1 = complete fitting, whereas 0 = < 50% voxels.

!!!Main Direction [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit > Main Direction''

The Main Direction feature of an image object is defined as the direction of the eigenvector belonging to the larger of the two eigenvalues, derived from the covariance matrix of the spatial distribution of the image object.

!!!!Parameters

* {$ Var X $} is the variance of {$ X $}

* {$ Var Y $} is the variance of {$ Y $}

* {$ \lambda_1 $} is the eigenvalue

!!!!Expression

%left%{$ \displaystyle \frac {180^{\circ}}{\pi}\mathrm{tan}^{-1}(\mathrm{Var}XY,\lambda_1-\mathrm{Var}Y) + {90^{\circ}} $}

Figure 94: The main direction is based on direction of the larger eigenvector.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 180] $}

!!!Main Direction [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Main Direction''

The Main Direction feature of a three-dimensional image object is computed as follows:

#For each (2D) image object slice, the centers of gravities are calculated.

#The co-ordinates of all centers of gravities a reused to calculate a line of best fit, according to the Weighted Least Square method.

#The angle a between the resulting line of best fit and the z-axis is returned as feature value.

Figure 95: The line of best fit (blue) calculated from centers of gravity of image object slices (light blue).

!!!!Feature Value Range

%left%{$ \displaystyle [0, 90] $}

!!!Radius of Largest Enclosed Ellipse [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Largest Enclosed Ellipse''

The Radius of Largest Enclosed Ellipse feature describes how similar an image object is to an ellipse. The calculation uses an ellipse with the same area as the object and based on the covariance matrix. This ellipse is scaled down until it is totally enclosed by the image object. The ratio of the radius of this largest enclosed ellipse to the radius of the original ellipse is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o) $}, where {$ (x_o,y_o) = min \ \varepsilon_v (x,y), (x,y) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Largest Enclosed Ellipse [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Largest Enclosed Ellipse''

The Radius of Largest Enclosed Ellipse feature describes how much the shape of an image object is similar to an ellipsoid.

The calculation is based on an ellipsoid with the same volume as the object and based on the covariance matrix. This ellipsoid is scaled down until it is totally enclosed by the image object. The ratio of the radius of this largest enclosed ellipsoid to the radius of the original ellipsoid is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y,z) $} is the elliptic distance at a pixel {$ (x,y,z) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o,z_o) $}, where {$ (x_o,y_o,z_o) = min \ \varepsilon_v (x,y,z), (x,y,z) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Smallest Enclosing Ellipse [for 2D Image Objects]

%gray%''Object Features > Geometry >Shape > Radius of Smallest Enclosing Ellipse''

The Radius of Smallest Enclosing Ellipse feature describes how much the shape of an image object is similar to an ellipse.

The calculation is based on an ellipse with the same area as the image object and based on the covariance matrix. This ellipse is enlarged until it encloses the image object in total. The ratio of the radius of this smallest enclosing ellipse to the radius of the original ellipse is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o) $}, where {$ (x_o,y_o) = max \ \varepsilon_v (x,y), (x,y) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Smallest Enclosing Ellipse [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Smallest Enclosing Ellipse''

The Radius of Smallest Enclosing Ellipse feature describes how much the shape of an image object is similar to an ellipsoid.

The calculation is based on an ellipsoid with the same volume as the image object and based on the covariance matrix. This ellipsoid is enlarged until it encloses the image object in total. The ratio of the radius of this smallest enclosing ellipsoid to the radius of the original ellipsoid is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y,z) $} is the elliptic distance at a pixel {$ (x,y,z) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o,z_o) $}, where {$ (x_o,y_o,z_o) = max \ \varepsilon_v (x,y,z), (x,y,z) \in \sigma P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Rectangular Fit [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Rectangular Fit''

The Rectangular Fit feature describes how well an image object fits into a rectangle of similar size and proportions. While 0 indicates no fit, 1 indicates for a complete fitting image object.

The calculation is based on a rectangle with the same area as the image object. The proportions of the rectangle are equal to the proportions of the length to width of the image object. The area of the image object outside the rectangle is compared with the area inside the rectangle.

!!!!Parameters

*{$ \rho_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \frac {\big \{\#(x,y)\epsilon P_v:\rho _v(x,y)\leq 1\big \}}{\#P_v} $}

Figure 96: Rectangular fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}; where 1 is a perfect rectangle.

!!!Rectangular Fit [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Rectangular Fit''

The Rectangular Fit feature describes how well an image object fits into a cuboid of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on a cuboid with the same volume as the considered image object. The proportions of the cuboid are equal to the proportions of the length to width to thickness of the image object. The volume of the image object outside the rectangle is compared with the volume inside the cuboid that is not filled out with the image object.

!!!!Parameters

*{$ \rho_v(x,y,z) $} is the rectangular distance at a pixel {$ (x,y,z) $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \frac {\big \{\#(x,y,z)\epsilon P_v:\rho _v(x,y,z)\leq 1\big \}}{\#P_v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $} ; 1 = complete fitting, whereas 0 = 0% fits inside the rectangular approximation.

!!!Roundness [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Roundness''

The Roundness feature describes how similar an image object is to an ellipse. It is calculated by the difference of the enclosing ellipse and the enclosed ellipse. The radius of the largest enclosed ellipse is subtracted from the radius of the smallest enclosing ellipse.

!!!!Parameters

*{$ \varepsilon_v^\mathrm{max} $} is the radius of the smallest enclosing ellipse

*{$ \varepsilon_v^\mathrm{min} $} is the radius of the largest enclosed ellipse

!!!!Expression

%left%{$ \displaystyle \varepsilon_v^\mathrm{max} - \varepsilon_v^\mathrm{min} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 0 = ideal.

!!!Roundness [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Roundness''

The Roundness feature describes how much the shape of an image object is similar to an ellipsoid. The more the shape of an image object is similar to an ellipsoid, the lower its roundness.

It is calculated by the difference of the enclosing ellipsoid and the enclosed ellipsoid. The radius of the largest enclosed ellipsoid is subtracted from the radius of the smallest enclosing ellipsoid.

!!!!Parameters

*{$ \varepsilon_v^\mathrm{max} $} is the radius of the smallest enclosing ellipsoid

*{$ \varepsilon_v^\mathrm{min} $} is the radius of the largest enclosed ellipsoid

!!!!Expression

%left%{$ \displaystyle \varepsilon_v^\mathrm{max} - \varepsilon_v^\mathrm{min} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 0 = ideal.

!!!Main Direction [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit > Main Direction''

The Main Direction feature of an image object is defined as the direction of the eigenvector belonging to the larger of the two eigenvalues, derived from the covariance matrix of the spatial distribution of the image object.

!!!!Parameters

* {$ VarX $} is the variance of {$ X $}

* {$ VarY $} is the variance of {$ Y $}

* {$ \lambda_1 $} is the eigenvalue

!!!!Expression

%left%{$ \displaystyle \frac {180^{\circ}}{\pi}\mathrm{tan}^{-1}(\mathrm{Var}XY,\lambda_1-\mathrm{Var}Y) + {90^{\circ}} $}

Equation 1: The main direction is based on the direction of the larger eigenvector

!!!!Feature Value Range

%left%{$ \displaystyle [0,180] $}

!!!Main Direction [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Main Direction''

The Main Direction feature of a three-dimensional image object is computed as follows:

#For each (2D) image object slice, the centers of gravities are calculated.

#The co-ordinates of all centers of gravities a reused to calculate a line of best fit, according to the Weighted Least Square method.

#The angle a between the resulting line of best fit and the {$ z $}-axis is returned as feature value.

Figure 97: The line of best fit (blue) calculated from centers of gravity of image object slices (light blue).

!!!!Feature Value Range

%left%{$ \displaystyle [0,90] $}

!!!Shape Index [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Shape Index''

The Shape index describes the smoothness of an image object border. The smoother the border of an image object is, the lower its shape index. It is calculated from the Border Length feature of the image object divided by four times the square root of its area.

!!!!Parameters

*{$ b_v $} is the image object border length

*{$ \sqrt[4] {\#P_v} $} is the border of square with area {$ \# P_v $}

!!!!Expression

%left%{$ \displaystyle \frac {b_v}{\sqrt[4]{\# P_v}} $}

Figure 98: Shape index of an image object {$ v $}

!!!!Feature Value Range

%left%{$ \displaystyle [1, \infty] $}; 1 = ideal.

!!!Shape Index [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Shape Index''

The Shape Index describes the smoothness of the surface of an image object. The smoother the surface of an image object is, the lower its shape index. It is calculated from the Border Length feature of the image object divided by four times the square root of its area.

!!!!Parameters

*{$ b_v $} is the image object border length

*{$ V_v $} is the volume of image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \frac {b_v}{V_v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [1, \infty] $}; 1 = ideal.

!!To Superobject

%gray%''Object Features > Geometry > To Superobject''

Use the To Superobject feature to describe an image object by its shape and relationship to one of its superobjects, where appropriate. Editing the feature distance determines which superobject is referred to. When working with thematic layers these features can be of interest.

!!!Rel. Area to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Area to Superobject''

The area of an image object divided by the area of its superobject. If the feature value is 1, the image object is identical to its superobject. Use this feature to describe an image object in terms of the amount of area it shares with its superobject.

!!!!Parameters

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ \# P_{Uv(d)} $} is the the size of the superobject of {$ v $} in the image object level of the level distance {$ d $}

!!!!Expression

%left%{$ \displaystyle \frac {\# P_v}{\# P_{Uv(d)}} $}

!!!!Conditions

If {$ U_v(d) = \varnothing \therefore $} the formula is undefined.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. Rad. Position to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Rad. Position to Superobject''

This value is calculated by dividing the distance between the center of a selected image object and the center of its superobject, by the distance of the center of the most distant image object (which has the same superobject). Use this feature to describe an image object by its position relative to the center of its superobject.

!!!!Parameters

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ \#P_{Uv( d)} $} is the the size of the superobject of an image object {$ v $}

*{$ d_g( v,Uv( d)) $} is the distance of {$ v $} to the center of gravity of the superobject {$ U_v( d) $}

!!!!Expression

Figure 99: Relative radial position to superobject.

%left%{$ \displaystyle \frac {d_g \big( v,U_v(d) \big)}{\underset {u\in S_{U{v(d)^{( d)}}}} {\mathrm{max}} d_g \big( u,U_v (d)\big)} $}

!!!!Conditions

If {$ U_v(d) = \varnothing \therefore $} the formula is undefined.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. Inner Border to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Inner Border to Superobject''

This feature is calculated by dividing the sum of the border shared with other image objects, which have the same superobject, by the total border of the image object. If the relative inner border to the superobject is 1, the image object of concern is not situated on the border of its superobject. Use this feature to describe how much of an image object is situated at the edge of its superobject.

!!!!Parameters

*{$ N_u(v) $} are neighbors of {$ v $} that exist within the superobject {$ N_u(v): \{ u \in N_v:U_u(d) - U_v(d) \} $}

*{$ b_v $} is the image object border length

!!!!Expression

%left%{$ \displaystyle \frac {\sum_ { u \in N_U( v) } b( v,m)}{b_v} $}

Figure 100: Relative inner border of an image object {$ v $} to superobject {$ u $}.

!!!!Conditions

If the feature range is 0 then {$ v=U_v(d) $}

If the feature range is 1 then {$ v $} is an inner object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Distance to Superobject Center

%gray%''Object Features > Geometry > To Superobject > Distance to Superobject Center''

The distance of an image object's center to the center of its superobject. This might not be the shortest distance between the two points, since the way to the center of the superobject must be within the borders of the superobject.

!!!!Expression

%left%{$ \displaystyle d_g( v,U_v(d)) $} is the distance of {$ v $} to the center of gravity of the superobject {$ U_v(d) $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, sx \times sy] $}

!!!Elliptic Distance to Superobject Center

%gray%''Object Features > Geometry > To Superobject > Elliptic Distance to Superobject Center''

Distance of objects to the center of the superobject.

!!!!Expression

%left%{$ \displaystyle d_e( v,U_v(d)) $}

Figure 101: Distance between the distance from the superobject's center to the center of a sub-objectt.

!!!!Feature Value Range

Typically {$ [0, 5] $}

!!!Is End of Superobject

%gray%''Object Features > Geometry > To Superobject > Is End of Superobject''

This feature is true for two image objects {$ a $} and {$ b $} if following conditions are true:

*{$ a $} and {$ b $} are sub-objects of the same superobject.

*{$ a $} is the image object with the maximum distance to the superobject.

*{$ b $} is the image object with the maximum distance to {$ a $}.

!!!!Editable Parameter

*Level Distance

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Is Center of Superobject

%gray%''Object Features > Geometry > To Superobject > Is Center of Superobject''

This feature is true if the image object is the center of its superobject.

!!!!Editable Parameter

*Level Distance

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. X Position to Superobject

%gray%''Object Features > Geometry > To Superobject Rel. X Position to Superobject''

This feature returns the relative{$ x $}position of an image object with regard to its superobject, based on the centers of gravity of both objects.

!!!!Editable Parameters

*Level Distance `- the upward distance of image object levels in the image object hierarchy between the image object and the superobject.

!!!!Expression

%left%{$ \displaystyle \Delta x = x_{CG} $} of current image object {$ - x_{CG} $} of superobject (where {$ x_{CG} $} is the center of gravity)

!!!!Feature Value Range

%left%{$ \displaystyle - \frac {\mathrm{scene \ width}}{2} + \frac {\mathrm{scene \ width}}{2} $}

!!!Rel. Y Position to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Y Position to Superobject''

This feature returns the relative{$ y $}position of an image object with regard to its superobject, based on the centers of gravity of both objects.

!!!!Editable Parameter

*Level Distance: Upward distance of image object levels in the image object hierarchy between the image object and the superobject.

!!!!Expression

%left%{$ \displaystyle \Delta y = y_{CG} $} of current image object {$ - y_{CG} $} of superobject (where {$ y_{CG} $} is the center of gravity)

!!!!Feature Value Range

%left%{$ \displaystyle - \frac {\mathrm{scene \ height}}{2} + \frac {\mathrm{scene \ height}}{2} $}

!!Based on Polygons

%gray%''Object Features > Geometry > Based on Polygons''

The polygon features provided by Definiens Developer XD 1.2.5 are based on the vectorization of the pixels that form an image object.

Figure 102: Raster image object (black area) with its polygon object (red lines) after vectorization.

!!!Edges Longer Than

%gray%''Object Features > Geometry > Based on Polygons > Edges Longer Than''

!!!!Editable Parameters

*Minimum Length

!!!Number of Right Angles With Edges Longer Than

%gray%''Object Features > Geometry > Based on Polygons > Number of Right Angles with Edges Longer Than''

The number of right angles that have at least one side edge longer than a given threshold.

!!!!Editable Parameters

*Minimum length

Figure 103: A polygon with one rectangular angle.

!!!Area (Excluding Inner Polygons)

%gray%''Object Features > Geometry > Based on Polygons > Area (Excluding Inner Polygons)''

The Area (Excluding Inner Polygons) feature calculates the area of a polygon based on Green's Theorem in a plane. In contrast to the Area (Including Inner Polygons) feature, the feature value does not include the areas of any existing inner polygons.

!!!!Parameters

*{$ (x_i, y_i), i = 0, \dots , n, $} with {$ x_o = x_n $} and {$ y_o = y_n $} as the given points

*{$ a_i = x_iy_{i+1} - x_{i+1}y_i $}

!!!!Expression

%left%{$ \displaystyle \frac {1}{2}\sum_{i=0}^{n-1} a_i $}

Figure 104: A polygon with an inner polygon that is not included in the feature value.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {scene \ size}}] $}

!!!Area (Including Inner Polygons)

%gray%''Object Features > Geometry > Based on Polygons > Area (Including Inner Polygons)''

The Area (Excluding Inner Polygons) feature calculates the area of a polygon based on Green's Theorem in a plane. Different to the Area (Excluding Inner Polygons) feature, the feature value includes the areas of any existing inner polygons (for instance the single polygon formed in the center of a donut-shaped object).

Figure 105: A polygon with an inner polygon that is included in the feature value.

!!!Average Length of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > average Length of Edges (Polygon)''

The average length of all edges in a polygon.

!!!!Parameters

*{$ X_i $} is the length of edge {$ i $}

*{$ n $} is the total number of edges

!!!!Expression

%left%{$ \displaystyle \mathrm{Average} = \frac {\displaystyle \sum_{i=1}^{n} X_{i}} {n} $}

!!!Compactness (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Compactness (Polygon)''

The ratio of the area of a polygon to the area of a circle with the same perimeter.

!!!!Parameters

*Area

*Perimeter

!!!!Expression

%left%{$ \displaystyle \frac {4 \times \pi \times \mathrm{Area}} {\mathrm{Perimeter}^2} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {1 \ for \ a \ circle}}] $}

!!!Length of Longest Edge (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Length of Longest Edge (Polygon)''

The length of the longest edge of a polygon.

!!!Number of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Number of Edges (Polygon)''

The number of edges of a polygon.

!!!Number of Inner Objects (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Number of Inner Objects (Polygon)''

The number of inner polygons that are completely surrounded by a selected outer polygon.

!!!Perimeter (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Perimeter (Polygon)''

The sum of the lengths of all the edges of a polygon.

!!!Polygon Self-Intersection (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Polygon Self-Intersection (Polygon)''

The Polygon Self-Intersection (Polygon) feature allows the identification of a rare arrangement of image objects, leading to a polygon self-intersection when exported as a polygon vector file.

This feature enables you to identify the affected image objects and take measures To avoid this self-intersection. All image objects with a value of 1 will cause a polygon self-intersection when exported to a shapefile.

Figure 106: This type of image object leads to a self-intersection at the circled point.

To avoid the self-intersection, the enclosed image object needs to be merged with the enclosing image object.

(:div class=frame:)

->'''TIP: '''Use the Image Object Fusion algorithm to remove polygon intersections. To do so, set the domain to all image objects with a value larger than 0 for the polygon intersection feature. In the algorithm parameter, set the Fitting Function Threshold to Polygon Self-Intersection (Polygon) feature to zero and in the Weighted Sum group, set Target Value Factor to 1. This will merge all image objects with a value of 1 for the Polygon Self-Intersection (Polygon) feature, so that the resulting image object will not include a self-intersection.

(:divend:)

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Std. Dev. of Length of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Stddev of Length of Edges (Polygon)''

The Std. Dev. of Length of Edges (Polygon) feature measures how the lengths of edges deviate from their mean value.

!!!!Parameters

*{$ x_i $} is the length of edge {$ i $}

*{$ \bar X $} is the mean value of all lengths

*{$ n $} is the total number of edges

!!!!Expression

%left%{$ \displaystyle \sqrt \frac {\displaystyle \sum_{i=1}^{n} {(x_i-\bar x)^2}} {n} $}

!!Based on Skeletons

%gray%''Object Features > Geometry > Based on Skeletons''

For the better understanding of the following descriptions, the skeleton is structured in a main line and subordinate branches. A node is a mid-point of the triangles created by the Delaunay triangulation.

!!!Number of Segments of Order

%gray%''Object Features > Geometry > Based on Skeletons > Number of Segments of Order''

The number of line segments of branches of an object that are of a given order. Note that only segments that do not belong to a lower order are counted

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Branches of Order

%gray%''Object Features > Geometry > Based on Skeletons > Number of Branches of Order''

The number of branches of an object that are of a given order.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Average Length of Branches of Order

%gray%''Object Features > Geometry > Based on Skeletons > average Length of Branches of Order''

The average length of branches of an object that are of a given order. The length of the branch of the selected order is measured from the intersect point of the whole branch and the main line to the end of the branch.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Branches of Length

%gray%''Object Features > Geometry > Based on Skeletons > Number of Branches of Length''

The number of branches of an object that are of a special length up to a selected order. All ends of branches are counted up to the selected order.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

*Minimum length

*Maximum length

!!!!Feature Value Range

[0; depending on shape of objects]

!!!Average Branch Length

%gray%''Object Features > Geometry > Based on Skeletons > Average Branch Length''

The average length of all branches of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Avrg. Area Represented by Segments

%gray%''Object Features > Geometry > Based on Skeletons > Avrg. Area Represented by Segments''

The average area of all triangles created by a Delaunay triangulation.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Curvature/Length (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Curvature/Length (only main line)''

The length-to-curvature ratio of the main line of an object. The curvature is the sum of all changes in direction of the main line. Changes in direction are expressed by the acute angle a in which sections of the main line, built by the connection between the nodes, cross each other.

Figure 107: The main line (green) connects the mid-points of triagles (black and blue) created by a Delaunay triangulation of the objects' shape (not depicted).

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Degree of Skeleton Branching

%gray%''Object Features > Geometry > Based on Skeletons > Degree of Skeleton Branching''

The highest order of branching in an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length of Main Line (No Cycles)

%gray%''Object Features > Geometry > Based on Skeletons > Length of Main Line (No Cycles)''

The sum of all distances between the nodes of the main line of an object. If an object contains an island polygon `- a polygon derived from the inner borders of an image object `- it is ignored and the main line may cross it (no cycles). This is different to the Length of Main Line (regarding cycles) feature where the main line goes around the island polygon. This feature does not visualize skeletons.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length of Main Line (Regarding Cycles)

%gray%''Object Features > Geometry > Based on Skeletons > Length of Main Line (regarding cycles)''

The sum of all distances between the nodes of the main line of an object. If an object contains an island polygon `- a polygon derived from the inner borders of an image object `- the main line is calculated so as not to cross it (Regarding Cycles).

In contrast to the Length of Main Line (No Cycles) feature, the skeletons are visualized.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length/Width (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons >Length/Width (Only Main Line)''

The length-to-width ratio of the main line of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Maximum Branch Length

%gray%''Object Features > Geometry > Based on Skeletons > Maximum Branch Length''

The length of the longest branch of an object. It is measured from the intersect point of the branch and the main line to the end of the branch.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Segments

%gray%''Object Features > Geometry > Based on Skeletons > Number of Segments''

The number of all segments of the main line and the branches of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Stddev Curvature (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Stddev Curvature (Only Main Line)''

The standard deviation of the curvature is the result of the standard deviation of the changes in direction of the main line. Changes in direction are expressed by the acute angle in which sections of the mainline, built by the connection between the nodes, cross each other.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Stddev of Area Represented by Segments

%gray%''Object Features > Geometry > Based on Skeletons > Stddev. of Area Represented by Segments''

The standard deviation of all triangles created by the Delaunay triangulation.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Width (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Width (Only Main Line)''

The width of an object based on the height of triangles created by a Delaunay triangulation. It is calculated by the average height{$ h $}of all triangles crossed by the main line.

Figure 108: Height {$ h $} of an triangle that is crossed by the main line.

An exception is triangles where the height {$ h $} does not cross one of the sides of the triangle. In this case, the nearest side {$ s $} is used to define the height.

Figure 109: Height of an triangle that is crossed by the main line. In this case the side {$ s $} defines the height.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

Geometry features are based on an image object's shape, calculated from the pixels that form it. Because images are raster-based, geometry features may be rotation variant: after image objects are rotated, different feature values may arise.

!!Extent

%gray%''Object Features > Geometry > Extent''

!!!Area

%gray%''Object Features > Geometry > Extent > Area''

The number of pixels forming an image object. If unit information is A_vailable, the number of pixels can be converted into a measurement.

In scenes that provide no unit information, the area of a single pixel is 1 and the area is simply the number of pixels that form it. If the image data provides unit information, the area can be multiplied using the appropriate factor.

!!!!Parameters

*{$ A_v $} is the area of image object {$ v $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ u $} is the pixel size in co-ordinate system units. If the unit is a pixel, then {$ u=1. $}

!!!!Expression

%left%{$ \displaystyle A_v= \#P_v \times u^2 $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \mathrm {scene \ size}] $}

!!!Border Length [for 2D Image Objects]

%gray%''Object Features > Geometry > Extent > Border Length''

The border length of an image object is defined as the sum of edges of the image object shared with other image objects, or situated on the edge of the entire scene. For a torus `- and other image objects with holes `- the border length is the sum of the inner and outer borders.

!!!!Parameters

*{$ b_v $} is the border length of image object

*{$ b_o $} is the length of outer border

*{$ b_i $} is the length of inner border

!!!!Expression

%left%{$ \displaystyle b_v = b_o+b_i $}

Figure 84: Border length of an image object {$ v $} or between two objects v, u.

Figure 85: Inner and outer border length of a torus image object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Border Length [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > Border Length''

The border length of a 3D image object is the sum of border lengths of all image object slices, multiplied by the spatial distance between them.

Image object slices are 2D pieces of the image object in each slice. The border length of an image object slice is defined as the sum of edges shared with other image object pieces, or are situated on the edge of the entire slice. For a torus and other image objects with holes the border length sums the inner and outer border.

!!!!Parameters

* {$ b_v $} is the border length of image object {$ v $}

* {$ b_v (\mathrm {slice}) $} is the border length of image object slice

* {$ b_v(z) $} is the border length of image object in z-direction

* {$ u_{\mathrm {slices}} $} is the spatial distance between slices in the co-ordinate system unit

* {$ b_o $} is the length of the outer border

* {$ b_i $} is the length of the inner border

!!!!Expression

%left%{$ \displaystyle b_v = \Bigg(\sum_{n=1}^{\# (\mathrm {slices})} b_v (\mathrm {slice}) \Bigg) \times u_{\mathrm {slices}} + b_v (z) $}

Figure 86: Border length of an image object {$ v $} or between two objects v, u.

Figure 87: Inner and outer border length of a torus image object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length [for 2D Image Objects]

%gray%''Object Features > Geometry > Extent > Length''

The length of a 2D image object is calculated using the length-to-width ratio.

!!!!Parameters

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ \gamma_v $} is the length-width ratio of an image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \sqrt {\# P_v \cdot \gamma_v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > Length''

The length of an image object is the largest of three eigenvalues of a rectangular 3D space that is defined by the same volume, and same proportions of eigenvalues, as the image object. The length of an image object can be smaller or equal than the largest of dimensions of the smallest rectangular 3D space enclosing the image object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length/Thickness

%gray%''Object Features > Geometry > Extent > Length/Thickness''

The length-to-thickness ratio of an image object.

!!!!Parameters

*Length of the image object

*Thickness of the image object

!!!!Expression

%left%{$ \displaystyle \frac {\mathrm {Length}}{\mathrm {Thickness}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length/Width [for 2D Image Objects]

%gray%''Object Features > Geometry > Extent > Length/Width''

The length-to-width ratio of an image object. There are two methods to approximate this:

1. The ratio of length to width is identical to the ratio of the eigenvalues of the covariance matrix, with the larger eigenvalue being the numerator of the fraction:

%left%{$ \displaystyle \gamma_v^{EV} = \frac {\lambda_1 (v)} {\lambda_2(v)} $}

2. The ratio of length to width can also be approximated using the bounding box:

%left%{$ \displaystyle \gamma_v^{BB} = \frac {\big(k_v^{bb'} \big)^2} {\#P_v} $}

Both calculations are compared; the smaller of both results is returned as the feature value.

!!!!Parameters

* {$ \# P_v $} is the Size of a set of pixels of an image object {$ v $}

* {$ \lambda_1 \lambda_2 $} are eigenvalues

* {$ \gamma_v^ {\mathrm {EV}} $} is the ratio length of {$ v $} of the eigenvalues

* {$ \gamma_v^ {\mathrm {BB}} $} is the ratio length of {$ v $} of the bounding box

* {$ \gamma_v $} is the length-width ratio of an image object {$ v $}

* {$ k_v^ {\mathrm {BB'}} $}

* {$ h_v^ {\mathrm {BB'}} $}

* {$ a $} is the bounding box fill rate

* {$ \#Pxl $}

* {$ h $}

* {$ w $} is the image layer weight

*{$ k_v^{bb^1} = \sqrt{ {(k_v^{bb'})^2} + (1-a)(h_v^{bb'})^2} $}

*{$ a = \frac {\#P_v}{k_v^{bb'} - h_v^{bb'}} $}

*{$ k\cdot h = \# P_v \Rightarrow k=\frac {\# P_v} {w}, h = \frac {\# P_v} {k} \Rightarrow \frac {k} {w} = \frac {k^2} {\# P_{xl}} = \frac {\# P_{xl}} {w^2} $}

!!!!Expression

%left%{$ \displaystyle \gamma_v = \mathrm{min} \gamma_v^{EV}, \mathrm{max} \gamma_v^{BB} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Length/Width [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > Length/Width''

The length-to-width ratio of an image object.

!!!!Parameters

*Length of the image object

*Width of the image object

!!!!Expression

%left%{$ \displaystyle \frac {\mathrm {Length}}{\mathrm {Width}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Number of Pixels

%gray%''Object Features > Geometry > Extent > Number of Pixels''

The number of pixels forming an image object. Unit information is not taken into account.

!!!!Parameters

* {$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \mathrm {scene \ size}] $}

!!!Thickness

%gray%''Object Features > Geometry > Extent > Thickness''

The thickness of an image object is the smallest of three eigenvalues of a rectangular 3D space with the same volume as the image object and the same proportions of eigenvalues as the image object. The thickness of an image object can be smaller or equal to the smallest of dimensions of the smallest rectangular 3D space enclosing the image object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Volume

%gray%''Object Features > Geometry > Extent > Volume''

The number of voxels forming an image object rescaled by using unit information for{$ x $}and{$ y $}co-ordinates and distance information between slices.

!!!!Parameters

* {$ V_v $} is the volume of image object {$ v $}

* {$ \# P_v $} is the total number of voxels contained in {$ P_v $}

* {$ u $} is the size of a slice pixel in the co-ordinate system unit

* {$ u_{\mathrm {slices}} $} is the spatial distance between slices in the co-ordinate system unit

!!!!Expression

%left%{$ \displaystyle V_v = \# P_v \times u^2 \times u_{\mathrm {slices}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \mathrm {scene \ size}] $}

!!!Width [for 2D Image Objects]

%gray%''Object Features > Geometry > Extent > Width''

The width of an image object is calculated using the length-to-width ratio.

!!!!Parameters

* {$ \# P_v $} is the total number of pixels contained in {$ P_v $}

* {$ \gamma_v $} is the length/width ratio of an image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \frac {\# P_v} {\gamma _v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Width [for 3D Image Objects]

%gray%''Object Features > Geometry > Extent > Width''

The width of an image object is the mid-point of three eigenvalues of a rectangular 3D space with the same volume as the image object and the same proportions of eigenvalues as the image object. The width of an image object can be smaller or equal to the mid-point of dimensions of the smallest rectangular 3D space enclosing the image object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!Shape

%gray%''Object Features > Geometry > Shape''

!!!Asymmetry [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Asymmetry''

The Asymmetry feature describes the relative length of an image object, compared to a regular polygon. An ellipse is approximated around a given image object, which can be expressed by the ratio of the lengths of its minor and the major axes. The feature value increases with this asymmetry.

(:div class=frame:)

->'''NOTE:'''We recommend that you use the Length/Width ratio because it is more accurate.

(:divend:)

!!!!Parameters

*Var X is the variance of X

*Var Y is the variance of Y

!!!!Expression

%left%{$ \displaystyle \frac{2 \sqrt {\frac {1}{4} (\mathrm{Var}X + \mathrm{Var}Y)^2 +(\mathrm{Var}XY)^2 - \mathrm{Var}X \cdot \mathrm{Var}Y}}{\textrm{Var}X + \mathrm{Var}Y} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Asymmetry [for 3D Image Objects]

%gray%''Object Features > Geometry >Shape > Asymmetry''

The Asymmetry feature describes the relative length of an image object, in the same manner as 2D image objects. The asymmetry is calculated from the ratio between the smallest and largest eigenvalues of the image object.

!!!!Parameters

*{$ \lambda_{\mathrm {min}} $} is the minimal eigenvalue

*{$ \lambda_{\mathrm {max}} $} is the maximal eigenvalue

!!!!Expression

%left%{$ \displaystyle 1- \sqrt \frac {\lambda_{\mathrm{min}}} {\lambda_{\mathrm{max}}} $}

Figure 88: Asymmetry based on maximal and minimal eigenvalues.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Border Index

%gray%''Object Features > Geometry >Shape > Border Index''

The Border Index feature describes how jagged an image object is; the more jagged, the higher its border index. This feature is similar to the Shape Index feature, but the Border Index feature uses a rectangular approximation instead of a square. The smallest rectangle enclosing the image object is created and the border index is calculated as the ratio between the border lengths of the image object and the smallest enclosing rectangle.

!!!!Parameters

*{$ b_v $} is the image object border length

*{$ l_v $} is the length of an image object {$ v $}

*{$ w_v $} is the width of an image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \frac {b_v}{2(l_v + w_v)} $} [[<<]]

Figure 89: Border index of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 1 = ideal.

!!!Compactness [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Compactness''

The Compactness feature describes how compact an image object is. It is similar to Border Index, but is based on area. However, the more compact an image object is, the smaller its border appears. The compactness of an image object is the product of the length and the width, divided by the number of pixels.

!!!!Parameters

*{$ l_v $} is the length of an image object {$ v $}

*{$ w_v $} is the width of an image object {$ v $}

* {$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \frac {2\lambda_1 \times 2\lambda_2 \times 2\lambda_3}{V_v} $}

Figure 90: Compactness of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 1 = ideal.

!!!Compactness [for 3D Image Objects]

%gray%''Object Features > Geometry >Shape > Compactness''

Compactness describes how compact a 3D image object is. Appropriately scaled eigenvectors of an image object's covariance matrix provide a rough figure of the object's extent in three dimensions.

A figure for the compactness of a 3D image object is calculated by a scaled product of its three eigenvalues {$ (2 \times \lambda_1, 2 \times \lambda_2, 2 \times \lambda_3) $} divided by the number of its pixel/voxel. We include a factor of 2 with each eigenvalue, since {$ \lambda_i \times $} eigenvectors represent otherwise half axes of an ellipsoid defined by its covariance matrix. The chosen approach therefore provides an estimate of a cuboid occupied by the object.

!!!!Parameters

*{$ \lambda_1 $} is eigenvalue 1 of a 3D image object {$ v $}

*{$ \lambda_2 $} is the eigenvalue 2 of a 3D image object {$ v $}

*{$ \lambda_3 $} is eigenvalue 3 of a 3D image object {$ v $}

*{$ V_v $} is the volume of image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \frac {2\lambda_1 \times 2\lambda_2 \times 2\lambda_3}{V_v} $}

Figure 91: Compactness of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 1 = ideal.

!!!Density [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Density''

The Density feature describes the distribution in space of the pixels of an image object. In Definiens Developer XD 1.2.5 the most "dense" shape is a square; the more an object is shaped like a filament, the lower its density.

The density is calculated by the number of pixels forming the image object divided by its approximated radius, based on the covariance matrix.

!!!!Parameters

* {$ \sqrt {\#P_v} $} is the diameter of a square object with {$ \# P_v $} pixels

* {$ \sqrt {VarX + VarY} $} is the diameter of the ellipse

!!!!Expression

%left%{$ \displaystyle \frac {\sqrt {\# P_v}}{1+ \sqrt {VarX+VarY}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ image \ object}}] $}

!!!Density [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Density''

Using the same principle as Density [for 2D Image Objects], the most "dense" shape for a 3D object is a cube. The more filament-shaped an image object is, the lower its density. The value is calculated by dividing the edge of the volume of a fitted cuboid by the radius of a fitted sphere.

!!!!Parameters

*{$ V_v $} is the volume of image object {$ v $}

*{$ \sqrt[3]{V_v} $} is the edge of the volume fitted cuboid

*{$ \sqrt {\mathrm{Var}(X) + \mathrm{Var}(Y) + \mathrm{Var}(Z)} $} is the radius of the fitted sphere

!!!!Expression

%left%{$ \displaystyle \frac {\sqrt[3]{V_v}} {\sqrt {\mathrm{Var}(X) + \mathrm{Var}(Y) + \mathrm{Var}(Z)}} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ image \ object}}] $}

!!!Elliptic Fit [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit''

The Elliptic Fit feature describes how well an image object fits into an ellipse of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on an ellipse with the same area as the selected image object. The proportions of the ellipse are equal to the length to the width of the image object. The area of the image object outside the ellipse is compared with the area inside the ellipse that is not filled by the image object.

!!!!Parameters

*{$ \varepsilon_v(x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

*{$ P_v $} is the set of pixels of an image object {$ v $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \varphi =2 \cdot \frac {\#\big \{(x,y)\epsilon P_v:\varepsilon_v(x,y)\leq 1\big \}}{\# P_v}-1 $}

Figure 92: Elliptic fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}; 1 = complete fitting, 0 = <50% fit.

!!!Elliptic Fit [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit''

The Elliptic Fit feature describes how well an image object fits into an ellipsoid of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on an ellipsoid with the same volume as the considered image object. The proportions of the ellipsoid are equal to the proportions of the length, width and thickness of the image object. The volume of the image object outside the ellipsoid is compared with the volume inside the ellipsoid that is not filled out with the image object.

!!!!Parameters

*{$ \varepsilon_v(x,y,z) $} is the elliptic distance at a pixel {$ {(x,y,z)} $}

*{$ P_v $} is the set of pixels of an image object {$ v $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \varphi =2 \cdot \frac {\#\big \{(x,y,z)\epsilon P_v:\varepsilon_v(x,y,z)\leq 1\big \}}{\# P_v}-1 $}

Figure 93: Elliptic fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0,1] $}; 1 = complete fitting, whereas 0 = < 50% voxels.

!!!Main Direction [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit > Main Direction''

The Main Direction feature of an image object is defined as the direction of the eigenvector belonging to the larger of the two eigenvalues, derived from the covariance matrix of the spatial distribution of the image object.

!!!!Parameters

* {$ Var X $} is the variance of {$ X $}

* {$ Var Y $} is the variance of {$ Y $}

* {$ \lambda_1 $} is the eigenvalue

!!!!Expression

%left%{$ \displaystyle \frac {180^{\circ}}{\pi}\mathrm{tan}^{-1}(\mathrm{Var}XY,\lambda_1-\mathrm{Var}Y) + {90^{\circ}} $}

Figure 94: The main direction is based on direction of the larger eigenvector.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 180] $}

!!!Main Direction [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Main Direction''

The Main Direction feature of a three-dimensional image object is computed as follows:

#For each (2D) image object slice, the centers of gravities are calculated.

#The co-ordinates of all centers of gravities a reused to calculate a line of best fit, according to the Weighted Least Square method.

#The angle a between the resulting line of best fit and the z-axis is returned as feature value.

Figure 95: The line of best fit (blue) calculated from centers of gravity of image object slices (light blue).

!!!!Feature Value Range

%left%{$ \displaystyle [0, 90] $}

!!!Radius of Largest Enclosed Ellipse [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Largest Enclosed Ellipse''

The Radius of Largest Enclosed Ellipse feature describes how similar an image object is to an ellipse. The calculation uses an ellipse with the same area as the object and based on the covariance matrix. This ellipse is scaled down until it is totally enclosed by the image object. The ratio of the radius of this largest enclosed ellipse to the radius of the original ellipse is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o) $}, where {$ (x_o,y_o) = min \ \varepsilon_v (x,y), (x,y) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Largest Enclosed Ellipse [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Largest Enclosed Ellipse''

The Radius of Largest Enclosed Ellipse feature describes how much the shape of an image object is similar to an ellipsoid.

The calculation is based on an ellipsoid with the same volume as the object and based on the covariance matrix. This ellipsoid is scaled down until it is totally enclosed by the image object. The ratio of the radius of this largest enclosed ellipsoid to the radius of the original ellipsoid is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y,z) $} is the elliptic distance at a pixel {$ (x,y,z) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o,z_o) $}, where {$ (x_o,y_o,z_o) = min \ \varepsilon_v (x,y,z), (x,y,z) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Smallest Enclosing Ellipse [for 2D Image Objects]

%gray%''Object Features > Geometry >Shape > Radius of Smallest Enclosing Ellipse''

The Radius of Smallest Enclosing Ellipse feature describes how much the shape of an image object is similar to an ellipse.

The calculation is based on an ellipse with the same area as the image object and based on the covariance matrix. This ellipse is enlarged until it encloses the image object in total. The ratio of the radius of this smallest enclosing ellipse to the radius of the original ellipse is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o) $}, where {$ (x_o,y_o) = max \ \varepsilon_v (x,y), (x,y) \notin P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Radius of Smallest Enclosing Ellipse [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Radius of Smallest Enclosing Ellipse''

The Radius of Smallest Enclosing Ellipse feature describes how much the shape of an image object is similar to an ellipsoid.

The calculation is based on an ellipsoid with the same volume as the image object and based on the covariance matrix. This ellipsoid is enlarged until it encloses the image object in total. The ratio of the radius of this smallest enclosing ellipsoid to the radius of the original ellipsoid is returned as feature value.

!!!!Parameters

*{$ \varepsilon_v (x,y,z) $} is the elliptic distance at a pixel {$ (x,y,z) $}

!!!!Expression

%left%{$ \displaystyle \varepsilon_v(x_o,y_o,z_o) $}, where {$ (x_o,y_o,z_o) = max \ \varepsilon_v (x,y,z), (x,y,z) \in \sigma P_v $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}

!!!Rectangular Fit [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Rectangular Fit''

The Rectangular Fit feature describes how well an image object fits into a rectangle of similar size and proportions. While 0 indicates no fit, 1 indicates for a complete fitting image object.

The calculation is based on a rectangle with the same area as the image object. The proportions of the rectangle are equal to the proportions of the length to width of the image object. The area of the image object outside the rectangle is compared with the area inside the rectangle.

!!!!Parameters

*{$ \rho_v (x,y) $} is the elliptic distance at a pixel {$ (x,y) $}

!!!!Expression

%left%{$ \displaystyle \frac {\big \{\#(x,y)\epsilon P_v:\rho _v(x,y)\leq 1\big \}}{\#P_v} $}

Figure 96: Rectangular fit of an image object {$ v $}.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}; where 1 is a perfect rectangle.

!!!Rectangular Fit [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Rectangular Fit''

The Rectangular Fit feature describes how well an image object fits into a cuboid of similar size and proportions. While 0 indicates no fit, 1 indicates a perfect fit.

The calculation is based on a cuboid with the same volume as the considered image object. The proportions of the cuboid are equal to the proportions of the length to width to thickness of the image object. The volume of the image object outside the rectangle is compared with the volume inside the cuboid that is not filled out with the image object.

!!!!Parameters

*{$ \rho_v(x,y,z) $} is the rectangular distance at a pixel {$ (x,y,z) $}

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

!!!!Expression

%left%{$ \displaystyle \frac {\big \{\#(x,y,z)\epsilon P_v:\rho _v(x,y,z)\leq 1\big \}}{\#P_v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $} ; 1 = complete fitting, whereas 0 = 0% fits inside the rectangular approximation.

!!!Roundness [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Roundness''

The Roundness feature describes how similar an image object is to an ellipse. It is calculated by the difference of the enclosing ellipse and the enclosed ellipse. The radius of the largest enclosed ellipse is subtracted from the radius of the smallest enclosing ellipse.

!!!!Parameters

*{$ \varepsilon_v^\mathrm{max} $} is the radius of the smallest enclosing ellipse

*{$ \varepsilon_v^\mathrm{min} $} is the radius of the largest enclosed ellipse

!!!!Expression

%left%{$ \displaystyle \varepsilon_v^\mathrm{max} - \varepsilon_v^\mathrm{min} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 0 = ideal.

!!!Roundness [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Roundness''

The Roundness feature describes how much the shape of an image object is similar to an ellipsoid. The more the shape of an image object is similar to an ellipsoid, the lower its roundness.

It is calculated by the difference of the enclosing ellipsoid and the enclosed ellipsoid. The radius of the largest enclosed ellipsoid is subtracted from the radius of the smallest enclosing ellipsoid.

!!!!Parameters

*{$ \varepsilon_v^\mathrm{max} $} is the radius of the smallest enclosing ellipsoid

*{$ \varepsilon_v^\mathrm{min} $} is the radius of the largest enclosed ellipsoid

!!!!Expression

%left%{$ \displaystyle \varepsilon_v^\mathrm{max} - \varepsilon_v^\mathrm{min} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, \infty] $}; 0 = ideal.

!!!Main Direction [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Elliptic Fit > Main Direction''

The Main Direction feature of an image object is defined as the direction of the eigenvector belonging to the larger of the two eigenvalues, derived from the covariance matrix of the spatial distribution of the image object.

!!!!Parameters

* {$ VarX $} is the variance of {$ X $}

* {$ VarY $} is the variance of {$ Y $}

* {$ \lambda_1 $} is the eigenvalue

!!!!Expression

%left%{$ \displaystyle \frac {180^{\circ}}{\pi}\mathrm{tan}^{-1}(\mathrm{Var}XY,\lambda_1-\mathrm{Var}Y) + {90^{\circ}} $}

Equation 1: The main direction is based on the direction of the larger eigenvector

!!!!Feature Value Range

%left%{$ \displaystyle [0,180] $}

!!!Main Direction [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Main Direction''

The Main Direction feature of a three-dimensional image object is computed as follows:

#For each (2D) image object slice, the centers of gravities are calculated.

#The co-ordinates of all centers of gravities a reused to calculate a line of best fit, according to the Weighted Least Square method.

#The angle a between the resulting line of best fit and the {$ z $}-axis is returned as feature value.

Figure 97: The line of best fit (blue) calculated from centers of gravity of image object slices (light blue).

!!!!Feature Value Range

%left%{$ \displaystyle [0,90] $}

!!!Shape Index [for 2D Image Objects]

%gray%''Object Features > Geometry > Shape > Shape Index''

The Shape index describes the smoothness of an image object border. The smoother the border of an image object is, the lower its shape index. It is calculated from the Border Length feature of the image object divided by four times the square root of its area.

!!!!Parameters

*{$ b_v $} is the image object border length

*{$ \sqrt[4] {\#P_v} $} is the border of square with area {$ \# P_v $}

!!!!Expression

%left%{$ \displaystyle \frac {b_v}{\sqrt[4]{\# P_v}} $}

Figure 98: Shape index of an image object {$ v $}

!!!!Feature Value Range

%left%{$ \displaystyle [1, \infty] $}; 1 = ideal.

!!!Shape Index [for 3D Image Objects]

%gray%''Object Features > Geometry > Shape > Shape Index''

The Shape Index describes the smoothness of the surface of an image object. The smoother the surface of an image object is, the lower its shape index. It is calculated from the Border Length feature of the image object divided by four times the square root of its area.

!!!!Parameters

*{$ b_v $} is the image object border length

*{$ V_v $} is the volume of image object {$ v $}

!!!!Expression

%left%{$ \displaystyle \frac {b_v}{V_v} $}

!!!!Feature Value Range

%left%{$ \displaystyle [1, \infty] $}; 1 = ideal.

!!To Superobject

%gray%''Object Features > Geometry > To Superobject''

Use the To Superobject feature to describe an image object by its shape and relationship to one of its superobjects, where appropriate. Editing the feature distance determines which superobject is referred to. When working with thematic layers these features can be of interest.

!!!Rel. Area to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Area to Superobject''

The area of an image object divided by the area of its superobject. If the feature value is 1, the image object is identical to its superobject. Use this feature to describe an image object in terms of the amount of area it shares with its superobject.

!!!!Parameters

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ \# P_{Uv(d)} $} is the the size of the superobject of {$ v $} in the image object level of the level distance {$ d $}

!!!!Expression

%left%{$ \displaystyle \frac {\# P_v}{\# P_{Uv(d)}} $}

!!!!Conditions

If {$ U_v(d) = \varnothing \therefore $} the formula is undefined.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. Rad. Position to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Rad. Position to Superobject''

This value is calculated by dividing the distance between the center of a selected image object and the center of its superobject, by the distance of the center of the most distant image object (which has the same superobject). Use this feature to describe an image object by its position relative to the center of its superobject.

!!!!Parameters

*{$ \# P_v $} is the total number of pixels contained in {$ P_v $}

*{$ \#P_{Uv( d)} $} is the the size of the superobject of an image object {$ v $}

*{$ d_g( v,Uv( d)) $} is the distance of {$ v $} to the center of gravity of the superobject {$ U_v( d) $}

!!!!Expression

Figure 99: Relative radial position to superobject.

%left%{$ \displaystyle \frac {d_g \big( v,U_v(d) \big)}{\underset {u\in S_{U{v(d)^{( d)}}}} {\mathrm{max}} d_g \big( u,U_v (d)\big)} $}

!!!!Conditions

If {$ U_v(d) = \varnothing \therefore $} the formula is undefined.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. Inner Border to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Inner Border to Superobject''

This feature is calculated by dividing the sum of the border shared with other image objects, which have the same superobject, by the total border of the image object. If the relative inner border to the superobject is 1, the image object of concern is not situated on the border of its superobject. Use this feature to describe how much of an image object is situated at the edge of its superobject.

!!!!Parameters

*{$ N_u(v) $} are neighbors of {$ v $} that exist within the superobject {$ N_u(v): \{ u \in N_v:U_u(d) - U_v(d) \} $}

*{$ b_v $} is the image object border length

!!!!Expression

%left%{$ \displaystyle \frac {\sum_ { u \in N_U( v) } b( v,m)}{b_v} $}

Figure 100: Relative inner border of an image object {$ v $} to superobject {$ u $}.

!!!!Conditions

If the feature range is 0 then {$ v=U_v(d) $}

If the feature range is 1 then {$ v $} is an inner object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Distance to Superobject Center

%gray%''Object Features > Geometry > To Superobject > Distance to Superobject Center''

The distance of an image object's center to the center of its superobject. This might not be the shortest distance between the two points, since the way to the center of the superobject must be within the borders of the superobject.

!!!!Expression

%left%{$ \displaystyle d_g( v,U_v(d)) $} is the distance of {$ v $} to the center of gravity of the superobject {$ U_v(d) $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, sx \times sy] $}

!!!Elliptic Distance to Superobject Center

%gray%''Object Features > Geometry > To Superobject > Elliptic Distance to Superobject Center''

Distance of objects to the center of the superobject.

!!!!Expression

%left%{$ \displaystyle d_e( v,U_v(d)) $}

Figure 101: Distance between the distance from the superobject's center to the center of a sub-objectt.

!!!!Feature Value Range

Typically {$ [0, 5] $}

!!!Is End of Superobject

%gray%''Object Features > Geometry > To Superobject > Is End of Superobject''

This feature is true for two image objects {$ a $} and {$ b $} if following conditions are true:

*{$ a $} and {$ b $} are sub-objects of the same superobject.

*{$ a $} is the image object with the maximum distance to the superobject.

*{$ b $} is the image object with the maximum distance to {$ a $}.

!!!!Editable Parameter

*Level Distance

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Is Center of Superobject

%gray%''Object Features > Geometry > To Superobject > Is Center of Superobject''

This feature is true if the image object is the center of its superobject.

!!!!Editable Parameter

*Level Distance

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Rel. X Position to Superobject

%gray%''Object Features > Geometry > To Superobject Rel. X Position to Superobject''

This feature returns the relative{$ x $}position of an image object with regard to its superobject, based on the centers of gravity of both objects.

!!!!Editable Parameters

*Level Distance `- the upward distance of image object levels in the image object hierarchy between the image object and the superobject.

!!!!Expression

%left%{$ \displaystyle \Delta x = x_{CG} $} of current image object {$ - x_{CG} $} of superobject (where {$ x_{CG} $} is the center of gravity)

!!!!Feature Value Range

%left%{$ \displaystyle - \frac {\mathrm{scene \ width}}{2} + \frac {\mathrm{scene \ width}}{2} $}

!!!Rel. Y Position to Superobject

%gray%''Object Features > Geometry > To Superobject > Rel. Y Position to Superobject''

This feature returns the relative{$ y $}position of an image object with regard to its superobject, based on the centers of gravity of both objects.

!!!!Editable Parameter

*Level Distance: Upward distance of image object levels in the image object hierarchy between the image object and the superobject.

!!!!Expression

%left%{$ \displaystyle \Delta y = y_{CG} $} of current image object {$ - y_{CG} $} of superobject (where {$ y_{CG} $} is the center of gravity)

!!!!Feature Value Range

%left%{$ \displaystyle - \frac {\mathrm{scene \ height}}{2} + \frac {\mathrm{scene \ height}}{2} $}

!!Based on Polygons

%gray%''Object Features > Geometry > Based on Polygons''

The polygon features provided by Definiens Developer XD 1.2.5 are based on the vectorization of the pixels that form an image object.

Figure 102: Raster image object (black area) with its polygon object (red lines) after vectorization.

!!!Edges Longer Than

%gray%''Object Features > Geometry > Based on Polygons > Edges Longer Than''

!!!!Editable Parameters

*Minimum Length

!!!Number of Right Angles With Edges Longer Than

%gray%''Object Features > Geometry > Based on Polygons > Number of Right Angles with Edges Longer Than''

The number of right angles that have at least one side edge longer than a given threshold.

!!!!Editable Parameters

*Minimum length

Figure 103: A polygon with one rectangular angle.

!!!Area (Excluding Inner Polygons)

%gray%''Object Features > Geometry > Based on Polygons > Area (Excluding Inner Polygons)''

The Area (Excluding Inner Polygons) feature calculates the area of a polygon based on Green's Theorem in a plane. In contrast to the Area (Including Inner Polygons) feature, the feature value does not include the areas of any existing inner polygons.

!!!!Parameters

*{$ (x_i, y_i), i = 0, \dots , n, $} with {$ x_o = x_n $} and {$ y_o = y_n $} as the given points

*{$ a_i = x_iy_{i+1} - x_{i+1}y_i $}

!!!!Expression

%left%{$ \displaystyle \frac {1}{2}\sum_{i=0}^{n-1} a_i $}

Figure 104: A polygon with an inner polygon that is not included in the feature value.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {scene \ size}}] $}

!!!Area (Including Inner Polygons)

%gray%''Object Features > Geometry > Based on Polygons > Area (Including Inner Polygons)''

The Area (Excluding Inner Polygons) feature calculates the area of a polygon based on Green's Theorem in a plane. Different to the Area (Excluding Inner Polygons) feature, the feature value includes the areas of any existing inner polygons (for instance the single polygon formed in the center of a donut-shaped object).

Figure 105: A polygon with an inner polygon that is included in the feature value.

!!!Average Length of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > average Length of Edges (Polygon)''

The average length of all edges in a polygon.

!!!!Parameters

*{$ X_i $} is the length of edge {$ i $}

*{$ n $} is the total number of edges

!!!!Expression

%left%{$ \displaystyle \mathrm{Average} = \frac {\displaystyle \sum_{i=1}^{n} X_{i}} {n} $}

!!!Compactness (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Compactness (Polygon)''

The ratio of the area of a polygon to the area of a circle with the same perimeter.

!!!!Parameters

*Area

*Perimeter

!!!!Expression

%left%{$ \displaystyle \frac {4 \times \pi \times \mathrm{Area}} {\mathrm{Perimeter}^2} $}

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {1 \ for \ a \ circle}}] $}

!!!Length of Longest Edge (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Length of Longest Edge (Polygon)''

The length of the longest edge of a polygon.

!!!Number of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Number of Edges (Polygon)''

The number of edges of a polygon.

!!!Number of Inner Objects (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Number of Inner Objects (Polygon)''

The number of inner polygons that are completely surrounded by a selected outer polygon.

!!!Perimeter (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Perimeter (Polygon)''

The sum of the lengths of all the edges of a polygon.

!!!Polygon Self-Intersection (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Polygon Self-Intersection (Polygon)''

The Polygon Self-Intersection (Polygon) feature allows the identification of a rare arrangement of image objects, leading to a polygon self-intersection when exported as a polygon vector file.

This feature enables you to identify the affected image objects and take measures To avoid this self-intersection. All image objects with a value of 1 will cause a polygon self-intersection when exported to a shapefile.

Figure 106: This type of image object leads to a self-intersection at the circled point.

To avoid the self-intersection, the enclosed image object needs to be merged with the enclosing image object.

(:div class=frame:)

->'''TIP: '''Use the Image Object Fusion algorithm to remove polygon intersections. To do so, set the domain to all image objects with a value larger than 0 for the polygon intersection feature. In the algorithm parameter, set the Fitting Function Threshold to Polygon Self-Intersection (Polygon) feature to zero and in the Weighted Sum group, set Target Value Factor to 1. This will merge all image objects with a value of 1 for the Polygon Self-Intersection (Polygon) feature, so that the resulting image object will not include a self-intersection.

(:divend:)

!!!!Feature Value Range

%left%{$ \displaystyle [0, 1] $}

!!!Std. Dev. of Length of Edges (Polygon)

%gray%''Object Features > Geometry > Based on Polygons > Stddev of Length of Edges (Polygon)''

The Std. Dev. of Length of Edges (Polygon) feature measures how the lengths of edges deviate from their mean value.

!!!!Parameters

*{$ x_i $} is the length of edge {$ i $}

*{$ \bar X $} is the mean value of all lengths

*{$ n $} is the total number of edges

!!!!Expression

%left%{$ \displaystyle \sqrt \frac {\displaystyle \sum_{i=1}^{n} {(x_i-\bar x)^2}} {n} $}

!!Based on Skeletons

%gray%''Object Features > Geometry > Based on Skeletons''

For the better understanding of the following descriptions, the skeleton is structured in a main line and subordinate branches. A node is a mid-point of the triangles created by the Delaunay triangulation.

!!!Number of Segments of Order

%gray%''Object Features > Geometry > Based on Skeletons > Number of Segments of Order''

The number of line segments of branches of an object that are of a given order. Note that only segments that do not belong to a lower order are counted

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Branches of Order

%gray%''Object Features > Geometry > Based on Skeletons > Number of Branches of Order''

The number of branches of an object that are of a given order.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Average Length of Branches of Order

%gray%''Object Features > Geometry > Based on Skeletons > average Length of Branches of Order''

The average length of branches of an object that are of a given order. The length of the branch of the selected order is measured from the intersect point of the whole branch and the main line to the end of the branch.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Branches of Length

%gray%''Object Features > Geometry > Based on Skeletons > Number of Branches of Length''

The number of branches of an object that are of a special length up to a selected order. All ends of branches are counted up to the selected order.

!!!!Editable Parameter

*Branch order: The main line of the skeleton has the order 0.

*Minimum length

*Maximum length

!!!!Feature Value Range

[0; depending on shape of objects]

!!!Average Branch Length

%gray%''Object Features > Geometry > Based on Skeletons > Average Branch Length''

The average length of all branches of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Avrg. Area Represented by Segments

%gray%''Object Features > Geometry > Based on Skeletons > Avrg. Area Represented by Segments''

The average area of all triangles created by a Delaunay triangulation.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Curvature/Length (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Curvature/Length (only main line)''

The length-to-curvature ratio of the main line of an object. The curvature is the sum of all changes in direction of the main line. Changes in direction are expressed by the acute angle a in which sections of the main line, built by the connection between the nodes, cross each other.

Figure 107: The main line (green) connects the mid-points of triagles (black and blue) created by a Delaunay triangulation of the objects' shape (not depicted).

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Degree of Skeleton Branching

%gray%''Object Features > Geometry > Based on Skeletons > Degree of Skeleton Branching''

The highest order of branching in an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length of Main Line (No Cycles)

%gray%''Object Features > Geometry > Based on Skeletons > Length of Main Line (No Cycles)''

The sum of all distances between the nodes of the main line of an object. If an object contains an island polygon `- a polygon derived from the inner borders of an image object `- it is ignored and the main line may cross it (no cycles). This is different to the Length of Main Line (regarding cycles) feature where the main line goes around the island polygon. This feature does not visualize skeletons.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length of Main Line (Regarding Cycles)

%gray%''Object Features > Geometry > Based on Skeletons > Length of Main Line (regarding cycles)''

The sum of all distances between the nodes of the main line of an object. If an object contains an island polygon `- a polygon derived from the inner borders of an image object `- the main line is calculated so as not to cross it (Regarding Cycles).

In contrast to the Length of Main Line (No Cycles) feature, the skeletons are visualized.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Length/Width (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons >Length/Width (Only Main Line)''

The length-to-width ratio of the main line of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Maximum Branch Length

%gray%''Object Features > Geometry > Based on Skeletons > Maximum Branch Length''

The length of the longest branch of an object. It is measured from the intersect point of the branch and the main line to the end of the branch.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Number of Segments

%gray%''Object Features > Geometry > Based on Skeletons > Number of Segments''

The number of all segments of the main line and the branches of an object.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Stddev Curvature (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Stddev Curvature (Only Main Line)''

The standard deviation of the curvature is the result of the standard deviation of the changes in direction of the main line. Changes in direction are expressed by the acute angle in which sections of the mainline, built by the connection between the nodes, cross each other.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Stddev of Area Represented by Segments

%gray%''Object Features > Geometry > Based on Skeletons > Stddev. of Area Represented by Segments''

The standard deviation of all triangles created by the Delaunay triangulation.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

!!!Width (Only Main Line)

%gray%''Object Features > Geometry > Based on Skeletons > Width (Only Main Line)''

The width of an object based on the height of triangles created by a Delaunay triangulation. It is calculated by the average height{$ h $}of all triangles crossed by the main line.

Figure 108: Height {$ h $} of an triangle that is crossed by the main line.

An exception is triangles where the height {$ h $} does not cross one of the sides of the triangle. In this case, the nearest side {$ s $} is used to define the height.

Figure 109: Height of an triangle that is crossed by the main line. In this case the side {$ s $} defines the height.

!!!!Feature Value Range

%left%{$ \displaystyle [0, {\mathrm {depending \ on \ shape \ of \ objects}}] $}

11 September 2009 at 03:42 PM
by - restore page to previous version

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(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system~~ļoti šķības ļoti āņūļīšū lapš otnotes~~, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

to:

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

07 September 2009 at 06:52 AM
by - testing diacritics

Changed line 5 from:

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system~~: lists, tables, images, footnotes~~, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

to:

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing systemļoti šķības ļoti āņūļīšū lapš otnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

05 November 2008 at 06:44 PM
by - restore edited front page

Deleted lines 0-2:

اين نيز يك جمله ديگر.

Added lines 1-3:

اين يك جمله به زبان فارسي ميباشد.

اين نيز يك جمله ديگر.

اين نيز يك جمله ديگر.

02 November 2008 at 07:15 AM
by - repairing vandalism

Changed lines 1-22 from:

to:

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be recast as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those showing [[(PmWiki/wiki )trails]], [[PmWiki/page lists]] or [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document.

:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

(:typeset-trail toc=on colorlinks=on:)

The site is running {$Version} and {$WPVersion}.

01 November 2008 at 11:51 AM
by - dsad

Changed lines 1-22 from:

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be recast as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those showing [[(PmWiki/wiki )trails]], [[PmWiki/page lists]] or [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document.

:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

Find out more:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

(:typeset-trail toc=on colorlinks=on:)

The site is running {$Version} and {$WPVersion}.

to:

Hacked By.SoLideR

28 June 2008 at 09:28 PM
by - clarify typeset button explanation

Changed line 9 from:

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those ~~listing~~ [[(PmWiki/wiki )trails]] ~~and ~~[[PmWiki/~~categories~~]]~~, may have a ~~'@Typeset@' button; pressing this button composes the listed pages into a single document~~. Search results allow readers to select and typeset pages of interest~~.

to:

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those showing [[(PmWiki/wiki )trails]], [[PmWiki/page lists]] or [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document.

12 June 2008 at 03:05 PM
by - simplify words

Changed lines 3-4 from:

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be ~~reformulated~~ as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

to:

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be recast as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

Changed lines 9-10 from:

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results ~~are displayed as a form, allowing~~ readers to select and typeset pages of interest.

to:

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results allow readers to select and typeset pages of interest.

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to:

Find out more:

09 June 2008 at 05:25 PM
by - add typeset directive

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=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). ~~Read~~ the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

to:

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Press the ''Typeset trail'' button; read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

Added lines 19-20:

(:typeset-trail toc=on colorlinks=on:)

09 June 2008 at 04:56 PM
by - tidy abbreviations and wording

Changed lines 9-13 from:

:Make a print version of any page:Sites with ~~wikipublisher~~ installed look and act like normal wiki sites, ~~and have ~~a ~~pdf~~ icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results are displayed as a form, allowing readers to select and typeset pages of interest.

:Choose the print style:~~Visitors~~ can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the~~pdf~~ icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

:Choose the print style:

=<{*'''Try it:''' click the

to:

:Make a print version of any page:Sites with Wikipublisher installed look and act like normal wiki sites, with a `PDF icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results are displayed as a form, allowing readers to select and typeset pages of interest.

:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

:Choose the print style:Readers can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the `PDF icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

20 May 2008 at 11:15 AM
by - restore hacked front page

Changed lines 1-5 from:

by XSaMuX

WWW

to:

W;ikipublisher is a TypesettingEngine; that re-purposes Web content for print, with 2 mouse-clicks.

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be reformulated as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with wikipublisher installed look and act like normal wiki sites, and have a pdf icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results are displayed as a form, allowing readers to select and typeset pages of interest.

:Choose the print style:Visitors can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the pdf icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

For more information, see:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

The site is running {$Version} and {$WPVersion}.

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be reformulated as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with wikipublisher installed look and act like normal wiki sites, and have a pdf icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results are displayed as a form, allowing readers to select and typeset pages of interest.

:Choose the print style:Visitors can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the pdf icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

For more information, see:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

The site is running {$Version} and {$WPVersion}.

Changed lines 1-20 from:

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

:Make a print version of any page:Sites with wikipublisher installed look and act like normal wiki sites, and have a pdf icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results are displayed as a form, allowing readers to select and typeset pages of interest.

:Choose the print style:Visitors can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

=<{*'''Try it:''' click the pdf icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

For more information, see:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

The site is running {$Version} and {$WPVersion}.

to:

http://img520.imageshack.us/img520/8070/cs1gu1.jpg

by XSaMuX

WWW.PCHACK.NET

by XSaMuX

WWW.PCHACK.NET

15 April 2008 at 07:56 PM
by - use small acronym markup

Changed lines 3-5 from:

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be reformulated as [[Wikibook]] ~~XML~~ can be composed into a [[BasicFeatures | print-friendly]] {~~pdf~~|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and~~lets ~~Wikipublisher ~~take~~ care of presentation details. There is one authoritative source for Web and print.:)

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and

to:

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be reformulated as [[Wikibook]] `XML can be composed into a [[BasicFeatures | print-friendly]] {`PDF|Portable Document Format} document.

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and Wikipublisher takes care of presentation details. There is one authoritative source for Web and print.:)

29 October 2007 at 01:39 PM
by - highlight try it text

Changed lines 13-14 from:

=<'''Try it:''' click the pdf icon. Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

to:

=<{*'''Try it:''' click the pdf icon.*} Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

12 September 2007 at 11:36 AM
by - add one line summary

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to:

W;ikipublisher is a TypesettingEngine; that re-purposes Web content for print, with 2 mouse-clicks.

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be reformulated as [[Wikibook]] XML can be composed into a [[BasicFeatures | print-friendly]] {pdf|Portable Document Format} document.

:Turn Web pages into beautiful print:Wikipublisher is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be reformulated as [[Wikibook]] XML can be composed into a [[BasicFeatures | print-friendly]] {pdf|Portable Document Format} document.

24 August 2007 at 11:49 AM
by - link to welcome letter

Changed lines 11-12 from:

=<'''Try it:''' click the pdf icon. Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the UserGuide or~~ the~~ [[(WP)Slides]]how.

to:

=<'''Try it:''' click the pdf icon. Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the WelcomeLetter, UserGuide, or [[(WP)Slides]]how.

02 July 2007 at 10:47 AM
by - remove licence conditions

Changed lines 18-20 from:

The site is running {$Version} and {$WPVersion}. ~~Wikipublisher is distributed under the [[General Public Licence -> http://www.gnu.org/licenses/gpl.html]], in 2 parts:~~

* a script library which makes PmWiki generate output to the WikibookDTD, instead of XHTML

* a [[InstallTheServer | pdfserver]] application which, when given wikibook XML content, composes this into pdf

* a script library which makes PmWiki generate output to the WikibookDTD, instead of XHTML

* a [[InstallTheServer | pdfserver]] application which, when given wikibook XML content, composes this into pdf

to:

The site is running {$Version} and {$WPVersion}.

02 July 2007 at 10:40 AM
by - add links to more information

Changed lines 11-13 from:

=<'''Try it:''' click the pdf icon. Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font).

Wikipublisher is distributed under the [[~~General Public Licence -> http~~:~~//www.gnu.org/licenses/gpl.html]]. It is distributed~~ in 2 parts:

Wikipublisher is distributed under

to:

=<'''Try it:''' click the pdf icon. Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font). Read the UserGuide or the [[(WP)Slides]]how.

For more information, see:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

The site is running {$Version} and {$WPVersion}. Wikipublisher is distributed under the [[General Public Licence -> http://www.gnu.org/licenses/gpl.html]], in 2 parts:

For more information, see:

* WhyWeNeedWikipublisher

* WikipublisherIsUnique

* WikipublisherTechnologies

The site is running {$Version} and {$WPVersion}. Wikipublisher is distributed under the [[General Public Licence -> http://www.gnu.org/licenses/gpl.html]], in 2 parts:

Deleted lines 20-21:

Wikipublisher has an extensive UserGuide. Or view the [[(WP)Slides]]how, then create a [[UserGuide?action=pubtrail | personalised guide]]. The site is running {$Version} and {$WPVersion}.

30 June 2007 at 02:29 PM
by - tighten words

Changed lines 7-8 from:

:Make a ~~PDF~~ of any page:Sites with wikipublisher installed look and act like normal wiki sites, and have a pdf icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results are displayed as a form, allowing ~~information seekers~~ to select and typeset pages of interest.

to:

:Make a print version of any page:Sites with wikipublisher installed look and act like normal wiki sites, and have a pdf icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results are displayed as a form, allowing readers to select and typeset pages of interest.

Changed line 17 from:

Wikipublisher has an extensive UserGuide. Or view the [[(WP)Slides]]how~~ and [[Testimonials]]~~, then create a [[UserGuide?action=pubtrail | personalised guide]]. The site is running {$Version} and {$WPVersion}.

to:

Wikipublisher has an extensive UserGuide. Or view the [[(WP)Slides]]how, then create a [[UserGuide?action=pubtrail | personalised guide]]. The site is running {$Version} and {$WPVersion}.

14 May 2007 at 06:44 PM
by - add link to bibliography user guide

Changed lines 3-4 from:

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, and so on. The author focuses on content and lets Wikipublisher take care of presentation details. There is one authoritative source for Web and print.:)

to:

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, bibliographies, and so on. The author focuses on content and lets Wikipublisher take care of presentation details. There is one authoritative source for Web and print.:)

Changed lines 9-10 from:

:Choose the print style:Visitors can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look.

to:

:Choose the print style:Visitors can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look. If a page includes a [[bibliograph(ies.user guide)]]y, an author can specify numbered or author`-year citations.

26 February 2007 at 07:51 PM
by - link to pdfserver

Changed lines 15-16 from:

* a ~~pdfserver~~ application which, when given wikibook XML content, composes this into pdf

to:

* a [[InstallTheServer | pdfserver]] application which, when given wikibook XML content, composes this into pdf

07 September 2006 at 07:14 PM
by - simplify try it text

Changed lines 11-12 from:

=<'~~+~~''~~'~~Try it:'''~~+'~~ click the pdf icon ~~or press~~ the '@options@' ~~button~~.

to:

=<'''Try it:''' click the pdf icon. Experiment with the '+'@options@'+' (perhaps you prefer a sans-serif font).

12 July 2006 at 12:55 PM
by - move keywords after description

Added lines 3-4:

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, and so on. The author focuses on content and lets Wikipublisher take care of presentation details. There is one authoritative source for Web and print.:)

Deleted lines 6-7:

04 July 2006 at 05:13 PM
by - add subheadings

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to:

:Turn Web pages into beautiful print:[[Wikipublisher]] is an extension to PmWiki. It supports collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be reformulated as wikibook XML can be composed into a [[BasicFeatures | print-friendly]] {pdf|Portable Document Format} document.

Changed lines 5-12 from:

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, and so on. The author focuses on content and lets Wikipublisher take care of presentation details. There is one authoritative source for Web and print:)

~~PmWiki sites with wikipublisher installed look and act like normal wiki sites, except that they have a pdf icon on every~~ page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may ~~include~~ a '@Typeset@' button; pressing this button composes the listed pages into a single ~~rich pdf ~~document. Search results are displayed as a form, allowing information seekers to select and typeset pages of interest ~~as a single document.~~

Visitorscan customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts.

=<'''Try it:''' click the pdf icon or press the '@options@' button.

Visitors

=<'''Try it:'''

to:

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, and so on. The author focuses on content and lets Wikipublisher take care of presentation details. There is one authoritative source for Web and print.:)

:Make a PDF of any page:Sites with wikipublisher installed look and act like normal wiki sites, and have a pdf icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results are displayed as a form, allowing information seekers to select and typeset pages of interest.

:Choose the print style:Visitors can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look.

=<'+'''Try it:'''+' click the pdf icon or press the '@options@' button.

:Make a PDF of any page:Sites with wikipublisher installed look and act like normal wiki sites, and have a pdf icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may have a '@Typeset@' button; pressing this button composes the listed pages into a single document. Search results are displayed as a form, allowing information seekers to select and typeset pages of interest.

:Choose the print style:Visitors can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts. Authors can define a default look.

=<'+'''Try it:'''+' click the pdf icon or press the '@options@' button.

Changed line 17 from:

to:

Wikipublisher has an extensive UserGuide. Or view the [[(WP)Slides]]how and [[Testimonials]], then create a [[UserGuide?action=pubtrail | personalised guide]]. The site is running {$Version} and {$WPVersion}.

28 April 2006 at 11:39 AM
by - add keywords

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(:keywords collaborative authoring, ~~PDF, print on demand~~, print ~~web pages~~, ~~single source publishing~~, ~~typesetting, wiki, wikipublisher~~, XML:)

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features~~we expect~~ of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, and so on. The author focuses on content and lets Wikipublisher take care of ~~the ~~presentation details.:)

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features

to:

(:keywords collaborative authoring, HTML to LaTeX, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, and so on. The author focuses on content and lets Wikipublisher take care of presentation details. There is one authoritative source for Web and print:)

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features one expects of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, and so on. The author focuses on content and lets Wikipublisher take care of presentation details. There is one authoritative source for Web and print:)

27 April 2006 at 09:09 PM
by - add keywords and description

Changed lines 1-2 from:

[[Wikipublisher]] is an extension to PmWiki that supports the collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be reformulated as wikibook XML can be composed into a [[BasicFeatures | print-friendly]] document.

to:

[[Wikipublisher]] is an extension to PmWiki that supports the collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be reformulated as wikibook XML can be composed into a [[BasicFeatures | print-friendly]] {pdf|Portable Document Format} document.

(:keywords collaborative authoring, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features we expect of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, and so on. The author focuses on content and lets Wikipublisher take care of the presentation details.:)

(:keywords collaborative authoring, PDF, print on demand, print web pages, single source publishing, typesetting, wiki, wikipublisher, XML:)

(:description Wikipublisher combines easy-to-use wiki markup and browser-based document authoring with a powerful and robust typesetting engine, to produce beautiful printed output from web pages. The engine supports all the features we expect of a publishing system: lists, tables, images, footnotes, mathematical equations, table of contents, and so on. The author focuses on content and lets Wikipublisher take care of the presentation details.:)

Changed lines 9-10 from:

to:

Visitors can customise the look of the printed output, such as add a watermark, choose A4 or US letter page size, and use serif or sans serif fonts.

=<'''Try it:''' click the pdf icon or press the '@options@' button.

=<'''Try it:''' click the pdf icon or press the '@options@' button.

23 February 2006 at 02:12 PM
by - WhitePapers reference

Changed line 11 from:

This page introduces the wikipublisher UserGuide. Or view the [[(WP)Slides]]how, then create a [[UserGuide?action=pubtrail | personalised guide]].The site is running {$Version} and {$WPVersion}.

to:

This page introduces the wikipublisher UserGuide. Or view the [[(WP)Slides]]how and WhitePapers, then create a [[UserGuide?action=pubtrail | personalised guide]].The site is running {$Version} and {$WPVersion}.

31 January 2006 at 12:29 PM
by - add slides reference

Changed line 11 from:

This page introduces the wikipublisher UserGuide. Or create a [[UserGuide?action=pubtrail | personalised guide]].The site is running {$Version} and {$WPVersion}.

to:

This page introduces the wikipublisher UserGuide. Or view the [[(WP)Slides]]how, then create a [[UserGuide?action=pubtrail | personalised guide]].The site is running {$Version} and {$WPVersion}.

31 January 2006 at 12:21 PM
by - any web page

Changed lines 1-2 from:

[[Wikipublisher]] is an extension to PmWiki that supports the collaborative creation of print documents which draw their content from wiki web pages.

to:

[[Wikipublisher]] is an extension to PmWiki that supports the collaborative creation of print documents which draw their content from wiki web pages. In fact ''any web page'' able to be reformulated as wikibook XML can be composed into a [[BasicFeatures | print-friendly]] document.

13 October 2005 at 10:04 AM
by - link to personalised guide

Changed lines 3-4 from:

PmWiki sites with wikipublisher installed look and act like normal wiki sites, except that they have a pdf icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may include a '@Typeset@' button; pressing this button composes the listed pages into a single rich pdf document.

to:

PmWiki sites with wikipublisher installed look and act like normal wiki sites, except that they have a pdf icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may include a '@Typeset@' button; pressing this button composes the listed pages into a single rich pdf document. Search results are displayed as a form, allowing information seekers to select and typeset pages of interest as a single document.

Changed line 11 from:

This page introduces the wikipublisher UserGuide. The site is running {$Version} and {$WPVersion}.

to:

This page introduces the wikipublisher UserGuide. Or create a [[UserGuide?action=pubtrail | personalised guide]].The site is running {$Version} and {$WPVersion}.

14 September 2005 at 04:13 PM
by - add a try me offer

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=<Try it: click the pdf icon.

07 September 2005 at 02:57 PM
by - fix pmwiki name

Changed lines 3-4 from:

PmWiki sites with wikipublisher installed look and act like normal wiki sites, except that they have a pdf icon on every page. Some pages, such as those listing [[(~~pmwiki~~/wiki )trails]] and [[~~pmwiki~~/categories]], may include a '@Typeset@' button; pressing this button composes the listed pages into a single rich pdf document.

to:

PmWiki sites with wikipublisher installed look and act like normal wiki sites, except that they have a pdf icon on every page. Some pages, such as those listing [[(PmWiki/wiki )trails]] and [[PmWiki/categories]], may include a '@Typeset@' button; pressing this button composes the listed pages into a single rich pdf document.

Deleted lines 9-10:

To use the service, [[install]] the wikipublisher library and [[register]] your site.

07 September 2005 at 02:27 PM
by - install and register

Changed lines 9-11 from:

This page introduces the wikipublisher UserGuide. The site is running {$Version} and {$WPVersion}.

to:

This page introduces the wikipublisher UserGuide. The site is running {$Version} and {$WPVersion}.

To use the service, [[install]] the wikipublisher library and [[register]] your site.

To use the service, [[install]] the wikipublisher library and [[register]] your site.

05 September 2005 at 05:51 PM
by - correct category reference

Changed lines 3-4 from:

PmWiki sites with wikipublisher installed look and act like normal wiki sites, except that they have a pdf icon on every page. Some pages, such as those listing [[(pmwiki/wiki )trails]] and [[~~(~~pmwiki/~~using )~~categories]], may include a '@Typeset@' button; pressing this button composes the listed pages into a single rich pdf document.

to:

PmWiki sites with wikipublisher installed look and act like normal wiki sites, except that they have a pdf icon on every page. Some pages, such as those listing [[(pmwiki/wiki )trails]] and [[pmwiki/categories]], may include a '@Typeset@' button; pressing this button composes the listed pages into a single rich pdf document.

22 August 2005 at 09:47 PM
by - tidy prose

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This page ~~is part of~~ the wikipublisher UserGuide. The site is running {$Version} and {$WPVersion}.

to:

This page introduces the wikipublisher UserGuide. The site is running {$Version} and {$WPVersion}.

22 August 2005 at 09:26 PM
by - link to GPL

Changed line 5 from:

Wikipublisher is distributed under the [[General Public Licence -> http://www.gnu.org/licenses/]]. It is distributed in 2 parts:

to:

Wikipublisher is distributed under the [[General Public Licence -> http://www.gnu.org/licenses/gpl.html]]. It is distributed in 2 parts:

Changed lines 7-8 from:

* a pdfserver application which, when given wikibook XML content, ~~turns~~ this into pdf

to:

* a pdfserver application which, when given wikibook XML content, composes this into pdf

22 August 2005 at 09:22 PM
by - define wikipublisher

Added lines 1-9:

[[Wikipublisher]] is an extension to PmWiki that supports the collaborative creation of print documents which draw their content from wiki web pages.

PmWiki sites with wikipublisher installed look and act like normal wiki sites, except that they have a pdf icon on every page. Some pages, such as those listing [[(pmwiki/wiki )trails]] and [[(pmwiki/using )categories]], may include a '@Typeset@' button; pressing this button composes the listed pages into a single rich pdf document.

Wikipublisher is distributed under the [[General Public Licence -> http://www.gnu.org/licenses/]]. It is distributed in 2 parts:

* a script library which makes PmWiki generate output to the WikibookDTD, instead of XHTML

* a pdfserver application which, when given wikibook XML content, turns this into pdf

This page is part of the wikipublisher UserGuide. The site is running {$Version} and {$WPVersion}.

PmWiki sites with wikipublisher installed look and act like normal wiki sites, except that they have a pdf icon on every page. Some pages, such as those listing [[(pmwiki/wiki )trails]] and [[(pmwiki/using )categories]], may include a '@Typeset@' button; pressing this button composes the listed pages into a single rich pdf document.

Wikipublisher is distributed under the [[General Public Licence -> http://www.gnu.org/licenses/]]. It is distributed in 2 parts:

* a script library which makes PmWiki generate output to the WikibookDTD, instead of XHTML

* a pdfserver application which, when given wikibook XML content, turns this into pdf

This page is part of the wikipublisher UserGuide. The site is running {$Version} and {$WPVersion}.