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	<id>https://www.slicer.org/w/index.php?action=history&amp;feed=atom&amp;title=Documentation%2FNightly%2FModules%2FResampling</id>
	<title>Documentation/Nightly/Modules/Resampling - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://www.slicer.org/w/index.php?action=history&amp;feed=atom&amp;title=Documentation%2FNightly%2FModules%2FResampling"/>
	<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;action=history"/>
	<updated>2026-05-20T14:24:20Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.33.0</generator>
	<entry>
		<id>https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=62102&amp;oldid=prev</id>
		<title>Grundlett: Text replacement - &quot;\[http:\/\/wiki\.slicer\.org\/slicerWiki\/index\.php\/([^ ]+) ([^]]+)]&quot; to &quot;$2&quot;</title>
		<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=62102&amp;oldid=prev"/>
		<updated>2019-11-27T02:12:45Z</updated>

		<summary type="html">&lt;p&gt;Text replacement - &amp;quot;\[http:\/\/wiki\.slicer\.org\/slicerWiki\/index\.php\/([^ ]+) ([^]]+)]&amp;quot; to &amp;quot;&lt;a href=&quot;/w/index.php?title=$1&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;$1 (page does not exist)&quot;&gt;$2&lt;/a&gt;&amp;quot;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 02:12, 27 November 2019&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;noinclude&amp;gt;{{documentation/versioncheck}}&amp;lt;/noinclude&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;noinclude&amp;gt;{{documentation/versioncheck}}&amp;lt;/noinclude&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This page discusses Resampling of image and model data. [&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;http://wiki.slicer.org/slicerWiki/index.php/&lt;/del&gt;Category:Documentation/{{documentation/version}}/Modules/Registration '''See here for an overview of registration methods'''].&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This page discusses Resampling of image and model data. [&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[&lt;/ins&gt;Category:Documentation/{{documentation/version}}/Modules/Registration&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;|&lt;/ins&gt;'''See here for an overview of registration methods'''&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;]&lt;/ins&gt;].&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= Transforms and how they are displayed in 3DSlicer =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= Transforms and how they are displayed in 3DSlicer =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Grundlett</name></author>
		
	</entry>
	<entry>
		<id>https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37906&amp;oldid=prev</id>
		<title>Meier: /* Nesting &amp; Hardening Transforms */</title>
		<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37906&amp;oldid=prev"/>
		<updated>2014-05-06T21:01:36Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Nesting &amp;amp; Hardening Transforms&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 21:01, 6 May 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l37&quot; &gt;Line 37:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 37:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening is not the same as resampling''': in case of linear transforms, the new orientation is added to the physical orientation stored in the image header, without actually resampling the data itself. This is preferable in most cases as it avoids data degradation from interpolation artifacts associated with resampling. If you '''do''' need the transformed dataset resampled, use one of the resampling modules described below.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening is not the same as resampling''': in case of linear transforms, the new orientation is added to the physical orientation stored in the image header, without actually resampling the data itself. This is preferable in most cases as it avoids data degradation from interpolation artifacts associated with resampling. If you '''do''' need the transformed dataset resampled, use one of the resampling modules described below.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening''' is currently supported for volumes inside BSpline transforms, but '''not''' for the transform itself, i.e. the image on the right shows which hardening will work and which will not. Hardening cannot currently be used to concatenate linear and BSpline or multiple BSpline transforms.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening''' is currently supported for volumes inside BSpline transforms, but '''not''' for the transform itself, i.e. the image on the right shows which hardening will work and which will not. Hardening cannot currently be used to concatenate linear and BSpline or multiple BSpline transforms.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;br&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;br&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;

&lt;!-- diff cache key mediawiki_slicer:diff::1.12:old-37905:rev-37906 --&gt;
&lt;/table&gt;</summary>
		<author><name>Meier</name></author>
		
	</entry>
	<entry>
		<id>https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37905&amp;oldid=prev</id>
		<title>Meier: /* Nesting &amp; Hardening Transforms */</title>
		<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37905&amp;oldid=prev"/>
		<updated>2014-05-06T21:01:06Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Nesting &amp;amp; Hardening Transforms&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
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				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 21:01, 6 May 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l32&quot; &gt;Line 32:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 32:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= Nesting &amp;amp; Hardening Transforms =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= Nesting &amp;amp; Hardening Transforms =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Image:Registration_NestedTransformHardening.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline).&amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline).&amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Image:Registration_NestedTransformHardening.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Hardening''' is a term used to describe applying a transform or effect to a dataset. In the  [[Documentation/{{documentation/version}}/Modules/Data|''Data'' module]] a right-click onto a node produces a context-menu, which lists ''Harden Transform'' as an option if a nesting is present. Two important points to remember about this option:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Hardening''' is a term used to describe applying a transform or effect to a dataset. In the  [[Documentation/{{documentation/version}}/Modules/Data|''Data'' module]] a right-click onto a node produces a context-menu, which lists ''Harden Transform'' as an option if a nesting is present. Two important points to remember about this option:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening is not the same as resampling''': in case of linear transforms, the new orientation is added to the physical orientation stored in the image header, without actually resampling the data itself. This is preferable in most cases as it avoids data degradation from interpolation artifacts associated with resampling. If you '''do''' need the transformed dataset resampled, use one of the resampling modules described below.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening is not the same as resampling''': in case of linear transforms, the new orientation is added to the physical orientation stored in the image header, without actually resampling the data itself. This is preferable in most cases as it avoids data degradation from interpolation artifacts associated with resampling. If you '''do''' need the transformed dataset resampled, use one of the resampling modules described below.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Meier</name></author>
		
	</entry>
	<entry>
		<id>https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37904&amp;oldid=prev</id>
		<title>Meier: /* Nesting &amp; Hardening Transforms */</title>
		<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37904&amp;oldid=prev"/>
		<updated>2014-05-06T21:00:41Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Nesting &amp;amp; Hardening Transforms&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 21:00, 6 May 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l36&quot; &gt;Line 36:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 36:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Hardening''' is a term used to describe applying a transform or effect to a dataset. In the  [[Documentation/{{documentation/version}}/Modules/Data|''Data'' module]] a right-click onto a node produces a context-menu, which lists ''Harden Transform'' as an option if a nesting is present. Two important points to remember about this option:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Hardening''' is a term used to describe applying a transform or effect to a dataset. In the  [[Documentation/{{documentation/version}}/Modules/Data|''Data'' module]] a right-click onto a node produces a context-menu, which lists ''Harden Transform'' as an option if a nesting is present. Two important points to remember about this option:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening is not the same as resampling''': in case of linear transforms, the new orientation is added to the physical orientation stored in the image header, without actually resampling the data itself. This is preferable in most cases as it avoids data degradation from interpolation artifacts associated with resampling. If you '''do''' need the transformed dataset resampled, use one of the resampling modules described below.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening is not the same as resampling''': in case of linear transforms, the new orientation is added to the physical orientation stored in the image header, without actually resampling the data itself. This is preferable in most cases as it avoids data degradation from interpolation artifacts associated with resampling. If you '''do''' need the transformed dataset resampled, use one of the resampling modules described below.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening''' is currently supported for volumes inside BSpline transforms, but '''not''' for the transform itself, i.e. the image on the right shows which hardening will work and which will not. Hardening cannot be used to concatenate linear and BSpline or multiple BSpline transforms.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening''' is currently supported for volumes inside BSpline transforms, but '''not''' for the transform itself, i.e. the image on the right shows which hardening will work and which will not. Hardening cannot &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;currently &lt;/ins&gt;be used to concatenate linear and BSpline or multiple BSpline transforms.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;br&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;br&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;br&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Meier</name></author>
		
	</entry>
	<entry>
		<id>https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37903&amp;oldid=prev</id>
		<title>Meier: /* Nesting &amp; Hardening Transforms */</title>
		<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37903&amp;oldid=prev"/>
		<updated>2014-05-06T20:59:36Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Nesting &amp;amp; Hardening Transforms&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 20:59, 6 May 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l33&quot; &gt;Line 33:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 33:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline).&amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline).&amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Image:Registration_NestedTransformHardening.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Hardening''' is a term used to describe applying a transform or effect to a dataset. In the  [[Documentation/{{documentation/version}}/Modules/Data|''Data'' module]] a right-click onto a node produces a context-menu, which lists ''Harden Transform'' as an option if a nesting is present. Two important points to remember about this option:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Hardening''' is a term used to describe applying a transform or effect to a dataset. In the  [[Documentation/{{documentation/version}}/Modules/Data|''Data'' module]] a right-click onto a node produces a context-menu, which lists ''Harden Transform'' as an option if a nesting is present. Two important points to remember about this option:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening is not the same as resampling''': in case of linear transforms, the new orientation is added to the physical orientation stored in the image header, without actually resampling the data itself. This is preferable in most cases as it avoids data degradation from interpolation artifacts associated with resampling. If you '''do''' need the transformed dataset resampled, use one of the resampling modules described below.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening is not the same as resampling''': in case of linear transforms, the new orientation is added to the physical orientation stored in the image header, without actually resampling the data itself. This is preferable in most cases as it avoids data degradation from interpolation artifacts associated with resampling. If you '''do''' need the transformed dataset resampled, use one of the resampling modules described below.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening''' is currently supported for volumes inside BSpline transforms, but '''not''' for the transform itself, i.e. the image on the right shows which hardening will work and which will not. Hardening cannot be used to concatenate linear and BSpline or multiple BSpline transforms.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;*'''hardening''' is currently supported for volumes inside BSpline transforms, but '''not''' for the transform itself, i.e. the image on the right shows which hardening will work and which will not. Hardening cannot be used to concatenate linear and BSpline or multiple BSpline transforms.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

&lt;!-- diff cache key mediawiki_slicer:diff::1.12:old-37899:rev-37903 --&gt;
&lt;/table&gt;</summary>
		<author><name>Meier</name></author>
		
	</entry>
	<entry>
		<id>https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37899&amp;oldid=prev</id>
		<title>Meier at 20:46, 6 May 2014</title>
		<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37899&amp;oldid=prev"/>
		<updated>2014-05-06T20:46:16Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 20:46, 6 May 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l33&quot; &gt;Line 33:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 33:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline).&amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline).&amp;lt;br&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Hardening''' is a term used to describe applying a transform or effect to a dataset. In the&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;'''Hardening''' is a term used to describe applying a transform or effect to a dataset. In the &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt; [[Documentation/{{documentation/version}}/Modules/Data|''Data'' module]] a right-click onto a node produces a context-menu, which lists ''Harden Transform'' as an option if a nesting is present. Two important points to remember about this option:&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;*'''hardening is not the same as resampling''': in case of linear transforms, the new orientation is added to the physical orientation stored in the image header, without actually resampling the data itself. This is preferable in most cases as it avoids data degradation from interpolation artifacts associated with resampling. If you '''do''' need the transformed dataset resampled, use one of the resampling modules described below.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;*'''hardening''' is currently supported for volumes inside BSpline transforms, but '''not''' for the transform itself, i.e. the image on the right shows which hardening will work and which will not. Hardening cannot be used to concatenate linear and BSpline or multiple BSpline transforms.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Meier</name></author>
		
	</entry>
	<entry>
		<id>https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37898&amp;oldid=prev</id>
		<title>Meier: /* Nesting Transforms */</title>
		<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37898&amp;oldid=prev"/>
		<updated>2014-05-06T20:39:43Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Nesting Transforms&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 20:39, 6 May 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l30&quot; &gt;Line 30:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 30:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;So the effect of a linear transform is therefore visible right away. '''Nonlinear (BSpline) transforms are not visualized on the fly and must be resampled to see.''' Hence if you calculate a BSpline transform inside BRAINSfit and then place a volume inside this transform, you will '''not''' see an effect, because the Viewer can apply only linear transforms directly. So to see a nonrigid transform you must resample the image. We therefore recommend to always select an output volume when running a nonrigid registration. To apply a transform and resample an image see the [[Documentation/{{documentation/version}}/Modules/Resampling#Resampling_via_a_spatial_transform|resampling via a spatial transform]]section below.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;So the effect of a linear transform is therefore visible right away. '''Nonlinear (BSpline) transforms are not visualized on the fly and must be resampled to see.''' Hence if you calculate a BSpline transform inside BRAINSfit and then place a volume inside this transform, you will '''not''' see an effect, because the Viewer can apply only linear transforms directly. So to see a nonrigid transform you must resample the image. We therefore recommend to always select an output volume when running a nonrigid registration. To apply a transform and resample an image see the [[Documentation/{{documentation/version}}/Modules/Resampling#Resampling_via_a_spatial_transform|resampling via a spatial transform]]section below.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= Nesting Transforms =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= Nesting &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;amp; Hardening &lt;/ins&gt;Transforms =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[Image:Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline)&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;.&amp;lt;br&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;'''Hardening''' is a term used to describe applying a transform or effect to a dataset. In the&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Meier</name></author>
		
	</entry>
	<entry>
		<id>https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37897&amp;oldid=prev</id>
		<title>Meier: /* Nesting Transforms */</title>
		<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37897&amp;oldid=prev"/>
		<updated>2014-05-06T20:37:40Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Nesting Transforms&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 20:37, 6 May 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l31&quot; &gt;Line 31:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 31:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= Nesting Transforms =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= Nesting Transforms =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Image:Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline)&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline)&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Image:Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Meier</name></author>
		
	</entry>
	<entry>
		<id>https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37896&amp;oldid=prev</id>
		<title>Meier: /* Nesting Transforms */</title>
		<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37896&amp;oldid=prev"/>
		<updated>2014-05-06T20:37:20Z</updated>

		<summary type="html">&lt;p&gt;&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Nesting Transforms&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 20:37, 6 May 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l31&quot; &gt;Line 31:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 31:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= Nesting Transforms =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= Nesting Transforms =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;like this&lt;/del&gt;:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;as shown on the image on the right (example of an MRI registered to a CT in 2 steps of first affine, then BSpline)&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;[[Image&lt;/ins&gt;:&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Registration_TransformNesting.png|200px|right|example of nested transforms for an affine followed by a BSpline. Note that the order matters]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Meier</name></author>
		
	</entry>
	<entry>
		<id>https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37893&amp;oldid=prev</id>
		<title>Meier at 20:22, 6 May 2014</title>
		<link rel="alternate" type="text/html" href="https://www.slicer.org/w/index.php?title=Documentation/Nightly/Modules/Resampling&amp;diff=37893&amp;oldid=prev"/>
		<updated>2014-05-06T20:22:22Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 20:22, 6 May 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l29&quot; &gt;Line 29:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 29:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;So the effect of a linear transform is therefore visible right away. '''Nonlinear (BSpline) transforms are not visualized on the fly and must be resampled to see.''' Hence if you calculate a BSpline transform inside BRAINSfit and then place a volume inside this transform, you will '''not''' see an effect, because the Viewer can apply only linear transforms directly. So to see a nonrigid transform you must resample the image. We therefore recommend to always select an output volume when running a nonrigid registration. To apply a transform and resample an image see the [[Documentation/{{documentation/version}}/Modules/Resampling#Resampling_via_a_spatial_transform|resampling via a spatial transform]]section below.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;So the effect of a linear transform is therefore visible right away. '''Nonlinear (BSpline) transforms are not visualized on the fly and must be resampled to see.''' Hence if you calculate a BSpline transform inside BRAINSfit and then place a volume inside this transform, you will '''not''' see an effect, because the Viewer can apply only linear transforms directly. So to see a nonrigid transform you must resample the image. We therefore recommend to always select an output volume when running a nonrigid registration. To apply a transform and resample an image see the [[Documentation/{{documentation/version}}/Modules/Resampling#Resampling_via_a_spatial_transform|resampling via a spatial transform]]section below.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;= Nesting Transforms =&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;quot;Nesting&amp;quot; transforms is a term we use to describe the joining / concatenation of multiple transforms. This is supported in Slicer to some degree. The important thing to remember is that '''the order matters''', i.e. A*B is '''not''' the same as B*A. For example, a typical application is that you first perform a rigid or affine registration, followed by a separate nonrigid BSpline registration. Although you can combine both in one, there are cases where it is useful to separate the two, e.g. if robustness is an issue and there is a chance the linear portion might fail, or for visualization, when you want to look at the deformations incurring from the BSpline, you need to have them separate from the global &amp;quot;bulk&amp;quot; transform to see detail. So in this case you need to nest the '''Affine''' inside the '''BSpline''', not vice versa. If this seems counter-intuitive, remember that hierarchies are read/applied from the inside out, i.e. the first transform applied is the Affine and '''then''' the BSpline. So the arrangement within the data-module should look like this:&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt; &lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;= What we mean by ''Resampling'' =&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Meier</name></author>
		
	</entry>
</feed>