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{{WikiProject Robotics|importance=mid|attention=no}}
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==Error on 3D structure tensor image==
It seems that there is a little confusion between the images for the 3D structure tensor. The description for the surfel image seems wrong, with the egein value relation being the one for the line, and conversly for the line below. The ellipsoid images of the right seems also messed up, or am I missing something ? <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/185.116.129.142|185.116.129.142]] ([[User talk:185.116.129.142#top|talk]]) 14:59, 24 March 2023 (UTC)</small> <!--Autosigned by SineBot-->
==Conceptual Explanation Request==
IMO this article (like many other in it's class) is in desperate need of a more in depth conceptual summary. It's wonderful that we have these exact mathematical descriptions, but the concepts for understanding how some of these things work do not require a degree in math. However *reading* about those concepts in these articles *does*.
--[[User:Catskul|Andy]] ([[User talk:Catskul|talk]]) 21:26, 24 June 2011 (UTC)
==paper?==
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When referencing material from a rather extensive book, I included specific page number to make it possible for others to find the specific statements that are relevant for this article. This explanatory text was, however, removed by a previous editor. Does anyone know about a better way of inserting explicit page and section references, e.g. on the form (Author 2010; section 9.5), when referencing a particular section or page in a book? [[User:Tpl|Tpl]] ([[User talk:Tpl|talk]]) 08:15, 21 August 2010 (UTC)
* Sorry about that,too. Page and section references can often be better obtained from the book index and table-of-contents, or (for online reading) with search tools; so the value for readers who may want to check them should be weighted against the cost of cluttering the reference list with extra entries.<br/> An alternative to creating a separate <nowiki><ref>...</ref></nowiki> is the [[:Template:rp|"rp" template]]: the call <nowiki>{{rp|ch.23}}</nowiki> after the <nowiki></ref></nowiki> generates a superscript annotation, as in <sup>[1]</sup>{{rp|ch.23}}. Hope it helps, --[[User:Jorge Stolfi|Jorge Stolfi]] ([[User talk:Jorge Stolfi|talk]]) 23:17, 22 August 2010 (UTC)
==Anisotropy is too abstract==
The direction of gradient varies in the neighborhood of the pixel at the curved edge. Is it better to talk about curvature instead of anisotropy? The formula for curvature can be easily found from the distribution of gradient. See for example Documentation tab at [http://outliner.codeplex.com/documentation Outliner project] --[[User:Wladik Derevianko|Wladik Derevianko]] ([[User talk:Wladik Derevianko|talk]]) 21:32, 2 May 2011 (UTC)
:Curvature is only one aspect of anisotropy. If there are variations in the direction/orientation of the gradient it may also be related to, e.g., presens of noise or of two or more lines/edges in the neighborhood. --[[User:KYN|KYN]] ([[User talk:KYN|talk]]) 07:32, 3 May 2011 (UTC)
==Typo==
"If we keep the local scale parameter s fixed [...]" should be "If we keep the local scale parameter t fixed [...]" <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/92.230.48.68|92.230.48.68]] ([[User talk:92.230.48.68|talk]]) 23:07, 8 March 2012 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
== Is it a tensor? ==
This matrix seems to not be a proper tensor in the sense of obeying rotational transformation rules.
Anyone care to explain otherwise? <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/132.3.33.81|132.3.33.81]] ([[User talk:132.3.33.81|talk]]) 16:01, 1 October 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
Following that thought, the article begins "in mathematics", yet is entirly focused on image processing applications -- is there any reference to a formal treatment of this topic outside of computer graphics? <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/132.3.33.80|132.3.33.80]] ([[User talk:132.3.33.80|talk]]) 16:19, 1 October 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
:It does not strictly satisfy the expected transformation properties of a proper [[tensor]]. But note that it is, in principle, constructed as the outer product of the image gradient and, hence, forms a 2nd order covariant tensor. This is then modified by computing a local average, typically weighted by a Gaussian kernel. As a result the structure tensor no longer transforms as a proper tensor with respect to scaling of the coordinate system. However, it transforms like a tensor with respect to rotation transformations(!), and this is what counts for the applications where it is used. To be useful also for various image scales, the structure tensor can be applied to a [[scale space]], and this is done in some applications. Haven't seen it used in computer graphics though. --[[User:KYN|KYN]] ([[User talk:KYN|talk]]) 18:09, 1 October 2013 (UTC)
: Thanks -- I had trouble proving out the rotational transformation but I've got it now. Rotation invariance should be noted in the article, though I obviously lack the expertise to work on it. <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/132.3.33.79|132.3.33.79]] ([[User talk:132.3.33.79|talk]]) 20:09, 1 October 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
: The rotation transformation relies on the Gaussian kernel (called w in the article) being circular symmetric, something that is not mentioned in the intial definition of the structure tensor in the aricle. --[[User:KYN|KYN]] ([[User talk:KYN|talk]]) 20:23, 1 October 2013 (UTC)
== Possible error in equation? ==
Is there an incorrect equation in the section Complex Version?
The expression of <math>\lambda_2</math> (in terms of <math>\kappa_{20}</math> and <math>\kappa_{11}</math>) seems incorrect to me:
In my opinion it should be:
<math display="block">(|\kappa_{20}|-\kappa_{11})/2=\lambda_2</math>
instead of
<math display="block">(\kappa_{20}-|\kappa_{11}|)/2=\lambda_2</math>
as is stated there. <!-- Template:Unsigned --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Cocus|Cocus]] ([[User talk:Cocus#top|talk]] • [[Special:Contributions/Cocus|contribs]]) 11:52, 26 February 2018 (UTC)</small> <!--Autosigned by SineBot-->
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