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Tom.Reding (talk | contribs) m Remove unknown param from WP Robotics: past-selected |
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{{WikiProject
{{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==
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==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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