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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)
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