Talk:Structure tensor

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paper?

This article seems to be writen like an academic paper, and is therefore, not very encyclopedic. The original author or some other party should attempt to modify the article to make it read more like an encyclopedic text. CB Droege 19:55, 21 September 2006 (UTC)[reply]

The purpose of the page is both as an introduction and tutorial on structure tensors. I appreciate the feedback, nevertheless, this was not a published academic paper and the subject matter is geared especially to those needing help with structure tensors for computer vision in a reference, i.e. encyclopedic, fashion. I am open to specific suggestions as to how to make it "...read more like an encyclopedic text" other than adding a history section. Thanks again for the feedback. S. Arseneau, 22 September 2006

- This then is the problem with the article. It is a well done article, but Wikipedia is a place for encyclopedic articles, not tutorials or instructions. The article needs some work before it is apropriate for this context. CB Droege 14:09, 25 September 2006 (UTC)[reply]

Not fully wikified but (arguably) looking better and good enough until edited? Rich257 20:19, 25 September 2006 (UTC)[reply]

This article appears to have been taken from this page, almost verbatim: http://www.cs.cmu.edu/~sarsen/structureTensorTutorial/ 147.4.36.7 (talk) —Preceding undated comment added 18:27, 13 July 2010 (UTC).[reply]

Bogus theory?

The discussion about the eigenvalues and eigenvectors of this "structure tensor" seems to be nonsense.
The eigenvectors of the matrix S are the direction of the gradient and the same rotated 90 degrees. The eigenvalues are simply $\lambda _{1}=I_{x}^{2}+I_{y}^{2}$ (the square of the gradient modulus) and $\lambda _{2}=0$ , as one can check by the definitions. Thus the "coherence index" is simply "gradient != (0,0)". So what is the point of all this mathematical mumbo-jumbo (other than to publish a few more papers)?
This phrase seems to be meaningless,too: "A significant difference between a tensor and a matrix, which is also an array, is that a tensor represents a physical quantity the measurement of which is no more influenced by the coordinates with which one observes it than one can account for it." The matrix S obviously depends on the coordinate system.
--Jorge Stolfi (talk) 15:45, 19 August 2010 (UTC) [reply]

PS. The same holds for the three-dimensional case. The eigenvectors are the direction of the gradient and any two unit orthogonal vectors perpendicular to it. The eigenvalues are $\lambda _{1}=I_{x}^{2}+I_{y}^{2}+I_{z}^{2}$ and $\lambda _{2}=\lambda _{3}=0$ .
If no one disagrees, I will try to fix the article.
--Jorge Stolfi (talk) 15:55, 19 August 2010 (UTC)[reply]

Presumably what the author writes as $I_{x}^{2}$ is not the square of something, but rather the integral of the derivative Ix^2 within a window; and ditto for the other three elements of S. That seems to be the case in many applications. Yet the S matrix seems to be used in some cases as a surrogate of the Hessian of $I^{2}$ , which includes S but second derivatives too. --Jorge Stolfi (talk) 17:41, 19 August 2010 (UTC)[reply]

I have fixed the definition as above (added the missing integrals). I will soon be restoring the deleted content, with the proper fixes. --Jorge Stolfi (talk) 23:59, 19 August 2010 (UTC)[reply]