Talk:Structure tensor

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)

• 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)

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

Copied from net doc?

• 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).
  • The article has now been subtantially rewritten, so this is not a problem anymore.--Jorge Stolfi (talk) 00:12, 21 August 2010 (UTC)

Fixed incomplete definition

The definition of the structure tensor in this version of the article was incomplete and misleading. The eigenvalues of the matrix S, as defined in that version, are simply $\lambda _{1}=I_{x}^{2}+I_{y}^{2}$ (the square of the gradient modulus) and $\lambda _{2}=0$; the associated eigenvectors are the direction of the gradient and the same rotated 90 degrees. Thus that "structure tensor" is sumply a complicated way to express the gradient (minus its direction), and the coherence index is simply "gradient != (0,0)".
The structure tensor makes sense only when that matrix is integrated over some neighborhood; and then it summarizes the distribution of gradient directions within that neighborhood.
I have fixed that definition, hopefuly it is correct now. I also did some general cleanup of the article; I hope I did not lose anything important.
--Jorge Stolfi (talk) 06:26, 20 August 2010 (UTC)

Removed passage on coordinate invariance

I removed this sentence, since it does not seem understandable to readers who do not already know what it means: "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) 06:26, 20 August 2010 (UTC)

Removed passage on tensor addition

I removed this paragraph and picture, since they do not seem to be understandable to readers who do not already know what they mean: "[[Image:TensorAddition.png|thumb|Tensor addition of sphere and step-edge case]]Another desirable property of the structure tensor form is that the tensor addition equates itself to the adding of the elliptical forms. For example, if the structure tensors for the sphere case and step-edge case are added, the resulting structure tensor is an elongated ellipsoid along the direction of the step-edge case.
--Jorge Stolfi (talk) 06:26, 20 August 2010 (UTC)

Can the coherence index be defined on uniform regions?

The coherence index was defined in this version of the article as 0 when the two eigenvalues were zero, that is, when the gradient was uniformly zero within the window. However, the formula for the general case does not have a definite limit when λ₁ and λ₂ both tend to 0, so any definition is equally wrong. Essentially, such a region can be regarded as totally isotropic or totally coherent, or anything in between, depending on what value one chooses to assign to 0/0.
That article also stated that "[the coherence index] is capable of distinguishing between the isotropic and uniform cases." However, when λ₁ = λ₂ > 0, the first case of the definition yields 0, the same as the second case.
pending clarification, I have removed this claim and merely noted that "some authors" define the index as 0 in the uniform case.
--Jorge Stolfi (talk) 06:40, 20 August 2010 (UTC)

Name "Second moment matrix" ambigous/improper?

How standard is the name "second moment matrix"? I ask because the name is used in other areas, such as statistics and mechanics, but the meaning does not seem to be the same. Or is it? --Jorge Stolfi (talk) 00:19, 21 August 2010 (UTC)

The term "second-moment matrix" is a frequently used terminology in computer vision, because of an interpretation of the second-moment matrix in terms of second-order spectral moments of the Fourier spectrum. Formal statements about this can be found in the book by Lindeberg (1994) and the papers by Lindeberg and Garding (1996, 1997) cited among the references. Tpl (talk) 08:05, 21 August 2010 (UTC)

The multi-scale structure tensor

Yesterday, I complemented this article with a description about the multi-scale structure tensor/second-moment matrix. I was, however, somewhat surprised by the way this text has been edited, with almost nothing left from the original text. In the revised article, there were also several statements that are incorrect and appear to be based on misunderstandings concerning the properties of this descriptor. Thus, it appears as if the revisions were not based on an understanding of the technical contents in the cited references. In the current version, I have reformulated this section with specific emphasis on explaining aspects of this theory that may not have been fully explicit for the author of the revisions. Please, let me know if the current text is more self-contained.

When editing articles in Wikipedia it is good manners to keep important material from other authors and not to delete material from others without a very good understanding of the contents. Tpl (talk) 08:15, 21 August 2010 (UTC)

References to specific pages in references

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? Tpl (talk) 08:15, 21 August 2010 (UTC)