Talk:Structure tensor

message: 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 ?  — Preceding unsigned comment added by 185.116.129.142 (talk) 14:59, 24 March 2023 (UTC)
thread_title: Error on 3D structure tensor image

message: 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*.
--Andy (talk) 21:26, 24 June 2011 (UTC)
thread_title: Conceptual Explanation Request

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

message: * 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)
thread_title: Copied from net doc?

message: 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)
thread_title:  Fixed incomplete definition 

message: 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)
thread_title: Removed passage on coordinate invariance

message: I removed this paragraph and picture, since they do not seem to be understandable to readers who do not already know what they mean:  "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)
thread_title: Removed passage on tensor addition

message: 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)
thread_title:  Can the coherence index be defined on uniform regions? 

message: 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)
thread_title:  Name "Second moment matrix" ambigous/improper? 

message: 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)
thread_title:  The multi-scale structure tensor 

message: 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)
thread_title: References to specific pages in references

message: 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 Outliner project --Wladik Derevianko (talk) 21:32, 2 May 2011 (UTC)
replies: text: 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.  --KYN (talk) 07:32, 3 May 2011 (UTC)
thread_title: Anisotropy is too abstract

message: "If we keep the local scale parameter s fixed [...]" should be "If we keep the local scale parameter t fixed [...]"  — Preceding unsigned comment added by 92.230.48.68 (talk) 23:07, 8 March 2012 (UTC)
thread_title: Typo

message: This matrix seems to not be a proper tensor in the sense of obeying rotational transformation rules.
Anyone care to explain otherwise?  — Preceding unsigned comment added by 132.3.33.81 (talk) 16:01, 1 October 2013 (UTC)
replies: text: 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.  --KYN (talk) 18:09, 1 October 2013 (UTC)

text: 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.  — Preceding unsigned comment added by 132.3.33.79 (talk) 20:09, 1 October 2013 (UTC)

text: 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.  --KYN (talk) 20:23, 1 October 2013 (UTC)
thread_title:  Is it a tensor? 

message: Is there an incorrect equation in the section Complex Version?
The expression of \lambda_2 (in terms of \kappa_{20} and \kappa_{11}) seems incorrect to me:
In my opinion it should be:
(|\kappa_{20}|-\kappa_{11})/2=\lambda_2
instead of
(\kappa_{20}-|\kappa_{11}|)/2=\lambda_2
as is stated there.  — Preceding unsigned comment added by Cocus (talk • contribs) 11:52, 26 February 2018 (UTC)
thread_title:  Possible error in equation?