Talk:Scale space

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I’m quite concerned about the rewrite of this article. It has changed the scope of ”scale-space” quite dramatically– from the way it is used by the computer vision community for 2-D and 3-D images today towards an emphasis on coarse-to-fine segmentation approaches for 1-D signals as it was proposed in the 1980’s and towards implementation aspects.

If implementation issues should be emphasized, I would suggest that this topic could be addressed in another article on ”scale-space implementation”. Moreover, if the notion of ”scale-space segmentation” and coarse-to-fine approaches should be addressed, these topics could also be developed in another subarticle. There have been quite a number of works in these areas, and I would say that the current article does not give a balanced view of the different approaches that have been investigated over the years.

The approach I took when rewriting this article was to give a brief overview of ”scale-space” as it is used by the computer vision community today, and to list some of the main references in the field for a new reader to get familiar with the topic. The previous selection of ”References” was organised in this way. Then, I also listed some main references in related areas and listed those under ”Related work”.

Tpl 09:58, 8 June 2006 (UTC)

Tpl, my main problem with the article, which may be a problem with the current concept in the vision community, to some extent, is the over-reliance on the formal derivation of the uniqueness of the Gaussian based on too many constraining properties. You ossify that problem if you insist on the formal Gaussian in this article and relegate everything else to "implementation" issues. A number of the studies you cite have proven things about the characteristic function (Fourier transform) or generating function (Z transform) of the impulse response of an acceptable smoothing function based on various sensible criteria, and the conditions I cited for Z-plane poles and zeros come out of that, with as much formal validity as the unique Gaussian, for an appropriate set of constraints. That, I think, belongs in the main article, to help break the habit of thinking that only the Gaussian is ideally suited for scale space. Also, what do you mean by "causality" with respect to Gaussian smoothing? Isn't a Gaussian infinite in both directions and therefore not causal? As to the scale-space segmentation article, that's probably a good idea, since it's primarily 1D while the rest is primarily 2D. Dicklyon 16:45, 8 June 2006 (UTC)

ps: You don't have a user page, but I assume you are Tony P. Lindeberg, and therefore much more knowledgable about this stuff than I am. I recently ordered a copy of your (expensive!) book so I can get caught up on the thinking in this community. I used to work with Witkin at SPAR, and too much of my thinking is probably too old as a result of not having followed all your good work since then (but some, anyway). Dicklyon 16:53, 8 June 2006 (UTC)

I think that your comments are useful. As you point out, there are several theories and approaches that are not mentioned in the current article. On the other hand, if one would develop these notions the presentation might become rather technical such that the overview is lost. To remedy your concern, I have included another article on multi-scale approaches intended to describe some of the other multi-scale approaches that prevalent in the field. So far, it only lists the special scale-space theory for one-dimensional signals, but there are other theories that could be included such as the scale invariant semi-groups studied by Pauwels.

Concerning your question about "causality", there is an unfortunate confusion about terminology in this respect. In Koenderinks derivation of the uniqueness of the Gaussian kernel in 2-D, he makes use of a property of level curves over scales which he refers to as "causality". This notion bears som relation to causality as it is used in signal processing, but has nothing to do with one-sided kernels that do not access the future.

Concerning properties of poles, please fill in these details in the article on multi-scale approaches if you feel that this description is useful to others. Please, let me know your opinions on this compromise.

Tpl 12:45, 9 June 2006 (UTC)

Now that you've got it all organized into articles, why don't we just combine those as sections? Dicklyon 17:59, 10 June 2006 (UTC)

Well, there is quite a difference in style and levels of details. The overall scale-space article is at a comprehensive overview level describing scale-space methods as they are used today in the computer vision community, while the scale-space implementation article is more technical, the scale-space axioms article is more mathematical, the scale-space segmentation article is more historical and the multi-scale approaches article is not complete in its present form. Within one article, I think that it is importance to keep the level of presentation reasonably consistent. To merge these five articles into one article that is consistent in terms of mathematical and algorithmic detail as well as references would require a substantial amount of work and would be imply writing a longer review article. Then, I'm afraid that the encyclopedia style would be lost.

Tpl 10:55, 11 June 2006 (UTC)

I don't see the problem. To me, your main article "comprehensive overview" is actually rather deep and narrow. I'd like to see more breadth in the main article, even if different sections are at different levels of sophistication; that's how good wikipedia articles usually evolve.

Anyone else have opinions here? Dicklyon 20:14, 11 June 2006 (UTC)

Regarding the related topic of wavelets the presentation is split into several articles (continuous wavelet transform, discrete wavelet transform, multiresolution analysis) as well as a large number of pages for various types of specific wavelets. If we follow a similar approach regarding scale-space there could be more articles than those who are written up yet. For several sentences in the current scale space article it would be possible to write an entire article that explains the notion in more detail, including mathematical definitions, algorithmic details and a richer set of refernces.

[edit] N-jets

This term N-jets is used without definition. Can someone please add an explanation of exactly what it is. Dicklyon 05:16, 26 August 2006 (UTC)

Now, there is a link from the first occurrence of the word N-jet to a new article on the topic. More could definitely be added, but it is at least a first outline. Tpl 14:07, 4 September 2006 (UTC)

[edit] Arguments against the suggested merge

Concerning the suggestion to merge the current scale-space article with the articles on scale-space axioms and scale-space implementation, I'm sorry to say that I'm strongly agains this suggestion. The level of presentation is substantially different in each one of these articles, while the individual articles are now self-consistently in a uniform style and level of presentation. The scale-space article is an overview article, while the articles on scale-space axioms and scale-space implementation are very detailed and technical. If one would try to merge these articles, the result would become extremely unbalanced. Please, also note that the current scale-space article refers to other articles concerning more technical contents within the area of scale-space, in particular the articles on blob detection, corner detection, ridge detection, edge detection, scale-space segmentation and affine shape adaptation. Tpl 08:42, 16 January 2007 (UTC)

I'm OK either way on this. It's not bad as it is. Tpl had split it up after I had added a lot of new content to the original one article, and I agree it works this way. Dicklyon 16:25, 16 January 2007 (UTC)

Shouldn't we have a snippet on scale-space axioms and scale-space implementation at least? I understand how these topics deserve an article of their own, but the scale space article should definitely have at least a "preview" of the other articles as the axioms (esp) are key to understanding the theory. Showing snippets of "subarticles" seems to be a standard wikipedia format.

Now, I have added five pointers or "snippets" of topics that are treated in more detail in other articles. Please, let me know about your reactions to this. Tpl 10:32, 31 January 2007 (UTC)