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This is an old revision of this page, as edited by Amiruchka (talk | contribs) at 14:27, 2 July 2011 (→Discrete Green's theorem). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Discrete Green's theorem

Discrete Green's theorem (edit | talk | history | protect | delete | links | watch | logs | views) – (View log)
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Integral Image Theorem (edit | talk | history | protect | delete | links | watch | logs | views)
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The subject of the article appears as basically a lemma in the cited sources by Wang, Doretto, et al, but it's not the main focus of these works. These papers have been cited a few times, but it looks like these citations by an large do not emphasize the result, which suggests that its significance does not rise to the level of notability required for an encyclopedia article on the subject. Indeed, the theorem in the article is a trivial consequence of the Fundamental theorem of calculus, and is a routine calculus exercise. It is not uncommon in mathematical papers to state and prove such results in the process of carrying out some greater endeavor, and that seems to be the case with this particular result. But being some small part of a larger, perhaps very significant, work does not in itself lend notability to that particular part. Moreover, Wang et al do not use the term "Green's theorem" anywhere in their article. The moniker seems to have been assigned only by the author (User:Amiruchka), who has used the later sections to promote his own original research on the topic. Sławomir Biały (talk) 14:21, 28 June 2011 (UTC)[reply]

Comment - almost utterly beyond me - if I accept the existaence of Green's Theorem, reading of the article suggests the discrete version is original research. MarkDask 15:02, 28 June 2011 (UTC)[reply]
Comment - The theorem is not a lemma in Wang et al.'s work, please review this ("Theorem 1" in [1] and in [2]). In those papers, published by the highly important computer vision conference ICCV and an important Springer peer-reviewed journal, the authors bring the theorem as a key practical and theoretical result. The theorem forms a straight-forward generalization of the Integral Image algorithm (an algorithm that has been in intense use by computer vision researchers ever since Viola and Jones's work from 2001), into continuous domains. Further, the thorem is not a "trivial consequence of the Fundamental theorem of Calculus", On the contrary: it generalizes it into higher dimensions. Part of the beauty that this theorem reveals is the combination between continuous mathematics (because the theorem is formulated over continuous domains, and involves multiple integrals etc.) and discrete math (the discrete linear combination of the antiderivative's values at the domain's corners). Wang et al.'s paper was cited 37 times within just 4 years, and at least 2 generalizations were published to the theorem. To sum up, I feel that this is a significant theorem in the computer vision community and as such, it deserves to be part of Wikipedia. With best wishes, --amiruchka
Wrong. The theorem is an utterly trivial consequence of the FTC. Sławomir Biały (talk) 15:17, 28 June 2011 (UTC)[reply]
Actually, it's even simpler: It's a trivial consequence of the additivity of the integral. This is not a deep theorem: it's a totally routine calculus exercise. Sławomir Biały (talk) 15:31, 28 June 2011 (UTC)[reply]
Comment - Dear Sławomir Biały: It's a beautiful theorem that combines the inclusion-exclusion principle (a term from discrete mathematics) and calculus. Its proof is not more trivial than that of Green's theorem: you are welcome to review Wang et al.'s proof. Thank you. --amiruchka —Preceding undated comment added 15:41, 28 June 2011 (UTC).[reply]
Umm... No. Just decompose the region into rectangles and sum. Very simple stuff. Sławomir Biały (talk) 19:26, 28 June 2011 (UTC)[reply]
Comment - I can agree that while the theorem's proof is not trivial, its formulation is quite simple. Would you hold the theorem's simplicity and elegancy against it? You are probably familiar with Sir Isaac Newton's famous quote:
--amiruchka
Comment - Of the 3 cited papers that appear to be peer-reviewed, I see no mention of a "Green's theorem", discrete or otherwise. Was this name made-up by the author of the wikipedia article? Does anyone think that this is something other than original research? Also, the arXiv and Wolfram Demonstrations Project sources cited by the article are not reliable, nor do they prove notability. Justin W Smith talk/stalk 15:41, 28 June 2011 (UTC)[reply]
Comment - The arXiv and Wolfram citations are not brought there to emphasize the theorem's significance, but rather to explain the theorem's formulation. The article's name was indeed given by me, in the memory of George Green, whose theorem resembles this one (see the discussion in the second paragraph). The reason I did not name it "Wang's thorem" or "Wang's formula" is that Wang had 4 colleagues to his published paper, where the theorem first appeared. You are welcome to suggest another name to the theorem. Thank you. --amiruchka
Speedy Delete - You've verified that the name of the article and much of the content is the result of WP:OR, which is not permitted on Wikipedia. Do you still protest the deletion of this article? (With your support we could close this discussion per WP:SPEEDY G7 or WP:SNOW). Justin W Smith talk/stalk 17:05, 28 June 2011 (UTC)[reply]
Objection - Indeed, I protest. The "no original research" citerion implies to facts, allegations, ideas, and stories - which is not the case, in my opinion, with the theorem article's name. I gave a reasonable explaination to the choice of the name, which shows respect to one of the greatest mathematicians in history, George Green, due to the similarity between this theorem and his. Anyone who argues this selection, is welcome to suggest a different name. --amiruchka —Preceding undated comment added 19:18, 28 June 2011 (UTC).[reply]
Comment - It should also be made clear that Amiruchka, the primary author of the article; Amir Shachar, the "Israeli mathematician" mentioned/cited in the article; and Amir Finkelstein, cited 4 times in the article, are one and the same, as can be verified by looking here and here. Justin W Smith talk/stalk 15:45, 28 June 2011 (UTC)[reply]
Comment - Please let me clear up the personal issues. My name used to be Amir Finkelstein until a few months ago, when I changed my last name to "Shachar" in the memory of my beloved mother, Sarit, who unfortunately passed away a year ago. My publications at Wolfram Demonstrations Project and the talk I gave at the AMS meeting were held before I changed my name. Note that the main goal of all the self-citations that I bring at the paper is not to promote my own work, but rather to make the theorem clearer for one who first encounters it. Clearly, the demonstrations at Wolfram are aimed to help people understand mathematical results, and it is not the first Wikipedia article to include a Wolfram demonstration on that behalf. Note that I also embedded a demonstration at the Integral Image algorithm's article. Please note that in the current version of the article, my name is not mentioned even once (apart from the references part). I would appreciate it if the theorem's significance could be addressed, rather than personal issues. Thank you. --amiruchka


Request - I request to compromise, given that I have removed all my self-citations from the article. --amiruchka —Preceding undated comment added 20:12, 28 June 2011 (UTC).[reply]

References

  1. ^ Wang, Xiaogang. "Shape and Appearance Context Modeling" (PDF). in Proceedings of IEEE International Conference on Computer Vision (ICCV) 2007. {{cite conference}}: Unknown parameter |booktitle= ignored (|book-title= suggested) (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
  2. ^ Doretto, Gianfranco. "Appearance-based person reidentification in camera networks: Problem overview and current approaches" (PDF). Journal of Ambient Intelligence and Humanized Computing, pp. 1–25, Springer Berlin / Heidelberg, 2011. {{cite conference}}: Unknown parameter |booktitle= ignored (|book-title= suggested) (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
Note: This debate has been included in the list of Science-related deletion discussions. —I, Jethrobot drop me a line 20:42, 28 June 2011 (UTC)[reply]
  • Leaning toward Delete. The theorem is not very deep mathematics. As others have said it's more of a simple exercise. It is also unfortunate that the author has called it Discrete Green's Theorem as it doesn't seem to be a discrete version of Green's Theorem. Yes, it's sort of related, but not really closely enough to retain the same name. Perhaps some of this material could find a home in the Integral Image article. I think the main argument for deletion is on grounds of Notability rather than Original Research. And I do wish that we weren't calling this Green's Theorem. Dingo1729 (talk) 23:35, 28 June 2011 (UTC)[reply]
  • Delete: The closest I could find to notable use of the term is this paper by Luren Yang and Fritz Albregtsen, it's been cited in the literature fairly often but I couldn't find anything in the way of a significant mention or secondary source. The article does not mention this paper and it says it's presenting a "version" of the theorem, apparently not the one given in the paper. No reliable secondary sources given in the article and none found in search.--RDBury (talk) 04:07, 29 June 2011 (UTC)[reply]
  • Comment At the very least, this article is misrepresenting this result. A quick literature search reveals that "discrete" versions of the Green's theorem have been used for fast integral computations since at least the 1980s. Apparently with different people reiventing the wheel. There appear to be no notability as a mathematical theorem. There might be a case for notability as a technique in computer science, in particular for image recognition. If not, the present material at least gives a fairly clear presentation of the technique. I'd suggest finding a good place to merge the comment. Maybe image moment.TR 10:47, 29 June 2011 (UTC)[reply]
  • Delete. (A version of) the theorem seems to me to be marginally notable, trivial to state, and easy to prove. However, any reference to the name needs to be excised, as there are real theorems called "Discrete Green's theorem". If someone can provide a plausible name, then rename (without redirect) might be suitable. (A merge would still require a rename-without-redirect first.) — Arthur Rubin (talk) 14:35, 29 June 2011 (UTC)[reply]
Comment - I agree with Arthur Rubin's statement. My intention when I chose the name for this article was to mark it as one of the discrete Green's theorems that were mentioned above (Tang's theorem from the 1980's, Yang-Albregstsen's theorem etc.), as stated in the first paragraph of the article. Although my thought was to show respect to George Green, I am absolutely in favor of renaming the article, since afterthought it might indeed be a confusing name due to ambiguity with other discrete Green's theorems. I suggest to rename the article to the "Integral Image Theorem", since the theorem forms a rigorous extension of the Integral Image algorithm: to generalized rectangular curves over a continuous domain. "Antiderivative Theorem", since the antiderivative takes a decisive part in the theorem's formulation. I changed the name "Integral Image Theorem" which is not successful afterthought, since the term image implies two dimensions, where the general theorem is formulated to n dimensions. I was hoping that those of you who feel that this theorem is significant only, perhaps, in computer vision, would be satisfied with this name, which emphasizes the theorem's main application. I was hoping to hear your opinion regarding this name, and discuss other name suggestions. Thank you, --amiruchka —Preceding undated comment added 16:22, 29 June 2011 (UTC).[reply]
  • Keep. Since the beginning of this discussion I have performed the following changes in the article, due to the enlightening remarks of its participants:
  1. I Removed all the self-citations from the article. Those citations were aimed to help one understand the theorem better and not to promote myself nor my work; however, since those citations were not well-received here, I removed them.
  2. Since there were no objections to my suggestion above, I renamed the article to the "Integral Image Theorem""Antiderivative Theorem", and removed any mention of Green's theorem (other than in the "See Also" part) from the article, due to the above discussion.
  3. I changed the formulation of the theorem such that it will match the formulation in Wang et al.'s work (the article now addresses a k-dimensional hyperplane rather than the plane). Thus, the article is now more consistent with Wang et al.'s and Doretto et al.'s works. --amiruchka —Preceding undated comment added 09:25, 30 June 2011 (UTC).[reply]
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