704:- 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 Knowledge article to include a Wolfram demonstration on that behalf. Note that I also embedded a demonstration at the
350:
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
Knowledge. With best wishes, --
550:- 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. --
299:, 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 (
940:. 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
345:- The theorem is not a lemma in Wang et al.'s work, please review this ("Theorem 1" in and in ). 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
1046:
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
294:
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
967:
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
988:
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
987:
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
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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
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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.
1103:
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.
393:- 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. --
708:
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.
1092:
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
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431:- 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:
264:
1055:"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
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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
1061:
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.
150:
258:
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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.
1053:"Integral Image Theorem", since the theorem forms a rigorous extension of the Integral Image algorithm: to generalized rectangular curves over a continuous domain.
895:
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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
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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.
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619:- 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
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323:- almost utterly beyond me - if I accept the existaence of Green's Theorem, reading of the article suggests the discrete version is original research.
1100:"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.
1087:. Since the beginning of this discussion I have performed the following changes in the article, due to the enlightening remarks of its participants:
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575:, which is not permitted on Knowledge. Do you still protest the deletion of this article? (With your support we could close this discussion per
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1009:. (A version of) the theorem seems to me to be marginally notable, trivial to state, and easy to prove. However, any reference to the
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or otherwise. Was this name made-up by the author of the wikipedia article? Does anyone think that this is something other than
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be a confusing name due to ambiguity with other discrete Green's theorems. I suggest to rename the article to the
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Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a
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Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a
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I was hoping to hear your opinion regarding this name, and discuss other name suggestions. Thank you, --
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851:"Appearance-based person reidentification in camera networks: Problem overview and current approaches"
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Journal of
Ambient Intelligence and Humanized Computing, pp. 1–25, Springer Berlin / Heidelberg, 2011
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494:- Of the 3 cited papers that appear to be peer-reviewed, I see no mention of a "Green's theorem",
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seems to be a neologism. I couldn't find any sources referring to this theorem by this moniker.
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The following discussion is an archived debate of the proposed deletion of the article below.
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in the paper. No reliable secondary sources given in the article and none found in search.--
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571:- You've verified that the name of the article and much of the content is the result of
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303:), who has used the later sections to promote his own original research on the topic.
1042:'s statement. My intention when I chose the name for this article was to mark it as
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Since there were no objections to my suggestion above, I renamed the article to the
668:, cited 4 times in the article, are one and the same, as can be verified by looking
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Nature is pleased with simplicity, and affects not the pomp of superfluous causes.
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Umm... No. Just decompose the region into rectangles and sum. Very simple stuff.
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implies two dimensions, where the general theorem is formulated to n dimensions.
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in
Proceedings of IEEE International Conference on Computer Vision (ICCV) 2007
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664:, the "Israeli mathematician" mentioned/cited in the article; and
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Wrong. The theorem is an utterly trivial consequence of the FTC.
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The above discussion is preserved as an archive of the debate.
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963:: The closest I could find to notable use of the term is
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39:). No further edits should be made to this page.
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767:removed all my self-citations from the article
765:- I request to compromise, given that I have
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896:list of Science-related deletion discussions
894:Note: This debate has been included in the
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804:"Shape and Appearance Context Modeling"
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660:, the primary author of the article;
514:sources cited by the article are not
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654:- It should also be made clear that
1013:needs to be excised, as there are
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297:Fundamental theorem of calculus
18:Knowledge:Articles for deletion
511:Wolfram Demonstrations Project
1:
727:- The article does not pass
731:, and is clearly a case of
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1117:09:25, 30 June 2011 (UTC)
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1171:Please do not modify it.
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1144:02:44, 1 July 2011 (UTC)
1098:"Integral Image Theorem"
74:Discrete Green's theorem
66:Discrete Green's theorem
60:19:30, 5 July 2011 (UTC)
32:Please do not modify it.
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1130:integral image theorem
188:Integral Image Theorem
849:Doretto, Gianfranco.
518:, nor do they prove
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1151:- GNG, OR.
1111:—Preceding
1070:—Preceding
875:|coauthors=
828:|coauthors=
776:—Preceding
737:WP:SELFCITE
631:—Preceding
400:—Preceding
259:free images
151:free images
1153:Kilmer-san
920:per nom.
790:References
520:notability
1107:amiruchka
1066:amiruchka
946:Dingo1729
877:ignored (
830:ignored (
772:amiruchka
712:amiruchka
657:Amiruchka
627:amiruchka
617:Objection
577:WP:SPEEDY
553:amiruchka
474:amiruchka
396:amiruchka
353:amiruchka
879:|author=
832:|author=
516:reliable
496:discrete
118:View log
1126:Comment
1113:undated
1072:undated
1036:Comment
985:Comment
778:undated
763:Request
702:Comment
652:Comment
633:undated
621:theorem
581:WP:SNOW
548:Comment
492:Comment
429:Comment
402:undated
391:Comment
343:Comment
321:Comment
265:WPÂ refs
253:scholar
205:protect
200:history
157:WPÂ refs
145:scholar
91:protect
86:history
1149:Delete
1044:one of
1026:(talk)
1007:Delete
970:RDBury
961:Delete
938:Delete
918:Delete
729:WP:GNG
725:Delete
579:G7 or
237:Google
209:delete
129:Google
95:delete
46:delete
1093:them.
1057:image
1021:.) —
1019:first
854:(PDF)
807:(PDF)
750:stalk
733:WP:OR
687:stalk
594:stalk
573:WP:OR
533:stalk
505:arXiv
280:JSTOR
241:books
226:views
218:watch
214:links
172:JSTOR
133:books
112:views
104:watch
100:links
16:<
1157:talk
1140:talk
1085:Keep
1015:real
1011:name
974:talk
965:this
950:talk
926:talk
922:Ozob
883:help
836:help
769:. --
735:and
674:here
672:and
670:here
508:and
420:talk
382:talk
366:talk
327:Mark
311:talk
273:FENS
247:news
222:logs
196:talk
192:edit
165:FENS
139:news
108:logs
82:talk
78:edit
56:talk
51:Cirt
48:. —
583:).
522:.
287:TWL
179:TWL
116:– (
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