Stability and likelihood of views of three dimensional objects

Daphna Weinshall; Michael Werman; Naftali Tishby

doi:10.1007/3-540-57956-7_3

Stability and likelihood of views of three dimensional objects

Daphna Weinshall, Michael Werman, Naftali Tishby

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Scopus citations

Abstract

Can we say anything general about the distribution of two dimensional views of general three dimensional objects? In this paper we present a first formal analysis of the stability and likelihood of two dimensional views (under weak perspective projection) of three dimensional objects. This analysis is useful for various aspects of object recognition and database indexing. Examples are Bayesian recognition; indexing to a three dimensional database by invariants of two dimensional images; the selection of "good" templates that may reduce the complexity of correspondence between images and three dimensional objects; and ambiguity resolution using generic views. We show the following results: (1) Both the stability and likelihood of views do not depend on the particular distribution of points inside the object; they both depend on only three numbers, the three second moments of the object. (2) The most stable and the most likely views are the same view, which is the "flattest" view of the object. Under orthographic projection, we also show: (3) the distance between one image to another does not depend on the position of its viewpoint with respect to the object, but only on the (geodesic) distance between the viewpoints on the viewing sphere. We demonstrate these results with real and simulated data.

Original language	English
Title of host publication	Computer Vision — ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings
Editors	Jan-Olof Eklundh
Publisher	Springer Verlag
Pages	24-35
Number of pages	12
ISBN (Print)	9783540579564
DOIs	https://doi.org/10.1007/3-540-57956-7_3
State	Published - 1994
Event	3rd European Conference on Computer Vision, ECCV 1994 - Stockholm, Sweden Duration: 2 May 1994 → 6 May 1994

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	800 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd European Conference on Computer Vision, ECCV 1994
Country/Territory	Sweden
City	Stockholm
Period	2/05/94 → 6/05/94

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1994.

Access to Document

10.1007/3-540-57956-7_3

Cite this

Weinshall, D., Werman, M., & Tishby, N. (1994). Stability and likelihood of views of three dimensional objects. In J.-O. Eklundh (Ed.), Computer Vision — ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings (pp. 24-35). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 800 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-57956-7_3

Weinshall, Daphna ; Werman, Michael ; Tishby, Naftali. / Stability and likelihood of views of three dimensional objects. Computer Vision — ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings. editor / Jan-Olof Eklundh. Springer Verlag, 1994. pp. 24-35 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Can we say anything general about the distribution of two dimensional views of general three dimensional objects? In this paper we present a first formal analysis of the stability and likelihood of two dimensional views (under weak perspective projection) of three dimensional objects. This analysis is useful for various aspects of object recognition and database indexing. Examples are Bayesian recognition; indexing to a three dimensional database by invariants of two dimensional images; the selection of {"}good{"} templates that may reduce the complexity of correspondence between images and three dimensional objects; and ambiguity resolution using generic views. We show the following results: (1) Both the stability and likelihood of views do not depend on the particular distribution of points inside the object; they both depend on only three numbers, the three second moments of the object. (2) The most stable and the most likely views are the same view, which is the {"}flattest{"} view of the object. Under orthographic projection, we also show: (3) the distance between one image to another does not depend on the position of its viewpoint with respect to the object, but only on the (geodesic) distance between the viewpoints on the viewing sphere. We demonstrate these results with real and simulated data.",

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Weinshall, D , Werman, M & Tishby, N 1994, Stability and likelihood of views of three dimensional objects. in J-O Eklundh (ed.), Computer Vision — ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 800 LNCS, Springer Verlag, pp. 24-35, 3rd European Conference on Computer Vision, ECCV 1994, Stockholm, Sweden, 2/05/94. https://doi.org/10.1007/3-540-57956-7_3

Stability and likelihood of views of three dimensional objects. / Weinshall, Daphna ; Werman, Michael; Tishby, Naftali.
Computer Vision — ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings. ed. / Jan-Olof Eklundh. Springer Verlag, 1994. p. 24-35 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 800 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Weinshall D , Werman M, Tishby N. Stability and likelihood of views of three dimensional objects. In Eklundh JO, editor, Computer Vision — ECCV 1994 - 3rd European Conference on Computer Vision, Proceedings. Springer Verlag. 1994. p. 24-35. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-57956-7_3

Stability and likelihood of views of three dimensional objects

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