Revisiting single-view shape tensors: Theory and applications

Anat Levin; Amnon Shashua

doi:10.1007/3-540-47967-8_27

Revisiting single-view shape tensors: Theory and applications

Anat Levin, Amnon Shashua

The Rachel and Selim Benin School of Engineering and Computer Science

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

Abstract

Given the projection of a sufficient number of points it is possible to algebraically eliminate the camera parameters and obtain viewinvariant functions of image coordinates and space coordinates. These single view invariants have been introduced in the past, however, they are not as well understood as their dual multi-view tensors. In this paper we revisit the dual tensors (bilinear, trilinear and quadlinear), both the general and the reference-plane reduced version, and describe the complete set of synthetic constraints, properties of the tensor slices, reprojection equations, non-linear constraints and reconstruction formulas. We then apply some of the new results, such as the dual reprojection equations, for multi-view point tracking under occlusions.

Original language	American English
Title of host publication	Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings
Editors	Anders Heyden, Gunnar Sparr, Mads Nielsen, Peter Johansen
Publisher	Springer Verlag
Pages	399-414
Number of pages	16
ISBN (Print)	9783540437444
DOIs	https://doi.org/10.1007/3-540-47967-8_27
State	Published - 2002
Event	7th European Conference on Computer Vision, ECCV 2002 - Copenhagen, Denmark Duration: 28 May 2002 → 31 May 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2351
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th European Conference on Computer Vision, ECCV 2002
Country/Territory	Denmark
City	Copenhagen
Period	28/05/02 → 31/05/02

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

Access to Document

10.1007/3-540-47967-8_27

Cite this

Levin, A., & Shashua, A. (2002). Revisiting single-view shape tensors: Theory and applications. In A. Heyden, G. Sparr, M. Nielsen, & P. Johansen (Eds.), Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings (pp. 399-414). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2351). Springer Verlag. https://doi.org/10.1007/3-540-47967-8_27

Levin, Anat ; Shashua, Amnon. / Revisiting single-view shape tensors : Theory and applications. Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings. editor / Anders Heyden ; Gunnar Sparr ; Mads Nielsen ; Peter Johansen. Springer Verlag, 2002. pp. 399-414 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Levin, A & Shashua, A 2002, Revisiting single-view shape tensors: Theory and applications. in A Heyden, G Sparr, M Nielsen & P Johansen (eds), Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2351, Springer Verlag, pp. 399-414, 7th European Conference on Computer Vision, ECCV 2002, Copenhagen, Denmark, 28/05/02. https://doi.org/10.1007/3-540-47967-8_27

Revisiting single-view shape tensors: Theory and applications. / Levin, Anat; Shashua, Amnon.
Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings. ed. / Anders Heyden; Gunnar Sparr; Mads Nielsen; Peter Johansen. Springer Verlag, 2002. p. 399-414 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2351).

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

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Levin A, Shashua A. Revisiting single-view shape tensors: Theory and applications. In Heyden A, Sparr G, Nielsen M, Johansen P, editors, Computer Vision - 7th European Conference on Computer Vision, ECCV 2002, Proceedings. Springer Verlag. 2002. p. 399-414. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-47967-8_27

Revisiting single-view shape tensors: Theory and applications

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