Homography tensors: On algebraic entities that represent three views of static or moving planar points

Amnon Shashua; Lior Wolf

doi:10.1007/3-540-45054-8_33

Homography tensors: On algebraic entities that represent three views of static or moving planar points

Amnon Shashua, Lior Wolf

The Rachel and Selim Benin School of Engineering and Computer Science

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

29 Scopus citations

Abstract

We introduce a 3 × 3 × 3 tensor H^ijk and its dual H^ijk which represent the 2D projective mapping of points across three projections (views). The tensor H^ijk is a generalization of the well known 2D collineation matrix (homography matrix) and it concatenates two homography matrices to represent the joint mapping across three views. The dual tensor H_ijk concatenates two dual homography matrices (mappings of line space) and is responsible for representing the mapping associated with moving points along straight-line paths, i.e., H_ijk can be recovered from line-of-sight measurements only.

Original language	English
Title of host publication	Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings
Editors	David Vernon
Publisher	Springer Verlag
Pages	507-521
Number of pages	15
ISBN (Print)	3540676856
DOIs	https://doi.org/10.1007/3-540-45054-8_33
State	Published - 2000
Event	6th European Conference on Computer Vision, ECCV 2000 - Dublin, Ireland Duration: 26 Jun 2000 → 1 Jul 2000

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1842
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	6th European Conference on Computer Vision, ECCV 2000
Country/Territory	Ireland
City	Dublin
Period	26/06/00 → 1/07/00

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

Access to Document

10.1007/3-540-45054-8_33

Cite this

Shashua, A., & Wolf, L. (2000). Homography tensors: On algebraic entities that represent three views of static or moving planar points. In D. Vernon (Ed.), Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings (pp. 507-521). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1842). Springer Verlag. https://doi.org/10.1007/3-540-45054-8_33

Shashua, Amnon ; Wolf, Lior. / Homography tensors : On algebraic entities that represent three views of static or moving planar points. Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings. editor / David Vernon. Springer Verlag, 2000. pp. 507-521 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We introduce a 3 × 3 × 3 tensor Hijk and its dual Hijk which represent the 2D projective mapping of points across three projections (views). The tensor Hijk is a generalization of the well known 2D collineation matrix (homography matrix) and it concatenates two homography matrices to represent the joint mapping across three views. The dual tensor Hijk concatenates two dual homography matrices (mappings of line space) and is responsible for representing the mapping associated with moving points along straight-line paths, i.e., Hijk can be recovered from line-of-sight measurements only.",

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Shashua, A & Wolf, L 2000, Homography tensors: On algebraic entities that represent three views of static or moving planar points. in D Vernon (ed.), Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1842, Springer Verlag, pp. 507-521, 6th European Conference on Computer Vision, ECCV 2000, Dublin, Ireland, 26/06/00. https://doi.org/10.1007/3-540-45054-8_33

Homography tensors: On algebraic entities that represent three views of static or moving planar points. / Shashua, Amnon; Wolf, Lior.
Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings. ed. / David Vernon. Springer Verlag, 2000. p. 507-521 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1842).

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

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Shashua A, Wolf L. Homography tensors: On algebraic entities that represent three views of static or moving planar points. In Vernon D, editor, Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings. Springer Verlag. 2000. p. 507-521. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45054-8_33

Homography tensors: On algebraic entities that represent three views of static or moving planar points

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