Trilinear tensor: The fundamental construct of multiple-view geometry and its applications

Amnon Shashua

doi:10.1007/bfb0017868

Trilinear tensor: The fundamental construct of multiple-view geometry and its applications

Amnon Shashua^*

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

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

18 Scopus citations

Abstract

The topic of representation, recovery and manipulation of three-dimensional (3D) scenes from two-dimensional (2D) images thereof, provides a fertile ground for both intellectual theoretically inclined questions related to the algebra and geometry of the problem and to practical applications such as Visual Recognition, Animation and View Synthesis, recovery of scene structure and camera ego-motion, object detection and tracking, multi-sensor alignment, etc. The basic materials have been known since the turn of the century, but the full scope of the problem has been under intensive study since 1992, first on the algebra of two views and then on the algebra of multiple views leading to a relatively mature understanding of what is known as “multilinear matching constraints”, and the “trilinear tensor” of three or more views. The purpose of this paper is, first and foremost, to provide a coherent framework for expressing the ideas behind the analysis of multiple views. Secondly, to integrate the various incremented results that have appeared on the subject into one coherent manuscript.

Original language	English
Title of host publication	Algebraic Frames for the Perception-Action Cycle - International Workshop, AFPAC 1997, Proceedings
Editors	Gerald Sommer, Jan J. Koenderink
Publisher	Springer Verlag
Pages	190-206
Number of pages	17
ISBN (Print)	3540635173, 9783540635178
DOIs	https://doi.org/10.1007/bfb0017868
State	Published - 1997
Event	International Workshop on Algebraic Frames for the Perception and Action Cycle, AFPAC 1997 - Kiel, Germany Duration: 8 Sep 1997 → 9 Sep 1997

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1315
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Workshop on Algebraic Frames for the Perception and Action Cycle, AFPAC 1997
Country/Territory	Germany
City	Kiel
Period	8/09/97 → 9/09/97

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1997.

Access to Document

10.1007/bfb0017868

Cite this

Shashua, A. (1997). Trilinear tensor: The fundamental construct of multiple-view geometry and its applications. In G. Sommer, & J. J. Koenderink (Eds.), Algebraic Frames for the Perception-Action Cycle - International Workshop, AFPAC 1997, Proceedings (pp. 190-206). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1315). Springer Verlag. https://doi.org/10.1007/bfb0017868

Shashua, Amnon. / Trilinear tensor : The fundamental construct of multiple-view geometry and its applications. Algebraic Frames for the Perception-Action Cycle - International Workshop, AFPAC 1997, Proceedings. editor / Gerald Sommer ; Jan J. Koenderink. Springer Verlag, 1997. pp. 190-206 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The topic of representation, recovery and manipulation of three-dimensional (3D) scenes from two-dimensional (2D) images thereof, provides a fertile ground for both intellectual theoretically inclined questions related to the algebra and geometry of the problem and to practical applications such as Visual Recognition, Animation and View Synthesis, recovery of scene structure and camera ego-motion, object detection and tracking, multi-sensor alignment, etc. The basic materials have been known since the turn of the century, but the full scope of the problem has been under intensive study since 1992, first on the algebra of two views and then on the algebra of multiple views leading to a relatively mature understanding of what is known as “multilinear matching constraints”, and the “trilinear tensor” of three or more views. The purpose of this paper is, first and foremost, to provide a coherent framework for expressing the ideas behind the analysis of multiple views. Secondly, to integrate the various incremented results that have appeared on the subject into one coherent manuscript.",

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Shashua, A 1997, Trilinear tensor: The fundamental construct of multiple-view geometry and its applications. in G Sommer & JJ Koenderink (eds), Algebraic Frames for the Perception-Action Cycle - International Workshop, AFPAC 1997, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1315, Springer Verlag, pp. 190-206, International Workshop on Algebraic Frames for the Perception and Action Cycle, AFPAC 1997, Kiel, Germany, 8/09/97. https://doi.org/10.1007/bfb0017868

Trilinear tensor: The fundamental construct of multiple-view geometry and its applications. / Shashua, Amnon.
Algebraic Frames for the Perception-Action Cycle - International Workshop, AFPAC 1997, Proceedings. ed. / Gerald Sommer; Jan J. Koenderink. Springer Verlag, 1997. p. 190-206 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1315).

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

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Shashua A. Trilinear tensor: The fundamental construct of multiple-view geometry and its applications. In Sommer G, Koenderink JJ, editors, Algebraic Frames for the Perception-Action Cycle - International Workshop, AFPAC 1997, Proceedings. Springer Verlag. 1997. p. 190-206. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/bfb0017868

Trilinear tensor: The fundamental construct of multiple-view geometry and its applications

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