On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views

Amnon Shashua

doi:10.1007/3-540-58240-1_7

On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views

Amnon Shashua^*

^*Corresponding author for this work

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

3 Scopus citations

Abstract

This paper investigates the differences — conceptually and algorithmically — between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. The study is made by first proposing an affine framework for perspective views, captured by a single remarkably simple equation, which is based on a viewer-centered invariant we call relative affine structure. Via corollaries of the main result we make connections to previous work and show that Euclidean, affine and projective structure representations can be obtained by simple specializations and generalizations of our main results.

Original language	English
Title of host publication	Applications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings
Editors	Joseph L. Mundy, Andrew Zisserman, David Forsyth
Publisher	Springer Verlag
Pages	127-143
Number of pages	17
ISBN (Print)	9783540582403
DOIs	https://doi.org/10.1007/3-540-58240-1_7
State	Published - 1994
Externally published	Yes
Event	2nd Joint European–US Workshop on Applications of Invariance in Computer Vision, 1993 - Azores, Portugal Duration: 9 Oct 1993 → 14 Oct 1993

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	825 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	2nd Joint European–US Workshop on Applications of Invariance in Computer Vision, 1993
Country/Territory	Portugal
City	Azores
Period	9/10/93 → 14/10/93

Bibliographical note

Publisher Copyright:
© 1994, Springer Verlag. All rights reserved.

Access to Document

10.1007/3-540-58240-1_7

Cite this

Shashua, A. (1994). On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views. In J. L. Mundy, A. Zisserman, & D. Forsyth (Eds.), Applications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings (pp. 127-143). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 825 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-58240-1_7

Shashua, Amnon. / On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views. Applications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings. editor / Joseph L. Mundy ; Andrew Zisserman ; David Forsyth. Springer Verlag, 1994. pp. 127-143 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views",

abstract = "This paper investigates the differences — conceptually and algorithmically — between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. The study is made by first proposing an affine framework for perspective views, captured by a single remarkably simple equation, which is based on a viewer-centered invariant we call relative affine structure. Via corollaries of the main result we make connections to previous work and show that Euclidean, affine and projective structure representations can be obtained by simple specializations and generalizations of our main results.",

author = "Amnon Shashua",

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year = "1994",

doi = "10.1007/3-540-58240-1_7",

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Shashua, A 1994, On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views. in JL Mundy, A Zisserman & D Forsyth (eds), Applications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 825 LNCS, Springer Verlag, pp. 127-143, 2nd Joint European–US Workshop on Applications of Invariance in Computer Vision, 1993, Azores, Portugal, 9/10/93. https://doi.org/10.1007/3-540-58240-1_7

On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views. / Shashua, Amnon.
Applications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings. ed. / Joseph L. Mundy; Andrew Zisserman; David Forsyth. Springer Verlag, 1994. p. 127-143 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 825 LNCS).

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

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Shashua A. On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views. In Mundy JL, Zisserman A, Forsyth D, editors, Applications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings. Springer Verlag. 1994. p. 127-143. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-58240-1_7

On geometric and algebraic aspects of 3D affine and projective structures from perspective 2D views

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