Integrating algebraic curves and surfaces, algebraic invariants and bayesian methods for 2D and 3D object recognition

Daniel Keren; Jayashree Subrahmonia; David B. Cooper

doi:10.1007/3-540-58240-1_26

Integrating algebraic curves and surfaces, algebraic invariants and bayesian methods for 2D and 3D object recognition

Daniel Keren, Jayashree Subrahmonia, David B. Cooper

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

Abstract

This paper presents a new low-computational-cost approach to minimum probability of error recognition of freeform objects in 3D range data or in 2D curve data in the image plane. Objects are represented by implicit polynomials (i.e., 3D algebraic surfaces or 2D algebraic curves) of degrees greater than 2, and are recognized by computing and matching vectors of their algebraic invariants (which are functions of their coefficients that are invariant to translations, rotations, and general linear transformations). Such polynomials of 4th degree can represent objects considerably more complicated than superquadrics and realize object recognition at significantly lower computational cost. This paper presents the Bayesian (i.e., minimum probability of error) recognizers for these models and their invariants, which requires the use of asymptotic methods little used in computer vision previously, and presents a new approach to discovering suitable invariants. Our sytem results in practical recognizers that are robust to noise, considerable partial occlusion, arbitrary sensor viewpoint, and other a priori unknown perturbations of the data sets.

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	493-510
Number of pages	18
ISBN (Print)	9783540582403
DOIs	https://doi.org/10.1007/3-540-58240-1_26
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.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-58240-1_26

Cite this

Keren, D., Subrahmonia, J., & Cooper, D. B. (1994). Integrating algebraic curves and surfaces, algebraic invariants and bayesian methods for 2D and 3D object recognition. In J. L. Mundy, A. Zisserman, & D. Forsyth (Eds.), Applications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings (pp. 493-510). (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_26

Keren, Daniel ; Subrahmonia, Jayashree ; Cooper, David B. / Integrating algebraic curves and surfaces, algebraic invariants and bayesian methods for 2D and 3D object recognition. Applications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings. editor / Joseph L. Mundy ; Andrew Zisserman ; David Forsyth. Springer Verlag, 1994. pp. 493-510 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "This paper presents a new low-computational-cost approach to minimum probability of error recognition of freeform objects in 3D range data or in 2D curve data in the image plane. Objects are represented by implicit polynomials (i.e., 3D algebraic surfaces or 2D algebraic curves) of degrees greater than 2, and are recognized by computing and matching vectors of their algebraic invariants (which are functions of their coefficients that are invariant to translations, rotations, and general linear transformations). Such polynomials of 4th degree can represent objects considerably more complicated than superquadrics and realize object recognition at significantly lower computational cost. This paper presents the Bayesian (i.e., minimum probability of error) recognizers for these models and their invariants, which requires the use of asymptotic methods little used in computer vision previously, and presents a new approach to discovering suitable invariants. Our sytem results in practical recognizers that are robust to noise, considerable partial occlusion, arbitrary sensor viewpoint, and other a priori unknown perturbations of the data sets.",

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year = "1994",

doi = "10.1007/3-540-58240-1_26",

language = "English",

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Keren, D, Subrahmonia, J & Cooper, DB 1994, Integrating algebraic curves and surfaces, algebraic invariants and bayesian methods for 2D and 3D object recognition. 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. 493-510, 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_26

Integrating algebraic curves and surfaces, algebraic invariants and bayesian methods for 2D and 3D object recognition. / Keren, Daniel; Subrahmonia, Jayashree; Cooper, David B.
Applications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings. ed. / Joseph L. Mundy; Andrew Zisserman; David Forsyth. Springer Verlag, 1994. p. 493-510 (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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N2 - This paper presents a new low-computational-cost approach to minimum probability of error recognition of freeform objects in 3D range data or in 2D curve data in the image plane. Objects are represented by implicit polynomials (i.e., 3D algebraic surfaces or 2D algebraic curves) of degrees greater than 2, and are recognized by computing and matching vectors of their algebraic invariants (which are functions of their coefficients that are invariant to translations, rotations, and general linear transformations). Such polynomials of 4th degree can represent objects considerably more complicated than superquadrics and realize object recognition at significantly lower computational cost. This paper presents the Bayesian (i.e., minimum probability of error) recognizers for these models and their invariants, which requires the use of asymptotic methods little used in computer vision previously, and presents a new approach to discovering suitable invariants. Our sytem results in practical recognizers that are robust to noise, considerable partial occlusion, arbitrary sensor viewpoint, and other a priori unknown perturbations of the data sets.

AB - This paper presents a new low-computational-cost approach to minimum probability of error recognition of freeform objects in 3D range data or in 2D curve data in the image plane. Objects are represented by implicit polynomials (i.e., 3D algebraic surfaces or 2D algebraic curves) of degrees greater than 2, and are recognized by computing and matching vectors of their algebraic invariants (which are functions of their coefficients that are invariant to translations, rotations, and general linear transformations). Such polynomials of 4th degree can represent objects considerably more complicated than superquadrics and realize object recognition at significantly lower computational cost. This paper presents the Bayesian (i.e., minimum probability of error) recognizers for these models and their invariants, which requires the use of asymptotic methods little used in computer vision previously, and presents a new approach to discovering suitable invariants. Our sytem results in practical recognizers that are robust to noise, considerable partial occlusion, arbitrary sensor viewpoint, and other a priori unknown perturbations of the data sets.

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Keren D, Subrahmonia J, Cooper DB. Integrating algebraic curves and surfaces, algebraic invariants and bayesian methods for 2D and 3D object recognition. In Mundy JL, Zisserman A, Forsyth D, editors, Applications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings. Springer Verlag. 1994. p. 493-510. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-58240-1_26

Integrating algebraic curves and surfaces, algebraic invariants and bayesian methods for 2D and 3D object recognition

Abstract

Publication series

Conference

Bibliographical note

ASJC Scopus subject areas

Access to Document

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