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 proceedingConference contributionpeer-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 languageEnglish
Title of host publicationApplications of Invariance in Computer Vision - 2nd Joint European - US Workshop, Proceedings
EditorsJoseph L. Mundy, Andrew Zisserman, David Forsyth
PublisherSpringer Verlag
Pages493-510
Number of pages18
ISBN (Print)9783540582403
DOIs
StatePublished - 1994
Externally publishedYes
Event2nd Joint European–US Workshop on Applications of Invariance in Computer Vision, 1993 - Azores, Portugal
Duration: 9 Oct 199314 Oct 1993

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume825 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference2nd Joint European–US Workshop on Applications of Invariance in Computer Vision, 1993
Country/TerritoryPortugal
CityAzores
Period9/10/9314/10/93

Bibliographical note

Funding Information:
* This work was partially supported by NSF Grant #IRI-8715774, NSF-DARPA Grant #IRI-8905436, USAF Grant #F49620-93-1-0501ARPA, and NSF Grant #IRI-9224963

Funding Information:
This work was partially supported by NSF Grant #IRI-8715774, NSF-DARPA Grant #IRI-8905436, USAF Grant #F49620-93-1-0501ARPA, and NSF Grant #IRI-9224963

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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