Projectively invariant representations using implicit algebraic curves

David Forsyth, Joseph L. Mundy, Andrew Zisserman, Christopher M. Brown

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We demonstrate that it is possible to compute polynomial representations of image curves which are unaffected by the projective frame in which the representation is computed. This means that: The curve chosen to represent a projected set of points is the projection of the curve chosen to represent the original set. We achieve this by using algebraic invariants of the polynomial in the fitting process. We demonstrate that our procedure works for plane conic curves. We show that for higher order plane curves, or for aggregates of plane conics, algebraic invariants can yield powerful representations of shape that are unaffected by projection, and hence make good cues for model based vision. Tests on synthetic and real data have yielded excellent results.

Original languageEnglish (US)
Title of host publicationComputer Vision – ECCV 1990 - 1st European Conference on Computer Vision, Proceedings
EditorsOlivier Faugeras
PublisherSpringer-Verlag
Pages427-436
Number of pages10
ISBN (Print)9783540525226
DOIs
StatePublished - Jan 1 1990
Externally publishedYes
Event1st European Conference on Computer Vision, ECCV 1990 - Antibes, France
Duration: Apr 23 1990Apr 27 1990

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume427 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st European Conference on Computer Vision, ECCV 1990
CountryFrance
CityAntibes
Period4/23/904/27/90

Fingerprint

Algebraic curve
Polynomials
Curve
Invariant
Projection
Polynomial
Plane Curve
Set of points
Demonstrate
Higher Order
Model-based

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Forsyth, D., Mundy, J. L., Zisserman, A., & Brown, C. M. (1990). Projectively invariant representations using implicit algebraic curves. In O. Faugeras (Ed.), Computer Vision – ECCV 1990 - 1st European Conference on Computer Vision, Proceedings (pp. 427-436). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 427 LNCS). Springer-Verlag. https://doi.org/10.1007/BFb0014893

Projectively invariant representations using implicit algebraic curves. / Forsyth, David; Mundy, Joseph L.; Zisserman, Andrew; Brown, Christopher M.

Computer Vision – ECCV 1990 - 1st European Conference on Computer Vision, Proceedings. ed. / Olivier Faugeras. Springer-Verlag, 1990. p. 427-436 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 427 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Forsyth, D, Mundy, JL, Zisserman, A & Brown, CM 1990, Projectively invariant representations using implicit algebraic curves. in O Faugeras (ed.), Computer Vision – ECCV 1990 - 1st European Conference on Computer Vision, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 427 LNCS, Springer-Verlag, pp. 427-436, 1st European Conference on Computer Vision, ECCV 1990, Antibes, France, 4/23/90. https://doi.org/10.1007/BFb0014893
Forsyth D, Mundy JL, Zisserman A, Brown CM. Projectively invariant representations using implicit algebraic curves. In Faugeras O, editor, Computer Vision – ECCV 1990 - 1st European Conference on Computer Vision, Proceedings. Springer-Verlag. 1990. p. 427-436. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/BFb0014893
Forsyth, David ; Mundy, Joseph L. ; Zisserman, Andrew ; Brown, Christopher M. / Projectively invariant representations using implicit algebraic curves. Computer Vision – ECCV 1990 - 1st European Conference on Computer Vision, Proceedings. editor / Olivier Faugeras. Springer-Verlag, 1990. pp. 427-436 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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