Projectively invariant representations using implicit algebraic curves

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

doi:10.1007/BFb0014893

Projectively invariant representations using implicit algebraic curves

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

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Computer Vision – ECCV 1990 - 1st European Conference on Computer Vision, Proceedings
Editors	Olivier Faugeras
Publisher	Springer
Pages	427-436
Number of pages	10
ISBN (Print)	9783540525226
DOIs	https://doi.org/10.1007/BFb0014893
State	Published - 1990
Externally published	Yes
Event	1st European Conference on Computer Vision, ECCV 1990 - Antibes, France Duration: Apr 23 1990 → Apr 27 1990

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	427 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	1st European Conference on Computer Vision, ECCV 1990
Country/Territory	France
City	Antibes
Period	4/23/90 → 4/27/90

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Online availability

10.1007/BFb0014893

Library availability

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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. https://doi.org/10.1007/BFb0014893

Projectively invariant representations using implicit algebraic curves. / Forsyth, David; Mundy, Joseph L.; Zisserman, Andrew et al.

Computer Vision – ECCV 1990 - 1st European Conference on Computer Vision, Proceedings. ed. / Olivier Faugeras. Springer, 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 proceeding › Conference 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, 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. 1990. p. 427-436. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/BFb0014893

Forsyth, David ; Mundy, Joseph L. ; Zisserman, Andrew et al. / Projectively invariant representations using implicit algebraic curves. Computer Vision – ECCV 1990 - 1st European Conference on Computer Vision, Proceedings. editor / Olivier Faugeras. Springer, 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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title = "Projectively invariant representations using implicit algebraic curves",

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.",

author = "David Forsyth and Mundy, {Joseph L.} and Andrew Zisserman and Brown, {Christopher M.}",

note = "Funding Information: 1DAF acknowledges the support of Magdalen College, Oxford. AZ acknowledges the support of the Science and Engineering Research Council. JLM acknowledges the support of the General Electric Coolidge Fellowship. CMB acknowledges the support of the DARPA U.S. Army Engineering Topographic Laboratories Grant DACA76-85-C-0001 and the Air Force Systems Command (RADC, Griffiss AFB, NY) and Air Force OSR Contract F30602-85-C-0008, which supports the Northeast Artificial Intelligence Consortium. Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1990.; 1st European Conference on Computer Vision, ECCV 1990 ; Conference date: 23-04-1990 Through 27-04-1990",

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N1 - Funding Information: 1DAF acknowledges the support of Magdalen College, Oxford. AZ acknowledges the support of the Science and Engineering Research Council. JLM acknowledges the support of the General Electric Coolidge Fellowship. CMB acknowledges the support of the DARPA U.S. Army Engineering Topographic Laboratories Grant DACA76-85-C-0001 and the Air Force Systems Command (RADC, Griffiss AFB, NY) and Air Force OSR Contract F30602-85-C-0008, which supports the Northeast Artificial Intelligence Consortium. Publisher Copyright: © Springer-Verlag Berlin Heidelberg 1990.

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N2 - 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.

AB - 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.

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Projectively invariant representations using implicit algebraic curves

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