Projectively invariant representations using implicit algebraic curves

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

Research output: Contribution to journalArticlepeer-review


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 the procedure works for plane conic curves. For higher order plane curves, or for aggregates of plane conies, 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)
Pages (from-to)130-136
Number of pages7
JournalImage and Vision Computing
Issue number2
StatePublished - Apr 1991
Externally publishedYes


  • curves
  • model matching
  • polynomial representation
  • projection

ASJC Scopus subject areas

  • Signal Processing
  • Computer Vision and Pattern Recognition


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