### 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 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 language | English (US) |
---|---|

Pages (from-to) | 130-136 |

Number of pages | 7 |

Journal | Image and Vision Computing |

Volume | 9 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1991 |

Externally published | Yes |

### Fingerprint

### Keywords

- curves
- model matching
- polynomial representation
- projection

### ASJC Scopus subject areas

- Signal Processing
- Computer Vision and Pattern Recognition

### Cite this

*Image and Vision Computing*,

*9*(2), 130-136. https://doi.org/10.1016/0262-8856(91)90023-I

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

Research output: Contribution to journal › Article

*Image and Vision Computing*, vol. 9, no. 2, pp. 130-136. https://doi.org/10.1016/0262-8856(91)90023-I

}

TY - JOUR

T1 - Projectively invariant representations using implicit algebraic curves

AU - Forsyth, David

AU - Mundy, Joseph L.

AU - Zisserman, Andrew

AU - Brown, Christopher M.

PY - 1991/4

Y1 - 1991/4

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 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.

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 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.

KW - curves

KW - model matching

KW - polynomial representation

KW - projection

UR - http://www.scopus.com/inward/record.url?scp=0026135989&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026135989&partnerID=8YFLogxK

U2 - 10.1016/0262-8856(91)90023-I

DO - 10.1016/0262-8856(91)90023-I

M3 - Article

AN - SCOPUS:0026135989

VL - 9

SP - 130

EP - 136

JO - Image and Vision Computing

JF - Image and Vision Computing

SN - 0262-8856

IS - 2

ER -