## Abstract

Implicit representations of curves have certain advantages over explicit representation, one of them being the ability to determine with ease whether a point is inside or outside the curve (inside-outside functions). However, save for some special cases, it is not known how to construct implicit representations which are guaranteed to preserve the curve's topology. As a result, points may be erroneously classified with respect to the curve. The paper offers to overcome this problem by using a representation which is guaranteed to yield the correct topology of a simple closed curve by using homeomorphic mappings of the plane to itself. If such a map carries the curve onto the unit circle, then a point is inside the curve if and only if its image is inside the unit circle.

Original language | English |
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Pages (from-to) | 118-123 |

Number of pages | 6 |

Journal | IEEE Transactions on Pattern Analysis and Machine Intelligence |

Volume | 26 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2004 |

## Keywords

- Implicit fitting
- Jordan-Schoenflies theorem
- Topologically faithful fitting

## ASJC Scopus subject areas

- Software
- Artificial Intelligence
- Applied Mathematics
- Computer Vision and Pattern Recognition
- Computational Theory and Mathematics