Topologically Faithful Fitting of Simple Closed Curves

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)118-123
Number of pages6
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume26
Issue number1
DOIs
StatePublished - 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

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