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Topologically faithful fitting of simple closed curves

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1 Author(s)
D. Keren ; Dept. of Comput. Sci., Haifa Univ., Israel

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.

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:26 ,  Issue: 1 )