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Topologically Faithful Fitting of Simple Closed Curves
January 2004 (vol. 26 no. 1)
pp. 118-123

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.

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Index Terms:
Implicit fitting, topologically faithful fitting, Jordan-Schoenflies theorem.
Citation:
Daniel Keren, "Topologically Faithful Fitting of Simple Closed Curves," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 1, pp. 118-123, Jan. 2004, doi:10.1109/TPAMI.2004.10006
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