Salient and reentrant points of discrete sets

Authors:
Alain Daurat;Maurice Nivat
Affiliations:
LSIIT CNRS UMR, Université Louis Pasteur, Pôle API, Boulevard Sébastien Brant, Illkirch-Graffenstaden, France;LIAFA CNRS UMR, Université Denis Diderot, Paris Cedex, France
Venue:
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Year:
2005

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Abstract

The border-salient and reentrant points of a discrete set are special points of the border of the set. When they are given with multiplicity they completely characterize the set, and without multiplicity they characterize the set if all its 8-components are 4-connected. The inner-salient and reentrant are defined similarly to the border ones, but we show that, in general, they do not characterize the set, even if this set is 4-simply connected. We also show that the genus of a set can be easily computed from the number of salient and reentrant points.