Salient and reentrant points of discrete sets

Authors:
Alain Daurat;Maurice Nivat
Affiliations:
LSIIT CNRS UMR 7005, Université Louis Pasteur (Strasbourg 1), Pôle API, Boulevard Sébastien Brant, 67400 Illkirch-Graffenstaden, France;LIAFA CNRS UMR 7089, Université Denis Diderot (Paris 7), Case 7014, 2 place Jussieu, 75251 Paris Cedex 05, 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.