Salient and reentrant points of discrete sets

Alain Daurat (1) , Maurice Nivat (2)

1 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

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.

Mots clés: Discrete sets; Salient points; Reentrant points; Corners

Domaines: Mathématique discrète [cs.DM]

Alain Daurat, Maurice Nivat. Salient and reentrant points of discrete sets. Discrete Applied Mathematics, 2005, 151, pp.106-121. ⟨10.1016/j.dam.2005.02.024⟩. ⟨hal-00023087⟩