A note on 3-D simple points and simple-equivalence

Gilles Bertrand (1) , Michel Couprie (1) , Nicolas Passat (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

In this paper, we prove that in a particular case, a 3-D point can be removed while preserving topology if and only if it is a simple point. This property holds in the case of simply connected objects, that is, connected objects which have no tunnels.

Mots clés: computational geometry; simple point; digital topology; fundamental group; cubical complexes

Domaines: Topologie géométrique [math.GT]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Gilles Bertrand, Michel Couprie, Nicolas Passat. A note on 3-D simple points and simple-equivalence. Information Processing Letters, 2009, 109 (13), pp.700-704. ⟨10.1016/j.ipl.2009.03.002⟩. ⟨hal-00622395⟩