Minimal simple pairs in the 3-D cubic grid

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

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

Preserving topological properties of objects during thinning procedures is an important issue in the field of image analysis. This paper constitutes an introduction to the study of non-trivial simple sets in the framework of cubical 3-D complexes. A simple set has the property that the homotopy type of the object in which it lies is not changed when the set is removed. The main contribution of this paper is a characterisation of the non-trivial simple sets composed of exactly two voxels, such sets being called minimal simple pairs.

Mots clés: topology preservation; collapse; thinning; 3-D space; cubical complexes

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

Nicolas Passat, Michel Couprie, Gilles Bertrand. Minimal simple pairs in the 3-D cubic grid. Journal of Mathematical Imaging and Vision, 2008, 32 (3), pp.239-249. ⟨10.1007/s10851-008-0099-9⟩. ⟨hal-00622368⟩