Minimal Simple Pairs in the 3-D Cubic Grid

Authors:
N. Passat;M. Couprie;G. Bertrand
Affiliations:
LSIIT, UMR 7005 CNRS/ULP, Strasbourg 1 University, Strasbourg, France;LABINFO-IGM, UMR CNRS 8049, A2SI-ESIEE, Université Paris-Est, Marne-le-Vallée, France;LABINFO-IGM, UMR CNRS 8049, A2SI-ESIEE, Université Paris-Est, Marne-le-Vallée, France
Venue:
Journal of Mathematical Imaging and Vision
Year:
2008

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Abstract

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.