Discrete Topology of (An*) Optimal Sampling Grids. Interest in Image Processing and Visualization

Authors:
Chafiaâ Hamitouche;Luis Ibáñez;Christian Roux
Affiliations:
Département Image et Traitement de l'Information, LATIM INSERM U650 GET-ENST Bretagne, Brest, France 29238;Kitware Inc., New York, USA 12065;Département Image et Traitement de l'Information, LATIM INSERM U650 GET-ENST Bretagne, Brest, France 29238
Venue:
Journal of Mathematical Imaging and Vision
Year:
2005

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Abstract

A formal definition of a combinatorial topology is presented in this paper for the discrete N-dimensional space defined by the An* lattice. The use of this grid instead of the classical n is based on two arguments:It is the optimal sampling grid in the sense of Shannon's sampling theorem in 2 and 3 dimensions,It induces the simplest discrete topology definition because its dual is a K-simplex.Their interest in image processing and in the medical imaging field is presented with some examples.