Homology Computation on Cellular Structures in Image Context

Sylvie Alayrangues 1 Guillaume Damiand 2 Laurent Fuchs 1 Pascal Lienhardt 1 Samuel Peltier 1
1 SIC
XLIM - XLIM, Université de Poitiers
2 M2DisCo - Geometry Processing and Constrained Optimization
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : During the previous decade, many works have shown that topological properties are of interest in an image context. Among all topological invariants (Euler characteristic, Betti numbers, orientability...), homology groups are known to be powerful (in term of topological characterization) and computable in the same way in any dimension. In this paper, we recall briefly the cellular structures used in topology-based geometric modeling and image analysis, and propose different approaches for computing homology on such structures. These approaches are adaptations of classical methods from algebraic topology that had essentially been developed for simplicial or cubical complexes. We present two works in progress dealing with two different methods for computing homology information on structures derived from combinatorial maps: a method relying on the definition of a cellular border operator, the other following a constructive approach based on the works about effective homology.
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Communication dans un congrès
Computational Topology in Image Context, Aug 2009, St. Kathrein/Offenegg, Austria. Computational Topology in Image Context, pp.19--28, 2009
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Sylvie Alayrangues, Guillaume Damiand, Laurent Fuchs, Pascal Lienhardt, Samuel Peltier. Homology Computation on Cellular Structures in Image Context. Computational Topology in Image Context, Aug 2009, St. Kathrein/Offenegg, Austria. Computational Topology in Image Context, pp.19--28, 2009. <hal-00437766>

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