An iterative algorithm for homology computation on simplicial shapes

Dobrina Boltcheva 1, 2 David Canino 3 Sara Merino Aceituno 1 Jean-Claude Léon 4 de Floriani Leila 3 Franck Hétroy 1, 5
1 EVASION - Virtual environments for animation and image synthesis of natural objects
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
2 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
4 G-SCOP_SIREP - SIREP
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
5 MORPHEO - Capture and Analysis of Shapes in Motion
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : We propose a new iterative algorithm for computing the homology of arbitrary shapes discretized through simplicial complexes, We demonstrate how the simplicial homology of a shape can be effectively expressed in terms of the homology of its sub-components. The proposed algorithm retrieves the complete homological information of an input shape including the Betti numbers, the torsion coefficients and the representative homology generators. To the best of our knowledge, this is the first algorithm based on the constructive Mayer-Vietoris sequence, which relates the homology of a topological space to the homologies of its sub-spaces, i.e. the sub-components of the input shape and their intersections. We demonstrate the validity of our approach through a specific shape decomposition, based only on topological properties, which minimizes the size of the intersections between the sub-components and increases the efficiency of the algorithm.
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https://hal.inria.fr/hal-00644410
Contributor : Dobrina Boltcheva <>
Submitted on : Thursday, November 24, 2011 - 2:00:59 PM
Last modification on : Thursday, November 21, 2019 - 2:36:18 PM
Long-term archiving on : Saturday, February 25, 2012 - 2:25:07 AM

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Dobrina Boltcheva, David Canino, Sara Merino Aceituno, Jean-Claude Léon, de Floriani Leila, et al.. An iterative algorithm for homology computation on simplicial shapes. Computer-Aided Design, Elsevier, 2011, 43 (11), pp.1457-1467. ⟨10.1016/j.cad.2011.08.015⟩. ⟨hal-00644410v1⟩

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