Computing Homology Generators for Volumes Using Minimal Generalized Maps

Guillaume Damiand (1) , Samuel Peltier (2) , Laurent Fuchs (3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 IFPEN - IFP Energies nouvelles
3 SIC

In this paper, we present an algorithm for computing efficiently homology generators of 3D subdivided orientable objects which can contain tunnels and cavities. Starting with an initial subdivision, represented with a generalized map where every cell is a topological ball, the number of cells is reduced using simplification operations (removal of cells), while preserving homology. We obtain a minimal representation which is homologous to the initial object. A set of homology generators is then directly deduced on the simplified 3D object.

Keywords: topological features; homology generators; generalized maps

Domains: Data Structures and Algorithms [cs.DS]; Computational Geometry [cs.CG]

Guillaume Damiand, Samuel Peltier, Laurent Fuchs. Computing Homology Generators for Volumes Using Minimal Generalized Maps. International Workshop on Combinatorial Image Analysis, Apr 2008, Buffalo, NY, United States. pp.63-74, ⟨10.1007/978-3-540-78275-9_6⟩. ⟨hal-00305471⟩