Local contributions to the Euler-Poincare characteristic of a set

J.-P. Jernot (1) , Patricia Jouannot-Chesney (1) , Christian Lantuéjoul (2)

1 CRISMAT - Laboratoire de cristallographie et sciences des matériaux
2 GEOSCIENCES - Centre de Géosciences

The Euler–Poincaré characteristic (EPC) of a polyconvex subset X of Rd can be evaluated by covering the subset with an auxiliary tessellation, measuring its contribution within each cell of the tessellation and adding all contributions. Two different ways are proposed to define the contribution of a cell to the EPC of X. These contributions turn out to be related by duality formulae. Finally, three applications are given: the measurement of the EPC on adjacent fields, the measurement of the EPC on discretized images and the detection of defects in atomic structures.

Domains: Material chemistry; Signal and Image processing

J.-P. Jernot, Patricia Jouannot-Chesney, Christian Lantuéjoul. Local contributions to the Euler-Poincare characteristic of a set. Journal of Microscopy, 2004, 215 (1), pp.40-49. ⟨10.1111/j.0022-2720.2004.01336.x⟩. ⟨hal-02429446⟩