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Local contributions to the Euler-Poincare characteristic of a set

Abstract : 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.
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https://hal-normandie-univ.archives-ouvertes.fr/hal-02429446
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Submitted on : Monday, January 6, 2020 - 4:15:04 PM
Last modification on : Thursday, September 24, 2020 - 4:00:35 PM

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

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