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Poisson Skeleton Revisited: a New Mathematical Perspective

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Abstract

This paper is concerned with the computation of the skeleton of a shape Ω included in ℝ2. We show some connections between the Euclidean distance function d to ∂Ω and the solution u of the Poisson problem Δu(x)=−1 if x is in Ω and u(x)=0 if x is on ∂Ω. This enables us to propose a new and fast algorithm to compute an approximation of the skeleton of ∂Ω. We illustrate the approach with some numerical experiments.

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Acknowledgements

We would like to thank the reviewers for their usefuls comments and remarks that helped to improve the paper. We also would like to thank Professor El Maati Ouhabaz for having pointed out to us reference [25].

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Authors and Affiliations

  1. Laboratoire J.A. DIeudonne, UMR CNRS 7531, Université de Nice Sophia-Antipolis, Parc Valrose, 06108, Nice Cedex 02, France

    Gilles Aubert

  2. IMB, Universite Bordeaux 1, 351 Cours de la liberation, 33405, Talence Cedex, France

    Jean-Franois Aujol

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  1. Gilles Aubert
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  2. Jean-Franois Aujol
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Correspondence to Jean-Franois Aujol.

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Aubert, G., Aujol, JF. Poisson Skeleton Revisited: a New Mathematical Perspective. J Math Imaging Vis 48, 149–159 (2014). https://doi.org/10.1007/s10851-012-0404-5

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