Poisson skeleton Revisited: A new mathematical perspective

Abstract : This paper is concerned with the computation of the skeleton of a shape $\Omega$ included in $\R^2$. We show some connections between the Euclidean distance function $d$ to $\partial \Omega$ and the solution $u$ of the Poisson problem $\Delta u(x)=-1$ if $x$ is in $\Omega$ and $u(x)=0$ if $x$ is on $\partial \Omega$. This enables us to propose a new and fast algorithm to compute an approximation of the skeleton of $\partial \Omega$. We illustrate the approach with some numerical experiments.
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Gilles Aubert, Jean-François Aujol. Poisson skeleton Revisited: A new mathematical perspective. Journal of Mathematical Imaging and Vision, Springer Verlag, 2014, 48 (1), pp.149-159. ⟨hal-00714250⟩

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