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| HAL: hal-00714250, version 1 |
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| Poisson skeleton |
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| Gilles Aubert 1Jean-François Aujol 2 |
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| (2012-07-03) |
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| 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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| 1: | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS] |
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| 2: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| Subject | : | Computer Science/Image Processing |
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| Skeleton – Poisson equation – distance function – PDEs – ODEs |
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| Attached file list to this document: | |||||
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| hal-00714250, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00714250 | |
| oai:hal.archives-ouvertes.fr:hal-00714250 | |
| From: Jean-François Aujol | |
| Submitted on: Wednesday, 4 July 2012 10:38:55 | |
| Updated on: Wednesday, 4 July 2012 11:14:28 | |
