Morphological PDE and dilation/erosion semigroups on length spaces

Abstract : This paper gives a survey of recent research on Hamilton-Jacobi partial dierential equations (PDE) on length spaces. This theory provides the background to formulate morphological PDEs for processing data and images supported on a length space, without the need of a Riemmanian structure. We first introduce the most general pair of dilation/erosion semigroups on a length space, whose basic ingredients are the metric distance and a convex shape function. The second objective is to show under which conditions the solution of a morphological PDE in the length space framework is equal to the dilation/erosion semigroups.
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Communication dans un congrès
Springer-Verlag Berlin Heidelberg. 12th International Symposium on Mathematical Morphology, May 2015, Reykjavik, Iceland. LNCS 9082, pp.509-521, 2015, Proc. of ISMM'15 (12th International Symposium on Mathematical Morphology). <10.1007/978-3-319-18720-4_43>
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https://hal-mines-paristech.archives-ouvertes.fr/hal-01108145
Contributeur : Jesus Angulo <>
Soumis le : dimanche 17 janvier 2016 - 15:01:52
Dernière modification le : mardi 12 septembre 2017 - 11:41:19
Document(s) archivé(s) le : lundi 18 avril 2016 - 10:12:45

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Jesus Angulo. Morphological PDE and dilation/erosion semigroups on length spaces. Springer-Verlag Berlin Heidelberg. 12th International Symposium on Mathematical Morphology, May 2015, Reykjavik, Iceland. LNCS 9082, pp.509-521, 2015, Proc. of ISMM'15 (12th International Symposium on Mathematical Morphology). <10.1007/978-3-319-18720-4_43>. <hal-01108145v3>

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