Hausdorff distances between distributions using optimal transport and mathematical morphology

Abstract :

In this paper we address the question of defining and com- puting Hausdorff distances between distributions in a general sense. We exhibit some links between Prokhorov-Levy distances and dilation-based distances. In particular, mathematical morphology provides an elegant way to deal with periodic distributions. The case of possibility distribu- tions is addressed using fuzzy mathematical morphology. As an illustra- tion, the proposed approaches are applied to the comparison of spatial relations between objects in an image or a video sequence, when these relations are represented as distributions.

Type de document :
Communication dans un congrès
12th International Symposium on Mathematical Morphology, Jul 2015, Reykjavik, Iceland. LNCS 9082, pp.522-534, 2015
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https://hal-imt.archives-ouvertes.fr/hal-01172192
Contributeur : Admin Télécom Paristech <>
Soumis le : mardi 7 juillet 2015 - 09:37:00
Dernière modification le : jeudi 11 janvier 2018 - 06:23:39

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  • HAL Id : hal-01172192, version 1

Citation

Isabelle Bloch, J. Atif. Hausdorff distances between distributions using optimal transport and mathematical morphology. 12th International Symposium on Mathematical Morphology, Jul 2015, Reykjavik, Iceland. LNCS 9082, pp.522-534, 2015. 〈hal-01172192〉

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