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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.
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https://hal-imt.archives-ouvertes.fr/hal-01172192
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Submitted on : Tuesday, July 7, 2015 - 9:37:00 AM
Last modification on : Wednesday, October 14, 2020 - 4:20:45 AM

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Isabelle Bloch, J. Atif. Hausdorff distances between distributions using optimal transport and mathematical morphology. 12th International Symposium on Mathematical Morphology, Jul 2015, Reykjavik, Iceland. pp.522-534, ⟨10.1007/978-3-319-18720-4_44⟩. ⟨hal-01172192⟩

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