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Hausdorff distances between distributions using optimal transport and mathematical morphology

Isabelle Bloch 1, 2 J. Atif 3
1 IMAGES - Image, Modélisation, Analyse, GEométrie, Synthèse
LTCI - Laboratoire Traitement et Communication de l'Information
2 TSI - Département Traitement du Signal et des Images
3 Université Paris Dauphine-PSL
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.
Keywords : optimal transport Comparison of distributions fuzzy mathematical morphology Hausdorff Prokhorov Levy distances spatial relations. mathemat- ical morphology
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Conference papers
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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, November 17, 2021 - 12:32:16 PM

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INSTITUT-TELECOM | CNRS | PARISTECH | LTCI | IDS | IMAGES | UNIV-DAUPHINE | PSL

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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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