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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 : spatial relations. Levy distances Prokhorov Hausdorff fuzzy mathematical morphology Comparison of distributions optimal transport mathemat- ical morphology
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Conference papers
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https://hal-imt.archives-ouvertes.fr/hal-01172192
Contributor : Admin Télécom Paristech <>
Submitted on : Tuesday, July 7, 2015 - 9:37:00 AM
Last modification on : Monday, August 3, 2020 - 3:37:33 AM

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  • HAL Id : hal-01172192, version 1

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INSTITUT-TELECOM | CNRS | PARISTECH | LTCI | UNIV-PARIS-SACLAY | IDS | IMAGES | UNIV-DAUPHINE

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. pp.522-534. ⟨hal-01172192⟩

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