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 : Thursday, October 17, 2019 - 12:37:00 PM

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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. pp.522-534. ⟨hal-01172192⟩

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