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Conference Papers Year : 2015

Hausdorff distances between distributions using optimal transport and mathematical morphology

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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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Dates and versions

hal-01172192 , version 1 (07-07-2015)

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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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