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Defining and computing Hausdorff distances between distributions on the real line and on the circle: link between optimal transport and morphological dilations
Abstract Comparing probability or possibility distributions is important in many fields of information processing under uncertainty. In this paper we address the question of defining and computing Hausdorff distances between distributions in a general sense. We propose several dilations of distributions, and exhibit some links between Lévy-Prokhorov distances and dilation-based …