@inproceedings{93275256109d430d84b73fcab14aa984,
title = "Hausdorff distances between distributions using optimal transport and mathematical morphology",
abstract = "In this paper we address the question of defining and computing Hausdorff distances between distributions in a general sense. We exhibit some links between Prokhorov-L{\'e}vy distances and dilation-based distances. In particular, mathematical morphology provides an elegant way to deal with periodic distributions. The case of possibility distributions is addressed using fuzzy mathematical morphology. As an illustration, 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 = "Comparison of distributions, Fuzzy mathematical morphology, Hausdorff, L{\'e}vy distances, Mathematical morphology, Optimal transport, Prokhorov, Spatial relations",
author = "Isabelle Bloch and Jamal Atif",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 12th International Symposium on Mathematical Morphology, ISMM 2015 ; Conference date: 27-05-2015 Through 29-05-2015",
year = "2015",
month = jan,
day = "1",
doi = "10.1007/978-3-319-18720-4\_44",
language = "English",
isbn = "9783319187198",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "522--534",
editor = "Laurent Najman and Hugues Talbot and Benediktsson, \{Jon Atli\} and Jocelyn Chanussot",
booktitle = "Mathematical Morphology and its Applications to Signal and Image Processing - 12th International Symposium, ISMM 2015, Proceedings",
}