{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,28]],"date-time":"2023-11-28T08:35:53Z","timestamp":1701160553450},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2016,3,18]],"date-time":"2016-03-18T00:00:00Z","timestamp":1458259200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Comparing probability or possibility distributions is important in many fields of information processing\nunder uncertainty. In this paper we address the question of defining and computing Hausdorff distances\nbetween distributions in a general sense. We propose several dilations of distributions, and exhibit\nsome links between L\u00e9vy-Prokhorov distances and dilation-based distances. In particular, mathematical morphology\nprovides an elegant way to deal with periodic distributions. The case of possibility distributions is\naddressed using fuzzy mathematical morphology. As an illustration, the proposed approaches are applied to\nthe comparison of spatial relations between objects in an image or a video sequence, when these relations\nare represented as distributions.<\/jats:p>","DOI":"10.1515\/mathm-2016-0005","type":"journal-article","created":{"date-parts":[[2016,4,9]],"date-time":"2016-04-09T01:35:05Z","timestamp":1460165705000},"source":"Crossref","is-referenced-by-count":1,"title":["Defining and computing Hausdorff distances\nbetween distributions on the real line and on\nthe circle: link between optimal transport and\nmorphological dilations"],"prefix":"10.1515","volume":"1","author":[{"given":"Isabelle","family":"Bloch","sequence":"first","affiliation":[{"name":"LTCI, CNRS, T\u00e9l\u00e9com ParisTech, Universit\u00e9 Paris-Saclay, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jamal","family":"Atif","sequence":"additional","affiliation":[{"name":"PSL, Universit\u00e9 Paris-Dauphine, LAMSADE UMR 7243, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,3,18]]},"container-title":["Mathematical Morphology - Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/mathm.2016.1.issue-1\/mathm-2016-0005\/mathm-2016-0005.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0005\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0005\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T10:20:11Z","timestamp":1651054811000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0005\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,3,30]]}},"alternative-id":["10.1515\/mathm-2016-0005"],"URL":"https:\/\/doi.org\/10.1515\/mathm-2016-0005","relation":{},"ISSN":["2353-3390"],"issn-type":[{"value":"2353-3390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,18]]}}}