{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T05:52:44Z","timestamp":1757310764893},"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>Mathematical morphology on binary images can be fully described by set theory. However, it is not\nsufficient to formulate mathematical morphology for grey scale images. This type of images requires the introduction\nof the notion of partial order of grey levels, together with the definition of sup and inf operators.\nMore generally, mathematical morphology is now described within the context of the lattice theory. For a few\ndecades, attempts are made to use mathematical morphology on multivariate images, such as color images,\nmainly based on the notion of vector order. However, none of these attempts has given fully satisfying results.\nInstead of aiming directly at the multivariate case we propose first an extension of binary mathematical morphology\nto an intermediary situation: images composed of a finite number of independent unordered labels.\nWe propose then an second extension to a continuous case.<\/jats:p>","DOI":"10.1515\/mathm-2016-0003","type":"journal-article","created":{"date-parts":[[2016,3,18]],"date-time":"2016-03-18T23:03:51Z","timestamp":1458342231000},"source":"Crossref","is-referenced-by-count":4,"title":["N-ary Mathematical Morphology"],"prefix":"10.1515","volume":"1","author":[{"given":"Emmanuel","family":"Chevallier","sequence":"first","affiliation":[{"name":"MINES ParisTech, PSL-Research University, CMM-Centre de Morphologie Math\u00e9matique, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Augustin","family":"Chevallier","sequence":"additional","affiliation":[{"name":"Ecole Normale Sup\u00e9rieure de Cachan, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jes\u00fas","family":"Angulo","sequence":"additional","affiliation":[{"name":"MINES ParisTech, PSL-Research University, CMM-Centre de Morphologie Math\u00e9matique, 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-2016-0003\/mathm-2016-0003.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0003\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0003\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T10:20:14Z","timestamp":1651054814000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0003\/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-2016-0003"],"URL":"https:\/\/doi.org\/10.1515\/mathm-2016-0003","relation":{},"ISSN":["2353-3390"],"issn-type":[{"value":"2353-3390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,18]]}}}