{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T02:38:57Z","timestamp":1761964737879},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2016,4,19]],"date-time":"2016-04-19T00:00:00Z","timestamp":1461024000000},"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>Quantile filters, or rank-order filters, are local image filters which assign quantiles of intensities of\nthe input image within neighbourhoods as output image values. Combining a multivariate quantile definition\ndeveloped in matrix-valued morphology with a recently introduced mapping between the RGB colour space\nand the space of symmetric 2 \u00d7 2 matrices, we state a class of colour image quantile filters, along with a\nclass of morphological gradient filters derived from these.We consider variants of these filters based on three\nmatrix norms \u2013 the nuclear, Frobenius, and spectral norm \u2013 and study their differences. We investigate the\nproperties of the quantile and gradient filters and their links to dilation and erosion operators. Using amoeba\nstructuring elements,we devise image-adaptive versions of our quantile and gradient filters. Experiments are\npresented to demonstrate the favourable properties of the filters, and compare them to existing approaches\nin colour morphology.<\/jats:p>","DOI":"10.1515\/mathm-2016-0008","type":"journal-article","created":{"date-parts":[[2016,4,25]],"date-time":"2016-04-25T10:00:36Z","timestamp":1461578436000},"source":"Crossref","is-referenced-by-count":4,"title":["Quantile Filtering of Colour Images via\nSymmetric Matrices"],"prefix":"10.1515","volume":"1","author":[{"given":"Martin","family":"Welk","sequence":"first","affiliation":[{"name":"University for Health Sciences, Medical Informatics and Technology (UMIT), Hall\/Tyrol, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Kleefeld","sequence":"additional","affiliation":[{"name":"Brandenburg University of Technology Cottbus\u2013Senftenberg, Cottbus, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Breu\u00df","sequence":"additional","affiliation":[{"name":"Brandenburg University of Technology Cottbus\u2013Senftenberg, Cottbus, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,4,19]]},"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-2016-0008\/mathm-2016-0008.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0008\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0008\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T10:20:13Z","timestamp":1651054813000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0008\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,3,30]]}},"alternative-id":["10.1515\/mathm-2016-0008"],"URL":"https:\/\/doi.org\/10.1515\/mathm-2016-0008","relation":{},"ISSN":["2353-3390"],"issn-type":[{"value":"2353-3390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,19]]}}}