{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,7]],"date-time":"2024-07-07T07:28:48Z","timestamp":1720337328236},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2016,5,5]],"date-time":"2016-05-05T00:00:00Z","timestamp":1462406400000},"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>Path openings are morphological operators that are used to preserve long, thin, and curved structures\nin images. They have the ability to adapt to local image structures,which allows them to detect lines that\nare not perfectly straight. They are applicable in extracting cracks, roads, and similar structures. Although\npath openings are very efficient to implement for binary images, the greyscale case is more problematic. This\nstudy provides an analysis of the main existing greyscale algorithm, and shows that although its time complexity\ncan be quadratic in the number of pixels, this is optimal in terms of the output (if the full opening\ntransform is created). Also, it is shown that under many circumstances the worst-case running time is much\nless than quadratic. Finally, a new algorithm is provided,which has the same time complexity, but is simpler,\nfaster in practice and more amenable to parallelization<\/jats:p>","DOI":"10.1515\/mathm-2016-0010","type":"journal-article","created":{"date-parts":[[2016,5,15]],"date-time":"2016-05-15T11:59:27Z","timestamp":1463313567000},"source":"Crossref","is-referenced-by-count":2,"title":["Efficient Computation of Greyscale Path\nOpenings"],"prefix":"10.1515","volume":"1","author":[{"given":"Herman","family":"Schubert","sequence":"first","affiliation":[{"name":"University of Groningen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jasper J.","family":"van de Gronde","sequence":"additional","affiliation":[{"name":"University of Groningen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos B. T. M.","family":"Roerdink","sequence":"additional","affiliation":[{"name":"University of Groningen"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,5,5]]},"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-2016-0010\/mathm-2016-0010.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0010\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0010\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T10:20:08Z","timestamp":1651054808000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2016-0010\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,3,30]]}},"alternative-id":["10.1515\/mathm-2016-0010"],"URL":"https:\/\/doi.org\/10.1515\/mathm-2016-0010","relation":{},"ISSN":["2353-3390"],"issn-type":[{"value":"2353-3390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,5]]}}}