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The algorithm runs in <jats:italic>O(N<jats:sup>2<\/jats:sup>)<\/jats:italic> time for an <jats:italic>N \u00d7 N<\/jats:italic> binary image, and it also works for other distances that appear in machine\u2010vision applications, such as city block and chessboard. Its parallel version runs in <jats:italic>O(N<jats:sup>2<\/jats:sup>\/p)<\/jats:italic> time with <jats:italic>p<\/jats:italic>(1 \u2264 <jats:italic>p<\/jats:italic> \u2264 <jats:italic>N<\/jats:italic>) processors.<\/jats:p>","DOI":"10.1002\/scj.4690270702","type":"journal-article","created":{"date-parts":[[2007,7,8]],"date-time":"2007-07-08T11:18:25Z","timestamp":1183893505000},"page":"18-24","source":"Crossref","is-referenced-by-count":4,"title":["An efficient algorithm for the euclidean distance transformation"],"prefix":"10.1002","volume":"27","author":[{"given":"Toshihiro","family":"Kato","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomio","family":"Hirata","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toyofumi","family":"Saito","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenji","family":"Kise","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,3,21]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/34.391389"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(94)00062-X"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0146-664X(80)90054-4"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"A.Fujiwara T.MasuzawaandH.Fujiwara.An optimal parallel algorithm for the Euclidean distance maps of 2\u2010D binary images SIGAL workshop AL\u201343 (1995).","DOI":"10.1016\/0020-0190(95)00041-A"},{"key":"e_1_2_1_6_2","unstructured":"T.HirataandT.Kato.An algorithm for Euclidean distance transformation. 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