{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T05:16:08Z","timestamp":1769145368115,"version":"3.49.0"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2008,8]]},"abstract":"<jats:p> The Hausdorff distance between two sets of curves is a measure for the similarity of these objects and therefore an interesting feature in shape recognition. If the curves are algebraic computing the Hausdorff distance involves computing the intersection points of the Voronoi edges of the one set with the curves in the other. Since computing the Voronoi diagram of curves is quite difficult we characterize those points algebraically and compute them using the computer algebra system SYNAPS. This paper describes in detail which points have to be considered, by what algebraic equations they are characterized, and how they actually are computed. <\/jats:p>","DOI":"10.1142\/s0218195908002647","type":"journal-article","created":{"date-parts":[[2008,8,13]],"date-time":"2008-08-13T11:09:14Z","timestamp":1218625754000},"page":"307-320","source":"Crossref","is-referenced-by-count":41,"title":["COMPUTING THE HAUSDORFF DISTANCE BETWEEN CURVED OBJECTS"],"prefix":"10.1142","volume":"18","author":[{"given":"HELMUT","family":"ALT","sequence":"first","affiliation":[{"name":"Freie Universit\u00e4t Berlin, Fachbereich Mathematik und Informatik, Takustr. 9, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LUDMILA","family":"SCHARF","sequence":"additional","affiliation":[{"name":"Freie Universit\u00e4t Berlin, Fachbereich Mathematik und Informatik, Takustr. 9, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01530830"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-005-1192-0"},{"key":"rf3","volume-title":"Handbook of Computational Geometry","author":"Alt H.","year":"1999"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0010-4485(98)00065-7"},{"key":"rf5","first-page":"76","author":"Elber G.","journal-title":"IEEE Computer Graphics and Applications"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195998000291"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(98)00211-8"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(98)00223-4"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(89)90058-4"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195908002647","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:23:04Z","timestamp":1565137384000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195908002647"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8]]},"references-count":9,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,8]]}},"alternative-id":["10.1142\/S0218195908002647"],"URL":"https:\/\/doi.org\/10.1142\/s0218195908002647","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,8]]}}}