{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T10:33:00Z","timestamp":1682332380222},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2008,12]]},"abstract":"<jats:p> The medial axis of a shape is known to carry a lot of information about the shape. In particular, a recent result of Lieutier establishes that every bounded open subset of \u211d<jats:sup>n<\/jats:sup> has the same homotopy type as its medial axis. In this paper we provide an algorithm that computes a structure we call the core for the approximation of the medial axis of a shape with smooth boundary from a discrete sample of its boundary. The core is a piecewise linear cell complex that is guaranteed to capture the topology of the medial axis of the shape provided the sample of its boundary is sufficiently dense but not necessarily uniform. We also present a natural method for augmenting the core in order to extend it geometrically while maintaining the topological guarantees. The definition of the core and its extension are based on the steepest ascent flow map that results from the distance function induced by the sample point set. We also provide a geometric guarantee on the closeness of the core and the actual medial axis. <\/jats:p>","DOI":"10.1142\/s0218195908002751","type":"journal-article","created":{"date-parts":[[2008,12,15]],"date-time":"2008-12-15T01:07:59Z","timestamp":1229303279000},"page":"533-565","source":"Crossref","is-referenced-by-count":1,"title":["MEDIAL AXIS APPROXIMATION AND UNSTABLE FLOW COMPLEX"],"prefix":"10.1142","volume":"18","author":[{"given":"JOACHIM","family":"GIESEN","sequence":"first","affiliation":[{"name":"Friedrich-Schiller-Universit\u00e4t Jena, Ernst-Abbe-Platz 2, D-07743 Jena, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"EDGAR A.","family":"RAMOS","sequence":"additional","affiliation":[{"name":"Escuela de Matem\u00e1ticas, Universidad Nacional de Colombia, Medell\u00edn, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"BARDIA","family":"SADRI","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Toronto, Toronto, Ontario M5S 3G4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009475"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/gmip.1998.0465"},{"key":"rf3","volume-title":"Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration","author":"Attali D.","year":"2004"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(01)00017-7"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(01)00048-7"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2003.07.008"},{"key":"rf8","first-page":"304","volume":"67","author":"Chazal F.","journal-title":"Graph. Mod. Imag. Process."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-003-1049-y"},{"key":"rf13","first-page":"357","volume":"54","author":"Grove K.","journal-title":"Symp. Pure Mathematics"},{"key":"rf14","volume-title":"Algebraic Topology","author":"Hatcher A.","year":"2001"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2004.01.011"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195908002751","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:16:28Z","timestamp":1565190988000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195908002751"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12]]},"references-count":11,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,12]]}},"alternative-id":["10.1142\/S0218195908002751"],"URL":"https:\/\/doi.org\/10.1142\/s0218195908002751","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,12]]}}}