{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T05:27:53Z","timestamp":1747805273122},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2007,10]]},"abstract":"<jats:p> We present a novel algorithm to compute a simplified medial axis of a polyhedron. Our simplification algorithm tends to remove unstable features of Blum's medial axis. Moreover, our algorithm preserves the topological structure of the original medial axis and ensures that the simplified medial axis has the same homotopy type as Blum's medial axis. We use the separation angle formed by connecting a point on the medial axis to closest points on the boundary as a measure of the stability of the medial axis at the point. The medial axis is decomposed into its parts that are the sheets, seams and junctions. We present a stability measure of each part of the medial axis based on separation angles and examine the relation between the stability measures of adjacent parts. Our simplification algorithm uses iterative pruning of the parts based on efficient local tests. We have applied the algorithm to compute a simplified medial axis of complex models with tens of thousands of triangles and complex topologies. <\/jats:p>","DOI":"10.1142\/s0218195907002434","type":"journal-article","created":{"date-parts":[[2007,11,14]],"date-time":"2007-11-14T06:26:47Z","timestamp":1195021607000},"page":"423-451","source":"Crossref","is-referenced-by-count":9,"title":["HOMOTOPY-PRESERVING MEDIAL AXIS SIMPLIFICATION"],"prefix":"10.1142","volume":"17","author":[{"given":"AVNEESH","family":"SUD","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MARK","family":"FOSKEY","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DINESH","family":"MANOCHA","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/cviu.1997.0536"},{"key":"rf3","volume-title":"Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration","author":"Attali D.","year":"2004"},{"key":"rf5","unstructured":"H.\u00a0Blum, Models for the Perception of Speech and Visual Form, ed. W.\u00a0Wathen-Dunn (MIT Press, 1967)\u00a0pp. 362\u2013380."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0031-3203(78)90025-0"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1023\/B:JODS.0000024119.38784.ff"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(01)00056-6"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1006\/cviu.1995.1062"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1109\/34.161346"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1016\/S0262-8856(97)00074-7"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1016\/0031-3203(94)00105-U"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026135101267"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(94)00025-9"},{"key":"rf33","first-page":"45","volume":"2","author":"Sherbrooke E. C.","journal-title":"IEEE Trans. Visual. Comput. Graph."},{"key":"rf34","doi-asserted-by":"publisher","DOI":"10.1006\/gmip.1997.0438"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016376116653"},{"key":"rf36","volume-title":"Algebraic Topology","author":"Spanier E. H.","year":"1989"},{"key":"rf39","author":"Tam R.","journal-title":"IEEE Visualization"},{"key":"rf41","author":"Varadhan G.","journal-title":"Eurographics Symp. Geometry Processing"},{"key":"rf44","doi-asserted-by":"publisher","DOI":"10.1142\/S0218001493000601"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195907002434","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:30:16Z","timestamp":1565123416000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195907002434"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,10]]},"references-count":19,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,10]]}},"alternative-id":["10.1142\/S0218195907002434"],"URL":"https:\/\/doi.org\/10.1142\/s0218195907002434","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,10]]}}}