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Graph."],"published-print":{"date-parts":[[2015,12,29]]},"abstract":"<jats:p>\n            The medial axis transform (MAT) is an important shape representation for shape approximation, shape recognition, and shape retrieval. Despite years of research, there is still a lack of effective methods for efficient, robust and accurate computation of the MAT. We present an efficient method, called\n            <jats:italic>Q-MAT<\/jats:italic>\n            , that uses quadratic error minimization to compute a structurally simple, geometrically accurate, and compact representation of the MAT. We introduce a new error metric for approximation and a new quantitative characterization of unstable branches of the MAT, and integrate them in an extension of the well-known quadric error metric (QEM) framework for mesh decimation. Q-MAT is fast, removes insignificant unstable branches effectively, and produces a simple and accurate piecewise linear approximation of the MAT. The method is thoroughly validated and compared with existing methods for MAT computation.\n          <\/jats:p>","DOI":"10.1145\/2753755","type":"journal-article","created":{"date-parts":[[2015,12,30]],"date-time":"2015-12-30T13:13:41Z","timestamp":1451481221000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":72,"title":["Q-MAT"],"prefix":"10.1145","volume":"35","author":[{"given":"Pan","family":"Li","sequence":"first","affiliation":[{"name":"Tsinghua University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Wang","sequence":"additional","affiliation":[{"name":"Tsinghua University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Feng","family":"Sun","sequence":"additional","affiliation":[{"name":"The Pennsylvania State University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaohu","family":"Guo","sequence":"additional","affiliation":[{"name":"University of Texas at Dallas"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Caiming","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shandong University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenping","family":"Wang","sequence":"additional","affiliation":[{"name":"University of Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2015,12,29]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/276884.276889"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/376957.376986"},{"key":"e_1_2_2_3_1","volume-title":"H","author":"Attali D.","year":"2009","unstructured":"D. Attali , J.-D. Boissonnat , and H. Edelsbrunner , H . 2009 . Stability and computation of medial axes-a state-of-the-art report. In Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration. Springer , 109--125. D. Attali, J.-D. Boissonnat, and H. Edelsbrunner, H. 2009. Stability and computation of medial axes-a state-of-the-art report. In Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration. Springer, 109--125."},{"key":"e_1_2_2_4_1","volume-title":"Proceedings of the International Conference on Image Processing.","volume":"3","author":"Attali D.","unstructured":"D. Attali , and A. Montanvert , A. 1996. Modeling noise for a better simplification of skeletons . In Proceedings of the International Conference on Image Processing. Vol. 3 . IEEE, 13--16. D. Attali, and A. Montanvert, A. 1996. Modeling noise for a better simplification of skeletons. In Proceedings of the International Conference on Image Processing. Vol. 3. IEEE, 13--16."},{"key":"e_1_2_2_5_1","first-page":"362","article-title":"A transformation for extracting new descriptors of shape","volume":"19","author":"Blum H.","year":"1967","unstructured":"H. Blum 1967 . A transformation for extracting new descriptors of shape . In Models for the Perception of Speech and Visual Form 19 , 5, 362 -- 380 . H. Blum et al. 1967. A transformation for extracting new descriptors of shape. 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(Beograd) N."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0010-4485(03)00061-7"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2542355.2542359"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.1631582"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258849"},{"key":"e_1_2_2_14_1","volume-title":"B-mesh: A modeling system for base meshes of 3d articulated shapes. In Computer Graphics Forum.","author":"Ji Z.","year":"2010","unstructured":"Z. Ji , L. Liu , and Y. Wang . 2010 . B-mesh: A modeling system for base meshes of 3d articulated shapes. In Computer Graphics Forum. Vol. 29 . Wiley Online Library , 2169--2177. Z. Ji, L. Liu, and Y. Wang. 2010. B-mesh: A modeling system for base meshes of 3d articulated shapes. In Computer Graphics Forum. Vol. 29. Wiley Online Library, 2169--2177."},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778838"},{"key":"e_1_2_2_16_1","unstructured":"Pixologic. 2001. Zbrush.  Pixologic. 2001. Zbrush."},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026135101267"},{"key":"e_1_2_2_18_1","doi-asserted-by":"crossref","unstructured":"K. Siddiqi and S. M. Pizer. 2008. Medial Representations. Mathematics Algorithms and Applications. Springer.   K. Siddiqi and S. M. Pizer. 2008. Medial Representations. Mathematics Algorithms and Applications. Springer.","DOI":"10.1007\/978-1-4020-8658-8"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1060244.1060250"},{"key":"e_1_2_2_20_1","unstructured":"F. Sun Y. Choi Y. Yu and W. Wang. 2013. Medial meshes for volume approximation. CoRR abs\/1308.3917.  F. Sun Y. Choi Y. Yu and W. Wang. 2013. Medial meshes for volume approximation. CoRR abs\/1308.3917."},{"key":"e_1_2_2_21_1","article-title":"Medial meshes: A compact and accurate medial shape representation","author":"Sun F.","year":"2014","unstructured":"F. Sun , Y. Choi , Y. Yu , and W. Wang . 2014 . Medial meshes: A compact and accurate medial shape representation . IEEE Transactions on Visualization and Computer Graphics. F. Sun, Y. Choi, Y. Yu, and W. Wang. 2014. Medial meshes: A compact and accurate medial shape representation. IEEE Transactions on Visualization and Computer Graphics.","journal-title":"IEEE Transactions on Visualization and Computer Graphics."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508384"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2753755","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2753755","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:16:39Z","timestamp":1750227399000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2753755"}},"subtitle":["Computing Medial Axis Transform By Quadratic Error Minimization"],"short-title":[],"issued":{"date-parts":[[2015,12,29]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,12,29]]}},"alternative-id":["10.1145\/2753755"],"URL":"https:\/\/doi.org\/10.1145\/2753755","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12,29]]},"assertion":[{"value":"2014-11-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-03-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-12-29","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}