{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:13:14Z","timestamp":1763467994213,"version":"3.41.0"},"reference-count":33,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2010,7,26]],"date-time":"2010-07-26T00:00:00Z","timestamp":1280102400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2010,7,26]]},"abstract":"<jats:p>\n            This paper addresses the fundamental problem of computing stable medial representations of 3D shapes. We propose a\n            <jats:italic>spatially adaptive<\/jats:italic>\n            classification of geometric features that yields a robust algorithm for generating medial representations at different levels of abstraction. The recently introduced continuous scale axis transform serves as the mathematical foundation of our algorithm. We show how geometric and topological properties of the continuous setting carry over to discrete shape representations. Our method combines scaling operations of medial balls for geometric simplification with filtrations of the medial axis and provably good conversion steps to and from union of balls, to enable efficient processing of a wide variety shape representations including polygon meshes, 3D images, implicit surfaces, and point clouds. We demonstrate the robustness and versatility of our algorithm with an extensive validation on hundreds of shapes including complex geometries consisting of millions of triangles.\n          <\/jats:p>","DOI":"10.1145\/1778765.1778838","type":"journal-article","created":{"date-parts":[[2010,7,15]],"date-time":"2010-07-15T12:48:46Z","timestamp":1279198126000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":67,"title":["Discrete scale axis representations for 3D geometry"],"prefix":"10.1145","volume":"29","author":[{"given":"Balint","family":"Miklos","sequence":"first","affiliation":[{"name":"ETH Zurich \/ EPFL"}]},{"given":"Joachim","family":"Giesen","sequence":"additional","affiliation":[{"name":"Friedrich-Schiller-Universit\u00e4t Jena"}]},{"given":"Mark","family":"Pauly","sequence":"additional","affiliation":[{"name":"EPFL"}]}],"member":"320","published-online":{"date-parts":[[2010,7,26]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073238"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/276884.276889"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/336154.336193"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(01)00033-5"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(01)00017-7"},{"volume-title":"Proceedings of International Conference on Image Processing, 13--16","author":"Attali D.","key":"e_1_2_2_6_1"},{"volume-title":"-D","year":"2009","author":"Attali D.","key":"e_1_2_2_7_1"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2007.01047.x"},{"key":"e_1_2_2_9_1","unstructured":"Blum H. 1967. A Transformation for Extracting New Descriptors of Shape. Models for the Perception of Speech and Visual Form 362--380.  Blum H. 1967. A Transformation for Extracting New Descriptors of Shape. Models for the Perception of Speech and Visual Form 362--380."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2005.01.004"},{"volume-title":"Symmetry Sets. Proc. of the Royal Society of Edinburgh 101","author":"Bruce J. 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Siddiqi K. and \n      Yushkevich P\n  . \n  2008\n  . Medial Representations vol. \n  37\n   of \n  Computational Imaging and Vision\n  . \n  Springer Netherlands Dordrecht.  Pizer S. Siddiqi K. and Yushkevich P. 2008. Medial Representations vol. 37 of Computational Imaging and Vision. Springer Netherlands Dordrecht.","DOI":"10.1007\/978-1-4020-8658-8"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141923"},{"key":"e_1_2_2_25_1","first-page":"1","article-title":"Morphological analysis of shapes","volume":"139","author":"Prasad L.","year":"1997","journal-title":"CNLS Newsletter"},{"volume-title":"VISSYM '02: Proceedings of the symposium on Data Visualisation","year":"2002","author":"Rumpf M.","key":"e_1_2_2_26_1"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016376116653"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISVD.2009.24"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026378916288"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/1060244.1060250"},{"key":"e_1_2_2_31_1","doi-asserted-by":"crossref","unstructured":"Svensson S. 2001. Reversible surface skeletons of 3d objects by iterative thinning of distance transforms. Digital and image geometry: advanced lectures 400--411.   Svensson S. 2001. Reversible surface skeletons of 3d objects by iterative thinning of distance transforms. Digital and image geometry: advanced lectures 400--411.","DOI":"10.1007\/3-540-45576-0_24"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1109\/VISUAL.2003.1250410"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2009.81"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1778765.1778838","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1778765.1778838","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T11:39:47Z","timestamp":1750246787000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1778765.1778838"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,26]]},"references-count":33,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,7,26]]}},"alternative-id":["10.1145\/1778765.1778838"],"URL":"https:\/\/doi.org\/10.1145\/1778765.1778838","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"type":"print","value":"0730-0301"},{"type":"electronic","value":"1557-7368"}],"subject":[],"published":{"date-parts":[[2010,7,26]]},"assertion":[{"value":"2010-07-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}