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Graph."],"published-print":{"date-parts":[[2026,6,30]]},"abstract":"<jats:p>The medial axis, a lower-dimensional descriptor that captures the extrinsic structure of a shape, plays an important role in digital geometry processing. Despite its importance, computing the medial axis transform robustly from diverse inputs, especially point clouds with defects, remains a challenging problem. In this article, we propose a new implicit method that deviates from traditional explicit medial axis computation. Our key technical insight is that the difference between the signed distance field (SDF) and the medial field (MF) of a solid shape relates to the unsigned distance field (UDF) of the shape\u2019s medial axis. This observation allows us to formulate medial axis extraction as an implicit reconstruction problem. By employing a modified double covering strategy, we recover the medial axis as the zero level-set of the UDF. Extensive experiments demonstrate that our method achieves higher accuracy and robustness in learning compact medial axis transforms from challenging meshes and point clouds, outperforming existing approaches.<\/jats:p>","DOI":"10.1145\/3795772","type":"journal-article","created":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T11:47:37Z","timestamp":1770983257000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Quasi-Medial Distance Field (Q-MDF): A Robust Method for Approximating and Discretizing Neural Medial Axes"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-6922-2354","authenticated-orcid":false,"given":"Jiayi","family":"Kong","sequence":"first","affiliation":[{"name":"College of Computing and Data Science (CCDS), Nanyang Technological University","place":["Singapore, Singapore"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4954-0780","authenticated-orcid":false,"given":"Chen","family":"Zong","sequence":"additional","affiliation":[{"name":"College of Computing and Data Science (CCDS), Nanyang Technological University","place":["Singapore, Singapore"]},{"name":"School of Mathematics, Nanjing University of Aeronautics and Astronautics","place":["Singapore, Singapore"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7036-5158","authenticated-orcid":false,"given":"Jun","family":"Luo","sequence":"additional","affiliation":[{"name":"College of Computing and Data Science (CCDS), Nanyang Technological University","place":["Singapore, Singapore"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8452-8723","authenticated-orcid":false,"given":"Shiqing","family":"Xin","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Shandong University","place":["Qingdao, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8226-6635","authenticated-orcid":false,"given":"Fei","family":"Hou","sequence":"additional","affiliation":[{"name":"Institute of Software Chinese Academy of Sciences","place":["Beijing, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9582-5539","authenticated-orcid":false,"given":"Hanqing","family":"Jiang","sequence":"additional","affiliation":[{"name":"SenseTime Research, SenseTime Group","place":["Hangzhou, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8761-5563","authenticated-orcid":false,"given":"Chen","family":"Qian","sequence":"additional","affiliation":[{"name":"SenseTime Group","place":["Beijing, China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6749-4485","authenticated-orcid":false,"given":"Ying","family":"He","sequence":"additional","affiliation":[{"name":"College of Computing and Data Science (CCDS), Nanyang Technological University","place":["Singapore, Singapore"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2026,4,24]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(01)00017-7"},{"key":"e_1_3_2_3_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/ICIP.1996.560357","volume-title":"Proceedings of 3rd IEEE International Conference on Image Processing","author":"Attali Dominique","year":"1996","unstructured":"Dominique Attali and Annick Montanvert. 1996. 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