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Graph."],"published-print":{"date-parts":[[2026,7,3]]},"abstract":"<jats:p>The Medial Axis Transform (MAT) is a complete shape descriptor capable of reconstructing the geometry of the original domain. A high-quality MAT should not only facilitate high-fidelity reconstruction but also capture structural features\u2014for instance, by aligning the MAT boundary with the locus of rolling ball centers within fillet regions. However, computing such an ideal MAT remains a significant challenge, particularly when the input is a discrete triangle mesh.<\/jats:p>\n                  <jats:p>In this paper, we follow the established technical pipeline of initializing the MAT via a 3D Voronoi diagram of surface samples and subsequently simplifying the Voronoi structure through a QEM-like scheme. Our key insight is to explicitly track the correspondence between MAT vertices and surface regions throughout the progressive simplification process, ensuring that the resulting MAT triangles accurately reflect the intrinsic symmetries between surface patches. We translate these geometric requirements into a suite of priority control strategies that govern the sequencing of edge collapses.<\/jats:p>\n                  <jats:p>\n                    Through extensive evaluation against state-of-the-art MAT algorithms, we validate the strong performance of our approach regarding runtime efficiency, structural alignment, boundary regularity, triangle quality, and robustness to noise. Our resulting MATs remain highly expressive for both articulated shapes and CAD models, even under extreme simplification\u2014effectively capturing the global structure of complex geometries with only a few hundred vertices. Finally, we showcase the utility of our approach through two potential applications: capturing the locus of rolling ball centers within fillet regions, a structural capability not previously demonstrated in the existing literature, and surface extraction from unsigned distance fields, where the medial axis of the\n                    <jats:italic toggle=\"yes\">\u0454<\/jats:italic>\n                    -isosurface naturally yields a clean single-layer result.\n                  <\/jats:p>\n                  <jats:p>Source code is available at https:\/\/github.com\/sssomeone\/structural-mat.<\/jats:p>","DOI":"10.1145\/3811291","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Structural MAT: Clean and Scalable Medial Axis Simplification via Explicit Surface Correspondence"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2079-275X","authenticated-orcid":false,"given":"Pengfei","family":"Wang","sequence":"first","affiliation":[{"name":"Shandong University, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0835-3316","authenticated-orcid":false,"given":"Shuangmin","family":"Chen","sequence":"additional","affiliation":[{"name":"Qingdao University of Science and Technology, Qingdao, China"},{"name":"Shandong Key Laboratory of Deep Sea Equipment Intelligent Networking, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2209-2404","authenticated-orcid":false,"given":"Dongming","family":"Yan","sequence":"additional","affiliation":[{"name":"Institute of Automation, Chinese Academy of Sciences, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6749-4485","authenticated-orcid":false,"given":"Ying","family":"He","sequence":"additional","affiliation":[{"name":"Nanyang Technological University, Singapore, Yunnan Garden, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8452-8723","authenticated-orcid":false,"given":"Shiqing","family":"Xin","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1231-3392","authenticated-orcid":false,"given":"Changhe","family":"Tu","sequence":"additional","affiliation":[{"name":"Shandong University, Qingdao, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2284-3952","authenticated-orcid":false,"given":"Wenping","family":"Wang","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University, Texas, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(01)00017-7"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICIP.1996.560357"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1006\/ciun.1994.1007"},{"key":"e_1_2_1_4_1","volume-title":"The \"\u03bb-medial axis\". 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