{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T05:22:00Z","timestamp":1766035320193,"version":"3.48.0"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T00:00:00Z","timestamp":1765843200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["6246070542"],"award-info":[{"award-number":["6246070542"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["62102213"],"award-info":[{"award-number":["62102213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["62262056"],"award-info":[{"award-number":["62262056"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Natural Science Youth Foundation of Qinghai Province","award":["2023-ZJ-947Q"],"award-info":[{"award-number":["2023-ZJ-947Q"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>Precise 3D shape correspondence is a fundamental prerequisite for critical applications ranging from medical anatomical modeling to visual recognition. However, non-isometric 3D shape matching remains a challenging task due to the limited sensitivity of traditional Laplace\u2013Beltrami (LB) bases to local geometric deformations such as stretching and bending. To address these limitations, this paper proposes a Sinkhorn-Regularized Elastic Functional Map framework (SRE-FMaps) that integrates entropy-regularized optimal transport with an elastic thin-shell energy basis. First, a sparse Sinkhorn transport plan is adopted to initialize a bijective correspondence with linear computational complexity. Then, a non-orthogonal elastic basis, derived from the Hessian of thin-shell deformation energy, is introduced to enhance high-frequency feature perception. Finally, correspondence stability is quantified through a cosine-based elastic distance metric, enabling retrieval and classification. Experiments on the SHREC2015, McGill, and Face datasets demonstrate that SRE-FMaps reduces the correspondence error by a maximum of 32% and achieves an average of 92.3% classification accuracy (with a peak of 94.74% on the Face dataset). Moreover, the framework exhibits superior robustness, yielding a recall of up to 91.67% and an F1-score of 0.94, effectively handling bending, stretching, and folding deformations compared with conventional LB-based functional map pipelines. The proposed framework provides a scalable solution for non-isometric shape correspondence in medical modeling, 3D reconstruction, and visual recognition.<\/jats:p>","DOI":"10.3390\/jimaging11120452","type":"journal-article","created":{"date-parts":[[2025,12,16]],"date-time":"2025-12-16T09:57:24Z","timestamp":1765879044000},"page":"452","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["SRE-FMaps: A Sinkhorn-Regularized Elastic Functional Map Framework for Non-Isometric 3D Shape Matching"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5676-0656","authenticated-orcid":false,"given":"Dan","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining 810016, China"},{"name":"The State Key Laboratory of Tibetan Intelligence, Xining 810016, China"},{"name":"The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Qinghai Normal University, Hutai, Xining 810008, China"},{"name":"Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing Normal University, Xining 810016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yue","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining 810016, China"},{"name":"The State Key Laboratory of Tibetan Intelligence, Xining 810016, China"},{"name":"The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Qinghai Normal University, Hutai, Xining 810008, China"},{"name":"Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing Normal University, Xining 810016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ning","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining 810016, China"},{"name":"The State Key Laboratory of Tibetan Intelligence, Xining 810016, China"},{"name":"The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Qinghai Normal University, Hutai, Xining 810008, China"},{"name":"Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing Normal University, Xining 810016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Computer, Qinghai Normal University, Xining 810016, China"},{"name":"The State Key Laboratory of Tibetan Intelligence, Xining 810016, China"},{"name":"The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Qinghai Normal University, Hutai, Xining 810008, China"},{"name":"Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing Normal University, Xining 810016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1016\/j.phrs.2018.11.002","article-title":"3. organ models\u2014Revolution in pharmacological research?","volume":"139","author":"Weinhart","year":"2019","journal-title":"Pharmacol. 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