{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T11:38:26Z","timestamp":1786621106076,"version":"3.56.0"},"reference-count":44,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T00:00:00Z","timestamp":1786579200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T00:00:00Z","timestamp":1786579200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We propose a novel variational method to compute a highly accurate global signed distance function (SDF) to a given point cloud. To this end, the jump set of the gradient of the SDF, which coincides with the medial axis of the surface, is explicitly taken into account through a higher\u2010order variational formulation that enforces linear growth along the gradient direction away from this discontinuity set. The eikonal equation and the zero\u2010level set of the SDF are enforced as constraints. To make this variational problem computationally tractable, a phase field approximation of Ambrosio\u2010Tortorelli type is employed. The associated phase field function implicitly describes the medial axis. The method is implemented for surfaces represented by unoriented point clouds using neural network approximations of both the SDF and the phase field. Experiments demonstrate the method's accuracy both in the near field and globally. Quantitative and qualitative comparisons with other approaches show the advantages of the proposed method.<\/jats:p>","DOI":"10.1111\/cgf.70517","type":"journal-article","created":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T11:15:17Z","timestamp":1786619717000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Medial Axis Aware Learning of Signed Distance Functions"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-7895-1194","authenticated-orcid":false,"given":"Samuel","family":"Weidemaier","sequence":"first","affiliation":[{"name":"University of Bonn  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-6689-5747","authenticated-orcid":false,"given":"Christoph","family":"Norden\u2010Smoch","sequence":"additional","affiliation":[{"name":"University of Bonn  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6049-9390","authenticated-orcid":false,"given":"Martin","family":"Rumpf","sequence":"additional","affiliation":[{"name":"University of Bonn  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,13]]},"reference":[{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s005260050144"},{"key":"e_1_2_8_3_2","first-page":"1","article-title":"A mathematical problem related to the physical theory of liquid crystal configurations","volume":"12","author":"Aviles Patricio","year":"1987","journal-title":"Proc. Centre Math. Anal. Austral. Nat. Univ."},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500023167"},{"issue":"7","key":"e_1_2_8_5_2","first-page":"105","article-title":"Tortorelli. On the approximation of free discontinuity problems","volume":"6","author":"Ambrosio Luigi","year":"1992","journal-title":"Bollettino dell'Unione Matematica Italiana, Sezione B"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5096(99)00028-9"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1145\/2451236.2451246"},{"key":"e_1_2_8_8_2","first-page":"362","volume-title":"Models for the Perception of Speech and Visual Form","author":"Blum Harry","year":"1967"},{"key":"e_1_2_8_9_2","unstructured":"YizhakBen-Shabat Chamin HewaKoneputugodage andStephenGould. Digs: Divergence guided shape implicit neural representation for unoriented point clouds. InProceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition pages19323\u201319332 New Orleans USA 2022. 1 2"},{"key":"e_1_2_8_10_2","first-page":"e15128","volume-title":"Computer Graphics Forum","author":"Guillaume Coiffier and Louis B\u00e9thune","year":"2024"},{"key":"e_1_2_8_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2023.06.012"},{"key":"e_1_2_8_12_2","doi-asserted-by":"publisher","DOI":"10.1145\/2516971.2516977"},{"key":"e_1_2_8_13_2","doi-asserted-by":"publisher","DOI":"10.1145\/3131280"},{"key":"e_1_2_8_14_2","unstructured":"AmerEssakine YanqiCheng Chun-WunCheng LipeiZhang ZhongyingDeng LeiZhu Carola-BibianeSch\u00f6nlieb andAngelica IAviles-Rivero. Where do we stand with implicit neural representations? a technical and performance survey.Transactions on Machine Learning Research 2025. Survey Certification. 2"},{"key":"e_1_2_8_15_2","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/019"},{"key":"e_1_2_8_16_2","doi-asserted-by":"publisher","DOI":"10.1145\/3658220"},{"key":"e_1_2_8_17_2","volume-title":"Geometric Measure Theory, volume 153 of Die Grundlehren der mathematischen Wissenschaften","author":"Federer Herbert","year":"1969"},{"key":"e_1_2_8_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5096(98)00034-9"},{"key":"e_1_2_8_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2020.01.007"},{"key":"e_1_2_8_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s003710050084"},{"key":"e_1_2_8_21_2","doi-asserted-by":"crossref","unstructured":"Kaiming He X.Zhang Shaoqing Ren and Jian Sun. Deep residual learning for image recognition.2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) pages770\u2013778 2015. 5","DOI":"10.1109\/CVPR.2016.90"},{"key":"e_1_2_8_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/s003329910014"},{"key":"e_1_2_8_23_2","article-title":"Adam: A method for stochastic optimization","volume":"1412","author":"Kingma Diederik P.","year":"2014","journal-title":"CoRR"},{"key":"e_1_2_8_24_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-22-1-77-108"},{"key":"e_1_2_8_25_2","unstructured":"MarianKleineberg.Mesh-to-sdf: Calculate signed distance fields for arbitrary meshes 2021. 7"},{"key":"e_1_2_8_26_2","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2002012"},{"key":"e_1_2_8_27_2","unstructured":"YaronLipman. Phase transitions distance functions and implicit neural representations. InInternational Conference on Machine Learning 2021. 1 2 4"},{"key":"e_1_2_8_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2024.102305"},{"key":"e_1_2_8_29_2","doi-asserted-by":"crossref","unstructured":"IshitMehta ManmohanChandraker andRaviRamamoorthi. A level set theory for neural implicit evolution under explicit flows. InEuropean Conference on Computer Vision pages711\u2013729 Tel Aviv Israel 2022. Springer. 1","DOI":"10.1007\/978-3-031-20086-1_41"},{"issue":"1","key":"e_1_2_8_30_2","first-page":"285","article-title":"Un esempio di \u0393-convergenza","volume":"14","author":"Modica Luciano","year":"1977","journal-title":"Boll. Un. Mat. Ital. B (5)"},{"key":"e_1_2_8_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2024.117104"},{"key":"e_1_2_8_32_2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160420503"},{"key":"e_1_2_8_33_2","doi-asserted-by":"crossref","unstructured":"Zo\u00ebMarschner SilviaSell\u00e1n Hsueh-Ti DerekLiu andAlecJacobson. Constructive solid geometry on neural signed distance fields. InSIGGRAPH Asia 2023 conference papers pages1\u201312 Sydney Australia 2023. 1","DOI":"10.1145\/3610548.3618170"},{"key":"e_1_2_8_34_2","volume-title":"PyTorch: an imperative style, high-performance deep learning library","author":"Paszke Adam","year":"2019"},{"key":"e_1_2_8_35_2","unstructured":"DanielRebain KeLi VincentSitzmann SorooshYazdani Kwang MooYi andAndreaTagliasacchi. Deep medial fields.arXiv preprint arXiv:2106.03804 2021. 2"},{"key":"e_1_2_8_36_2","unstructured":"VincentSitzmann Julien N. P.Martel Alexander W.Bergman David B.Lindell andGordonWetzstein.Implicit neural representations with periodic activation functions 2020. 1 2 4 5"},{"key":"e_1_2_8_37_2","doi-asserted-by":"publisher","DOI":"10.1145\/3243651"},{"key":"e_1_2_8_38_2","doi-asserted-by":"crossref","unstructured":"SamuelWeidemaier FlorineHartwig JosuaSassen SergioConti MirelaBen-Chen andMartinRumpf. Sdfs from unoriented point clouds using neural variational heat distances.Computer Graphics Forum n\/a(n\/a):e70296 2026. 1 2 6 7 14","DOI":"10.1111\/cgf.70296"},{"key":"e_1_2_8_39_2","unstructured":"ZimoWang ChengWang TaikiYoshino SiruiTao ZiyangFu andTzu-MaoLi. Hotspot: Signed distance function optimization with an asymptotically sufficient condition. InCVPR 2025. 1 2 5 6 7 8 9 13 14"},{"key":"e_1_2_8_40_2","first-page":"63515","volume-title":"Advances in Neural Information Processing Systems","author":"Wang Ruian","year":"2023"},{"key":"e_1_2_8_41_2","doi-asserted-by":"publisher","DOI":"10.1145\/3618331"},{"key":"e_1_2_8_42_2","doi-asserted-by":"crossref","unstructured":"ZhanXu YangZhou EvangelosKalogerakis andKaranSingh. Predicting animation skeletons for 3d articulated models via volumetric nets. InProceedings of the International Conference on 3D Vision (3DV) pages298\u2013307 2019. 2","DOI":"10.1109\/3DV.2019.00041"},{"issue":"8","key":"e_1_2_8_43_2","doi-asserted-by":"crossref","first-page":"1178","DOI":"10.1109\/TVCG.2010.124","article-title":"Template-based 3d model fitting using dual-domain relaxation","volume":"17","author":"Yeh I-Cheng","year":"2010","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"e_1_2_8_44_2","unstructured":"HuizongYang YuxinSun GaneshSundaramoorthi andAnthonyYezzi. Steik: stabilizing the optimization of neural signed distance functions and finer shape representation. InProceedings of the 37th International Conference on Neural Information Processing Systems NIPS '23 Red Hook USA 2023. Curran Associates Inc. 1 2"},{"key":"e_1_2_8_45_2","unstructured":"QingnanZhouandAlecJacobson. Thingi10k: A dataset of 10 000 3d-printing models.Preprint arXiv:1605.04797 2016. 7 14"}],"container-title":["Computer Graphics Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cgf.70517","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/cgf.70517","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cgf.70517","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T11:15:25Z","timestamp":1786619725000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/cgf.70517"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,13]]},"references-count":44,"alternative-id":["10.1111\/cgf.70517"],"URL":"https:\/\/doi.org\/10.1111\/cgf.70517","archive":["Portico"],"relation":{},"ISSN":["0167-7055","1467-8659"],"issn-type":[{"value":"0167-7055","type":"print"},{"value":"1467-8659","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,13]]},"assertion":[{"value":"2026-08-13","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70517"}}