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This means the true distance is never overestimated and the zero\u2010level set is a bounding volume for the shape. The method makes use of neural network architectures that ensure Lipschitz continuity by design in combination with a novel tailored training data selection scheme and constrained training strategy. We demonstrate that this yields both theoretical and empirical benefits over previous approaches to conservativeness (for non\u2010distance neural implicits), allowing for tighter approximation and additionally providing the valuable distance information.<\/jats:p>","DOI":"10.1111\/cgf.70528","type":"journal-article","created":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T11:07:06Z","timestamp":1786619226000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Strictly Conservative Neural Distance Fields"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-0304-1397","authenticated-orcid":false,"given":"I.","family":"Ludwig","sequence":"first","affiliation":[{"name":"Paderborn University  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2340-3462","authenticated-orcid":false,"given":"M.","family":"Campen","sequence":"additional","affiliation":[{"name":"Paderborn University  Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,8,13]]},"reference":[{"key":"e_1_2_12_2_2","first-page":"214","volume-title":"International conference on machine learning","author":"Arjovsky Martin","year":"2017"},{"key":"e_1_2_12_3_2","unstructured":"Araujo Alexandre Havens Aaron J Delattre Blaise et al. \u201cA Unified Algebraic Perspective on Lipschitz Neural Networks\u201d.The Eleventh International Conference on Learning Representations.20233 5."},{"key":"e_1_2_12_4_2","doi-asserted-by":"crossref","unstructured":"Amenta NinaandKolluri Ravi Krishna. \u201cAccurate and efficient unions of balls\u201d.Proc. 16th annual symposium on Computational geometry.2000 119\u20131285.","DOI":"10.1145\/336154.336193"},{"key":"e_1_2_12_5_2","first-page":"291","volume-title":"International conference on machine learning","author":"Anil Cem","year":"2019"},{"key":"e_1_2_12_6_2","doi-asserted-by":"crossref","first-page":"20077","DOI":"10.52202\/068431-1460","article-title":"Pay attention to your loss: understanding misconceptions about Lipschitz neural networks","volume":"35","author":"B\u00e9thune Louis","year":"2022","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_12_7_2","first-page":"2245","volume-title":"Proceedings of the 40th International Conference on Machine Learning","author":"B\u00e9thune Louis","year":"2023"},{"issue":"1","key":"e_1_2_12_8_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/966131.966132","article-title":"Adaptive medial\u2010axis approximation for sphere\u2010tree construction","volume":"23","author":"Bradshaw Gareth","year":"2004","journal-title":"ACM Transactions on Graphics"},{"key":"e_1_2_12_9_2","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex optimization","author":"Boyd Stephen","year":"2004"},{"issue":"5","key":"e_1_2_12_10_2","first-page":"10","article-title":"1\u2010Lipschitz Neural Distance Fields","volume":"43","author":"Coiffier Guillaume","year":"2024","journal-title":"Computer Graphics Forum."},{"key":"e_1_2_12_11_2","first-page":"854","volume-title":"Proceedings of the 34th International Conference on Machine Learning","author":"Cisse Moustapha","year":"2017"},{"key":"e_1_2_12_12_2","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.cag.2023.06.012","article-title":"Neural skeleton: Implicit neural representation away from the surface","volume":"114","author":"Matt\u00e9o Cl\u00e9mot","year":"2023","journal-title":"Computers & Graphics"},{"key":"e_1_2_12_13_2","first-page":"21638","article-title":"Neural unsigned distance fields for implicit function learning","volume":"33","author":"Chibane Julian","year":"2020","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_2_12_14_2","doi-asserted-by":"crossref","unstructured":"Chen ZhiqinandZhang Hao. \u201cLearning implicit fields for generative shape modeling\u201d.Proc. 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