Monge-Ampere Regularization for Learning Arbitrary Shapes from Point Clouds
As commonly used implicit geometry representations, the signed distance function (SDF) is limited to modeling watertight shapes, while the unsigned distance function (UDF) is capable of representing various surfaces. However, its inherent theoretical shortcoming, i.e., the non-differentiability at t...
| Publié dans: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - PP(2025) vom: 23. Apr. |
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| Auteur principal: | |
| Autres auteurs: | , , , , , |
| Format: | Article en ligne |
| Langue: | English |
| Publié: |
2025
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| Accès à la collection: | IEEE transactions on pattern analysis and machine intelligence |
| Sujets: | Journal Article |
| Résumé: | As commonly used implicit geometry representations, the signed distance function (SDF) is limited to modeling watertight shapes, while the unsigned distance function (UDF) is capable of representing various surfaces. However, its inherent theoretical shortcoming, i.e., the non-differentiability at the zero-level set, would result in sub-optimal reconstruction quality. In this paper, we propose the scaled-squared distance function (S2DF), a novel implicit surface representation for modeling arbitrary surface types. S2DF does not distinguish between inside and outside regions while effectively addressing the non-differentiability issue of UDF at the zero-level set. We demonstrate that S2DF satisfies a second-order partial differential equation of Monge-Ampere-type, allowing us to develop a learning pipeline that leverages a novel MongeAmpere regularization to directly learn S2DF from raw unoriented point clouds without supervision from ground-truth S2DF values. Extensive experiments across multiple datasets show that our method significantly outperforms state-of-the-art supervised approaches that require ground-truth surface information as supervision for training. The code will be publicly available at https://github.com/chuanxiang-yang/S2DF |
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| Description: | Date Revised 24.04.2025 published: Print-Electronic Citation Status Publisher |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2025.3563601 |