SDFs from Unoriented Point Clouds using Neural Variational Heat Distances
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910005721038848 |
|---|---|
| author | Weidemaier, Samuel Hartwig, Florine Sassen, Josua Conti, Sergio Ben-Chen, Mirela Rumpf, Martin |
| author_facet | Weidemaier, Samuel Hartwig, Florine Sassen, Josua Conti, Sergio Ben-Chen, Mirela Rumpf, Martin |
| contents | We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from unoriented point clouds. To this end, we replace the commonly used eikonal equation with the heat method, carrying over to the neural domain what has long been standard practice for computing distances on discrete surfaces. This yields two convex optimization problems for whose solution we employ neural networks: We first compute a neural approximation of the gradients of the unsigned distance field through a small time step of heat flow with weighted point cloud densities as initial data. Then we use it to compute a neural approximation of the SDF. We prove that the underlying variational problems are well-posed. Through numerical experiments, we demonstrate that our method provides state-of-the-art surface reconstruction and consistent SDF gradients. Furthermore, we show in a proof-of-concept that it is accurate enough for solving a PDE on the zero-level set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11212 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SDFs from Unoriented Point Clouds using Neural Variational Heat Distances Weidemaier, Samuel Hartwig, Florine Sassen, Josua Conti, Sergio Ben-Chen, Mirela Rumpf, Martin Numerical Analysis Graphics Machine Learning 65K10, 68T07, 65D18, 49J45 We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from unoriented point clouds. To this end, we replace the commonly used eikonal equation with the heat method, carrying over to the neural domain what has long been standard practice for computing distances on discrete surfaces. This yields two convex optimization problems for whose solution we employ neural networks: We first compute a neural approximation of the gradients of the unsigned distance field through a small time step of heat flow with weighted point cloud densities as initial data. Then we use it to compute a neural approximation of the SDF. We prove that the underlying variational problems are well-posed. Through numerical experiments, we demonstrate that our method provides state-of-the-art surface reconstruction and consistent SDF gradients. Furthermore, we show in a proof-of-concept that it is accurate enough for solving a PDE on the zero-level set. |
| title | SDFs from Unoriented Point Clouds using Neural Variational Heat Distances |
| topic | Numerical Analysis Graphics Machine Learning 65K10, 68T07, 65D18, 49J45 |
| url | https://arxiv.org/abs/2504.11212 |