Mathematics > Numerical Analysis arXiv:2504.11212 (math) [Submitted on 15 Apr 2025]

Title: SDFs from Unoriented Point Clouds using Neural Variational Heat Distances

Authors: Samuel Weidemaier, Florine Hartwig, Josua Sassen, Sergio Conti, Mirela Ben-Chen, Martin Rumpf

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Abstract: 我们提出了一种新颖的变分方法，用于从无向点云计算神经符号距离场（SDF）。为此，我们用热方法代替了常用的 Eikonal 方程，将长期以来在离散表面上计算距离的标准做法引入到神经领域。这产生了两个凸优化问题，我们使用神经网络来解决：我们首先通过带权重的点云密度作为初始数据的热流的一小步来计算无符号距离场的梯度的神经近似。然后，我们使用它来计算 SDF 的神经近似。我们证明了底层的变分问题是适定的。通过数值实验，我们证明了我们的方法提供了最先进的表面重建和一致的 SDF 梯度。此外，我们在概念验证中表明，它对于在零水平集上求解 PDE 足够准确。

Comments: | 14 pages, 16 figures, 4 tables ---|--- Subjects: | Numerical Analysis (math.NA); Graphics (cs.GR); Machine Learning (cs.LG) MSC classes: | 65K10, 68T07, 65D18, 49J45 Cite as: | arXiv:2504.11212 [math.NA] (or arXiv:2504.11212v1 [math.NA] for this version) https://doi.org/10.48550/arXiv.2504.11212 Focus to learn more arXiv-issued DOI via DataCite

Submission history

From: Martin Rumpf [view email] [v1] Tue, 15 Apr 2025 14:13:54 UTC (46,326 KB) Full-text links:

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View a PDF of the paper titled SDFs from Unoriented Point Clouds using Neural Variational Heat Distances, by Samuel Weidemaier and 5 other authors