标题： 使用神经变分热距离从无向点云中获取SDFs 显示英文标题

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

摘要： 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，我们将常用的Eikonal方程替换为热方法，将长期以来离散曲面上计算距离的标准做法推广到神经领域。 这产生了两个凸优化问题，我们使用神经网络来求解它们：首先通过热流的小时间步长计算无符号距离场梯度的神经近似值，初始数据为加权点云密度；然后利用它来计算SDF的神经近似值。 我们证明了潜在的变分问题是有良定的。 通过数值实验，我们展示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，它足够准确，可以解决零水平集上的偏微分方程。 显示英文摘要

摘要： 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.