用神经热距离方法从无方向点云重建高精度SDF
SDFs from Unoriented Point Clouds using Neural Variational Heat Distances
- 用热流方法替代传统Eikonal方程，构建可学习的距离场
- 在多个数据集上实现最优表面重建与一致梯度输出
- 适合需要精确SDF的几何建模与PDE求解任务
我们提出一种新颖的变分方法，从无方向点云中计算神经符号距离场（SDF）。为此，我们用热方法取代常用的Eikonal方程，将离散曲面上的标准距离计算方式推广到神经域。该方法生成两个凸优化问题，通过神经网络求解：首先利用短时间热流和加权点云密度作为初始条件，计算无符号距离场梯度的神经近似；随后基于此计算SDF的神经近似。我们证明了其背后的变分问题具有良定性。数值实验表明，本方法在表面重建方面达到当前最优水平，并生成一致的SDF梯度。此外，概念验证显示其足够精确，可用于零等值面的PDE求解。
原文摘要 · Abstract (English)
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.
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