SDFs from Unoriented Point Clouds using Neural Variational Heat Distances
This work addresses the challenge of accurate surface reconstruction from unoriented point clouds for applications in computer graphics and geometry processing, representing an incremental improvement by adapting the heat method to neural domains.
The paper tackles the problem of computing neural Signed Distance Fields (SDFs) from unoriented point clouds by proposing a novel variational approach that replaces the eikonal equation with the heat method, resulting in state-of-the-art surface reconstruction and consistent SDF gradients, as demonstrated through numerical experiments.
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.