Recent advances in geometric deep-learning introduce complex computational challenges for evaluating the distance between meshes. From a mesh model, point clouds are necessary along with a robust distance metric to assess surface quality or as part of the loss function for training models. Current methods often rely on a uniform random mesh discretization, which yields irregular sampling and noisy distance estimation. In this paper we introduce MongeNet, a fast and optimal transport based sampler that allows for an accurate discretization of a mesh with better approximation properties. We compare our method to the ubiquitous random uniform sampling and show that the approximation error is almost half with a very small computational overhead.

翻译：最近几何深层学习的进展在计算评估网外距离方面带来了复杂的挑战。 从网状模型看,点云与强健的距离测量一道,对于评估表面质量或作为培训模型损失函数的一部分,是必要的。目前的方法往往依靠统一的随机网外分解,得出不规则采样和吵闹的距离估计。在本文中,我们引入了蒙古网,这是一个快速和最佳的基于运输的取样器,可以精确地分解具有较好近似特性的网外线。我们比较了我们的方法和无处不在的随机统一抽样,并表明近似误差几乎是一半,计算间接费用很小。