MongeNet：用于几何深度学习的高效采样器
MongeNet: Efficient Sampler for Geometric Deep Learning
摘要：
几何深度学习的最新进展为评估网格之间的距离带来了复杂的计算挑战。对于网格模型，点云与鲁棒的距离度量一起是必要的，以评估表面质量或作为训练模型的损失函数的一部分。目前的方法往往依赖于一个统一的随机网格离散化，这会产生不规则的采样和噪声的距离估计。在本文中，我们介绍了MongeNet，一个快速和最佳的运输为基础的采样器，允许一个准确的离散化的网格具有更好的近似性能。我们比较我们的方法无处不在的随机均匀采样，并表明，近似误差几乎是一个非常小的计算开销的一半。
英文摘要：
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.
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