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.
@article{arxiv.2104.14554,
title = {MongeNet: Efficient Sampler for Geometric Deep Learning},
author = {Léo Lebrat and Rodrigo Santa Cruz and Clinton Fookes and Olivier Salvado},
journal= {arXiv preprint arXiv:2104.14554},
year = {2021}
}