MongeNet: Efficient Sampler for Geometric Deep Learning

TL;DR

MongeNet is a novel, efficient sampling method based on optimal transport that improves mesh discretization accuracy in geometric deep learning, reducing approximation errors significantly with minimal computational cost.

Contribution

We introduce MongeNet, a fast optimal transport-based sampler that enhances mesh discretization accuracy compared to uniform random sampling.

Findings

Approximation error is nearly halved with MongeNet.

MongeNet has minimal additional computational overhead.

It outperforms uniform random sampling in mesh discretization.

Abstract

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.