MongeNet: Efficient Sampler for Geometric Deep Learning
This addresses a computational bottleneck for researchers and practitioners in geometric deep learning by improving mesh discretization efficiency.
The paper tackles the problem of noisy distance estimation in geometric deep learning by introducing MongeNet, an optimal transport-based sampler that reduces approximation error by almost half compared to uniform random sampling with minimal computational overhead.
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.