MongeNet: Efficient Sampler for Geometric Deep Learning

• URL: http://arxiv.org/abs/2104.14554v1
• Date: Thu, 29 Apr 2021 17:59:01 GMT
• Title: MongeNet: Efficient Sampler for Geometric Deep Learning
• Authors: L\'eo Lebrat, Rodrigo Santa Cruz, Clinton Fookes, Olivier Salvado
• Abstract summary: MongeNet is 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.
• Score: 17.369783838267942
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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