# MongeNet: Efficient Sampler for Geometric Deep Learning

arXiv: https://arxiv.org/abs/2104.14554 · HTML: https://mlsanity.com/paper/2104.14554/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 49 references that are in the map.
- First posted on arXiv 29 Apr 2021.

## Builds on (most cited first, 16 of 16)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Weakly-Supervised Mesh-Convolutional Hand Reconstruction in the Wild](https://mlsanity.com/paper/2004.01946/) (2020)
- [Morphing and Sampling Network for Dense Point Cloud Completion](https://mlsanity.com/paper/1912.00280/) (2019)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Kaolin: A PyTorch Library for Accelerating 3D Deep Learning Research](https://mlsanity.com/paper/1911.05063/) (2019)
- [SampleNet: Differentiable Point Cloud Sampling](https://mlsanity.com/paper/1912.03663/) (2019)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [Point2Mesh: A Self-Prior for Deformable Meshes](https://mlsanity.com/paper/2005.11084/) (2020)
- [DeepCSR: A 3D Deep Learning Approach for Cortical Surface Reconstruction](https://mlsanity.com/paper/2010.11423/) (2020)
- [An algorithm for optimal transport between a simplex soup and a point cloud](https://mlsanity.com/paper/1707.01337/) (2017)

## Built on by (most cited first, 2 of 2)

- [NeRF Director: Revisiting View Selection in Neural Volume Rendering](https://mlsanity.com/paper/2406.08839/) (2024)
- [3D Reconstruction of non-visible surfaces of objects from a Single Depth View -- Comparative Study](https://mlsanity.com/paper/2501.16101/) (2025)

## Abstract (arXiv)

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.