# MeshCNN Fundamentals: Geometric Learning through a Reconstructable Representation

arXiv: https://arxiv.org/abs/2105.13277 · HTML: https://mlsanity.com/paper/2105.13277/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 72 references that are in the map.
- First posted on arXiv 27 May 2021.

## Builds on (most cited first, 30 of 39)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [SEGCloud: Semantic Segmentation of 3D Point Clouds](https://mlsanity.com/paper/1710.07563/) (2017)
- [3D Point Cloud Generative Adversarial Network Based on Tree Structured Graph Convolutions](https://mlsanity.com/paper/1905.06292/) (2019)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [Point Convolutional Neural Networks by Extension Operators](https://mlsanity.com/paper/1803.10091/) (2018)
- [3D-MPA: Multi Proposal Aggregation for 3D Semantic Instance Segmentation](https://mlsanity.com/paper/2003.13867/) (2020)
- [Generative and Discriminative Voxel Modeling with Convolutional Neural Networks](https://mlsanity.com/paper/1608.04236/) (2016)
- [DensePoint: Learning Densely Contextual Representation for Efficient Point Cloud Processing](https://mlsanity.com/paper/1909.03669/) (2019)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator](https://mlsanity.com/paper/1911.05856/) (2019)
- [Triplet-Center Loss for Multi-View 3D Object Retrieval](https://mlsanity.com/paper/1803.06189/) (2018)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [Fully Convolutional Mesh Autoencoder using Efficient Spatially Varying Kernels](https://mlsanity.com/paper/2006.04325/) (2020)
- [Deep Geometric Texture Synthesis](https://mlsanity.com/paper/2007.00074/) (2020)
- [Neural Subdivision](https://mlsanity.com/paper/2005.01819/) (2020)
- [Primal-Dual Mesh Convolutional Neural Networks](https://mlsanity.com/paper/2010.12455/) (2020)
- [DualConvMesh-Net: Joint Geodesic and Euclidean Convolutions on 3D Meshes](https://mlsanity.com/paper/2004.01002/) (2020)
- [A Simple Approach to Intrinsic Correspondence Learning on Unstructured 3D Meshes](https://mlsanity.com/paper/1809.06664/) (2018)

## Abstract (arXiv)

Mesh-based learning is one of the popular approaches nowadays to learn shapes. The most established backbone in this field is MeshCNN. In this paper, we propose infusing MeshCNN with geometric reasoning to achieve higher quality learning. Through careful analysis of the way geometry is represented through-out the network, we submit that this representation should be rigid motion invariant, and should allow reconstructing the original geometry. Accordingly, we introduce the first and second fundamental forms as an edge-centric, rotation and translation invariant, reconstructable representation. In addition, we update the originally proposed pooling scheme to be more geometrically driven. We validate our analysis through experimentation, and present consistent improvement upon the MeshCNN baseline, as well as other more elaborate state-of-the-art architectures. Furthermore, we demonstrate this fundamental forms-based representation opens the door to accessible generative machine learning over meshes.