# MeshCNN: A Network with an Edge

arXiv: https://arxiv.org/abs/1809.05910 · HTML: https://mlsanity.com/paper/1809.05910/

## Key facts

- Cited by 69 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2018.

## Built on by (most cited first, 30 of 69)

- [State of the Art on Diffusion Models for Visual Computing](https://mlsanity.com/paper/2310.07204/) (2023)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Nerflets: Local Radiance Fields for Efficient Structure-Aware 3D Scene Representation from 2D Supervision](https://mlsanity.com/paper/2303.03361/) (2023)
- [Text and Image Guided 3D Avatar Generation and Manipulation](https://mlsanity.com/paper/2202.06079/) (2022)
- [An Object is Worth 64x64 Pixels: Generating 3D Object via Image Diffusion](https://mlsanity.com/paper/2408.03178/) (2024)
- [3D Highlighter: Localizing Regions on 3D Shapes via Text Descriptions](https://mlsanity.com/paper/2212.11263/) (2022)
- [CADOps-Net: Jointly Learning CAD Operation Types and Steps from Boundary-Representations](https://mlsanity.com/paper/2208.10555/) (2022)
- [Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall](https://mlsanity.com/paper/2212.05023/) (2022)
- [An objective comparison of methods for augmented reality in laparoscopic liver resection by preoperative-to-intraoperative image fusion](https://mlsanity.com/paper/2401.15753/) (2024)
- [Differentiable Surface Triangulation](https://mlsanity.com/paper/2109.10695/) (2021)
- [iSeg: Interactive 3D Segmentation via Interactive Attention](https://mlsanity.com/paper/2404.03219/) (2024)
- [AutoMate: A Dataset and Learning Approach for Automatic Mating of CAD Assemblies](https://mlsanity.com/paper/2105.12238/) (2021)
- [M"obius Convolutions for Spherical CNNs](https://mlsanity.com/paper/2201.12212/) (2022)
- [Volumetric Disentanglement for 3D Scene Manipulation](https://mlsanity.com/paper/2206.02776/) (2022)
- [Zero-shot Pose Transfer for Unrigged Stylized 3D Characters](https://mlsanity.com/paper/2306.00200/) (2023)
- [HumanRig: Learning Automatic Rigging for Humanoid Character in a Large Scale Dataset](https://mlsanity.com/paper/2412.02317/) (2024)
- [Style2Fab: Functionality-Aware Segmentation for Fabricating Personalized 3D Models with Generative AI](https://mlsanity.com/paper/2309.06379/) (2023)
- [Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networks](https://mlsanity.com/paper/2101.03906/) (2021)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [DA Wand: Distortion-Aware Selection using Neural Mesh Parameterization](https://mlsanity.com/paper/2212.06344/) (2022)
- [Bringing Attention to CAD: Boundary Representation Learning via Transformer](https://mlsanity.com/paper/2504.07134/) (2025)
- [TransforMesh: A Transformer Network for Longitudinal modeling of Anatomical Meshes](https://mlsanity.com/paper/2109.00532/) (2021)
- [Mesh Convolutional Autoencoder for Semi-Regular Meshes of Different Sizes](https://mlsanity.com/paper/2110.09401/) (2021)
- [Semi-supervised 3D shape segmentation with multilevel consistency and part substitution](https://mlsanity.com/paper/2204.08824/) (2022)
- [Mimetic Neural Networks: A unified framework for Protein Design and Folding](https://mlsanity.com/paper/2102.03881/) (2021)
- [SphereDepth: Panorama Depth Estimation from Spherical Domain](https://mlsanity.com/paper/2208.13714/) (2022)
- [MVTN: Learning Multi-View Transformations for 3D Understanding](https://mlsanity.com/paper/2212.13462/) (2022)
- [STMT: A Spatial-Temporal Mesh Transformer for MoCap-Based Action Recognition](https://mlsanity.com/paper/2303.18177/) (2023)
- [Neural Part Priors: Learning to Optimize Part-Based Object Completion in RGB-D Scans](https://mlsanity.com/paper/2203.09375/) (2022)
- [QuadConv: Quadrature-Based Convolutions with Applications to Non-Uniform PDE Data Compression](https://mlsanity.com/paper/2211.05151/) (2022)

## Abstract (arXiv)

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of our task-driven pooling on various learning tasks applied to 3D meshes.