# Primal-Dual Mesh Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2010.12455 · HTML: https://mlsanity.com/paper/2010.12455/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 30 of 44)

- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [Deep Learning on Implicit Neural Representations of Shapes](https://mlsanity.com/paper/2302.05438/) (2023)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [Geometric Clifford Algebra Networks](https://mlsanity.com/paper/2302.06594/) (2023)
- [Segment Any Mesh](https://mlsanity.com/paper/2408.13679/) (2024)
- [3D Highlighter: Localizing Regions on 3D Shapes via Text Descriptions](https://mlsanity.com/paper/2212.11263/) (2022)
- [MeshMAE: Masked Autoencoders for 3D Mesh Data Analysis](https://mlsanity.com/paper/2207.10228/) (2022)
- [Equivariant Hypergraph Neural Networks](https://mlsanity.com/paper/2208.10428/) (2022)
- [Neural Trees for Learning on Graphs](https://mlsanity.com/paper/2105.07264/) (2021)
- [M"obius Convolutions for Spherical CNNs](https://mlsanity.com/paper/2201.12212/) (2022)
- [Laplacian2Mesh: Laplacian-Based Mesh Understanding](https://mlsanity.com/paper/2202.00307/) (2022)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [E(3)-Equivariant Mesh Neural Networks](https://mlsanity.com/paper/2402.04821/) (2024)
- [TetGAN: A Convolutional Neural Network for Tetrahedral Mesh Generation](https://mlsanity.com/paper/2210.05735/) (2022)
- [PoissonNet: A Local-Global Approach for Learning on Surfaces](https://mlsanity.com/paper/2510.14146/) (2025)
- [AttWalk: Attentive Cross-Walks for Deep Mesh Analysis](https://mlsanity.com/paper/2104.11571/) (2021)
- [Dense Graph Convolutional Neural Networks on 3D Meshes for 3D Object Segmentation and Classification](https://mlsanity.com/paper/2106.15778/) (2021)
- [Mesh Convolution with Continuous Filters for 3D Surface Parsing](https://mlsanity.com/paper/2112.01801/) (2021)
- [Random Walks for Adversarial Meshes](https://mlsanity.com/paper/2202.07453/) (2022)
- [Modeling Dynamics over Meshes with Gauge Equivariant Nonlinear Message Passing](https://mlsanity.com/paper/2310.19589/) (2023)
- [GeoScaler: Geometry and Rendering-Aware Downsampling of 3D Mesh Textures](https://mlsanity.com/paper/2311.16581/) (2023)
- [HodgeFormer: Transformers for Learnable Operators on Triangular Meshes through Data-Driven Hodge Matrices](https://mlsanity.com/paper/2509.01839/) (2025)
- [Mesh Compression with Quantized Neural Displacement Fields](https://mlsanity.com/paper/2504.01027/) (2025)
- [Dual Mesh Convolutional Networks for Human Shape Correspondence](https://mlsanity.com/paper/2103.12459/) (2021)
- [Smooth Mesh Estimation from Depth Data using Non-Smooth Convex Optimization](https://mlsanity.com/paper/2108.02957/) (2021)
- [From structure mining to unsupervised exploration of atomic octahedral networks](https://mlsanity.com/paper/2306.12272/) (2023)
- [SieveNet: Selecting Point-Based Features for Mesh Networks](https://mlsanity.com/paper/2308.12530/) (2023)
- [An Intrinsic Vector Heat Network](https://mlsanity.com/paper/2406.09648/) (2024)

## Abstract (arXiv)

Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution, and sometimes pooling, operations on triangle meshes. These methods, however, either consider the input mesh as a graph, and do not exploit specific geometric properties of meshes for feature aggregation and downsampling, or are specialized for meshes, but rely on a rigid definition of convolution that does not properly capture the local topology of the mesh. We propose a method that combines the advantages of both types of approaches, while addressing their limitations: we extend a primal-dual framework drawn from the graph-neural-network literature to triangle meshes, and define convolutions on two types of graphs constructed from an input mesh. Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them using an attention mechanism. At the same time, we introduce a pooling operation with a precise geometric interpretation, that allows handling variations in the mesh connectivity by clustering mesh faces in a task-driven fashion. We provide theoretical insights of our approach using tools from the mesh-simplification literature. In addition, we validate experimentally our method in the tasks of shape classification and shape segmentation, where we obtain comparable or superior performance to the state of the art.