# Subdivision-Based Mesh Convolution Networks

arXiv: https://arxiv.org/abs/2106.02285 · HTML: https://mlsanity.com/paper/2106.02285/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 95 references that are in the map.
- First posted on arXiv 4 Jun 2021.

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [Tangent Convolutions for Dense Prediction in 3D](https://mlsanity.com/paper/1807.02443/) (2018)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models](https://mlsanity.com/paper/1704.01222/) (2017)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [VNect: Real-time 3D Human Pose Estimation with a Single RGB Camera](https://mlsanity.com/paper/1705.01583/) (2017)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [MeshNet: Mesh Neural Network for 3D Shape Representation](https://mlsanity.com/paper/1811.11424/) (2018)
- [SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator](https://mlsanity.com/paper/1911.05856/) (2019)
- [Unsupervised Deep Learning for Structured Shape Matching](https://mlsanity.com/paper/1812.03794/) (2018)
- [Continuous and Orientation-preserving Correspondences via Functional Maps](https://mlsanity.com/paper/1806.04455/) (2018)

## Built on by (most cited first, 30 of 60)

- [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)
- [SCube: Instant Large-Scale Scene Reconstruction using VoxSplats](https://mlsanity.com/paper/2410.20030/) (2024)
- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [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)
- [Flexible Techniques for Differentiable Rendering with 3D Gaussians](https://mlsanity.com/paper/2308.14737/) (2023)
- [iSeg: Interactive 3D Segmentation via Interactive Attention](https://mlsanity.com/paper/2404.03219/) (2024)
- [AGConv: Adaptive Graph Convolution on 3D Point Clouds](https://mlsanity.com/paper/2206.04665/) (2022)
- [Neural Progressive Meshes](https://mlsanity.com/paper/2308.05741/) (2023)
- [SphereUFormer: A U-Shaped Transformer for Spherical 360 Perception](https://mlsanity.com/paper/2412.06968/) (2024)
- [Laplacian2Mesh: Laplacian-Based Mesh Understanding](https://mlsanity.com/paper/2202.00307/) (2022)
- [Single Mesh Diffusion Models with Field Latents for Texture Generation](https://mlsanity.com/paper/2312.09250/) (2023)
- [E(3)-Equivariant Mesh Neural Networks](https://mlsanity.com/paper/2402.04821/) (2024)
- [Bringing Attention to CAD: Boundary Representation Learning via Transformer](https://mlsanity.com/paper/2504.07134/) (2025)
- [Mesh Convolutional Autoencoder for Semi-Regular Meshes of Different Sizes](https://mlsanity.com/paper/2110.09401/) (2021)
- [TetGAN: A Convolutional Neural Network for Tetrahedral Mesh Generation](https://mlsanity.com/paper/2210.05735/) (2022)
- [Learning the Geodesic Embedding with Graph Neural Networks](https://mlsanity.com/paper/2309.05613/) (2023)
- [Neural Processing of Tri-Plane Hybrid Neural Fields](https://mlsanity.com/paper/2310.01140/) (2023)
- [Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems](https://mlsanity.com/paper/2206.07370/) (2022)
- [SphereDepth: Panorama Depth Estimation from Spherical Domain](https://mlsanity.com/paper/2208.13714/) (2022)
- [Keypoint Cascade Voting for Point Cloud Based 6DoF Pose Estimation](https://mlsanity.com/paper/2210.08123/) (2022)
- [Neural Shape Compiler: A Unified Framework for Transforming between Text, Point Cloud, and Program](https://mlsanity.com/paper/2212.12952/) (2022)
- [Neural Laplacian Operator for 3D Point Clouds](https://mlsanity.com/paper/2409.06506/) (2024)
- [Deep Learning on Object-centric 3D Neural Fields](https://mlsanity.com/paper/2312.13277/) (2023)
- [Mesh Convolution with Continuous Filters for 3D Surface Parsing](https://mlsanity.com/paper/2112.01801/) (2021)
- [Be Careful with Rotation: A Uniform Backdoor Pattern for 3D Shape](https://mlsanity.com/paper/2211.16192/) (2022)
- [TrIND: Representing Anatomical Trees by Denoising Diffusion of Implicit Neural Fields](https://mlsanity.com/paper/2403.08974/) (2024)
- [Knee Cartilage Defect Assessment by Graph Representation and Surface Convolution](https://mlsanity.com/paper/2201.04318/) (2022)
- [Transfer Learning using Spectral Convolutional Autoencoders on Semi-Regular Surface Meshes](https://mlsanity.com/paper/2212.05810/) (2022)

## Abstract (arXiv)

Convolutional neural networks (CNNs) have made great breakthroughs in 2D computer vision. However, their irregular structure makes it hard to harness the potential of CNNs directly on meshes. A subdivision surface provides a hierarchical multi-resolution structure, in which each face in a closed 2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these two observations, this paper presents SubdivNet, an innovative and versatile CNN framework for 3D triangle meshes with Loop subdivision sequence connectivity. Making an analogy between mesh faces and pixels in a 2D image allows us to present a mesh convolution operator to aggregate local features from nearby faces. By exploiting face neighborhoods, this convolution can support standard 2D convolutional network concepts, e.g. variable kernel size, stride, and dilation. Based on the multi-resolution hierarchy, we make use of pooling layers which uniformly merge four faces into one and an upsampling method which splits one face into four. Thereby, many popular 2D CNN architectures can be easily adapted to process 3D meshes. Meshes with arbitrary connectivity can be remeshed to have Loop subdivision sequence connectivity via self-parameterization, making SubdivNet a general approach. Extensive evaluation and various applications demonstrate SubdivNet's effectiveness and efficiency.