# Anisotropic Multi-Scale Graph Convolutional Network for Dense Shape Correspondence

arXiv: https://arxiv.org/abs/2210.09466 · HTML: https://mlsanity.com/paper/2210.09466/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 17 Oct 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (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)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)
- [Deep Shells: Unsupervised Shape Correspondence with Optimal Transport](https://mlsanity.com/paper/2010.15261/) (2020)
- [CorrNet3D: Unsupervised End-to-end Learning of Dense Correspondence for 3D Point Clouds](https://mlsanity.com/paper/2012.15638/) (2020)
- [Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching](https://mlsanity.com/paper/2204.13453/) (2022)
- [Spectral Graph Attention Network with Fast Eigen-approximation](https://mlsanity.com/paper/2003.07450/) (2020)
- [Continuous Geodesic Convolutions for Learning on 3D Shapes](https://mlsanity.com/paper/2002.02506/) (2020)
- [MGCN: Descriptor Learning using Multiscale GCNs](https://mlsanity.com/paper/2001.10472/) (2020)

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

- [A Recipe for Geometry-Aware 3D Mesh Transformers](https://mlsanity.com/paper/2411.00164/) (2024)
- [Hierarchical Mesh Transformers with Topology-Guided Pretraining for Morphometric Analysis of Brain Structures](https://mlsanity.com/paper/2604.05215/) (2026)

## Abstract (arXiv)

This paper studies 3D dense shape correspondence, a key shape analysis application in computer vision and graphics. We introduce a novel hybrid geometric deep learning-based model that learns geometrically meaningful and discretization-independent features with a U-Net model as the primary node feature extraction module, followed by a successive spectral-based graph convolutional network. To create a diverse set of filters, we use anisotropic wavelet basis filters, being sensitive to both different directions and band-passes. This filter set overcomes the over-smoothing behavior of conventional graph neural networks. To further improve the model's performance, we add a function that perturbs the feature maps in the last layer ahead of fully connected layers, forcing the network to learn more discriminative features overall. The resulting correspondence maps show state-of-the-art performance on the benchmark datasets based on average geodesic errors and superior robustness to discretization in 3D meshes. Our approach provides new insights and practical solutions to the dense shape correspondence research.