Anisotropic Multi-Scale Graph Convolutional Network for Dense Shape Correspondence

TL;DR

This paper presents a novel anisotropic multi-scale graph convolutional network that improves dense 3D shape correspondence by learning discretization-independent features with state-of-the-art accuracy and robustness.

Contribution

It introduces a hybrid geometric deep learning model with anisotropic wavelet filters and a feature perturbation technique for enhanced shape correspondence.

Findings

Achieves state-of-the-art performance on benchmark datasets.

Demonstrates superior robustness to mesh discretization.

Learns geometrically meaningful features that are discretization-independent.

Abstract

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.