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

Area of Science:

• Computer Vision
• Computer Graphics
• Geometric Deep Learning

Background:

• 3D dense shape correspondence is crucial for shape analysis.
• Existing methods often struggle with discretization sensitivity and feature robustness.

Purpose of the Study:

• To develop a novel hybrid geometric deep learning model for 3D dense shape correspondence.
• To learn geometrically meaningful and discretization-independent features.

Main Methods:

• A U-Net model extracts node features, followed by a spectral graph convolutional network.
• Anisotropic wavelet basis filters are used to create diverse, directionally sensitive filters.
• Feature map perturbation enhances discriminative learning.

Main Results:

• The model achieves state-of-the-art performance on benchmark datasets using average geodesic errors.
• Demonstrates superior robustness to discretization in 3D meshes.
• Learned features are geometrically meaningful and discretization-independent.

Conclusions:

• The proposed hybrid model offers a practical and effective solution for 3D dense shape correspondence.
• Advances the field by overcoming common limitations of graph neural networks.
• Provides new insights into learning robust shape features.