Hierarchical Mesh Representation Learning With Spectral Dictionary Embedding.

Area of Science:

• Computer Vision
• 3D Geometry Processing
• Machine Learning

Background:

• Mesh representation is crucial for 3D tasks, but irregular vertex neighbors challenge conventional convolutions.
• Existing methods for handling mesh irregularity include isotropic filters, predefined coordinate systems, and learning vertex-specific weighting matrices.
• Learning weighting matrices is effective but leads to large model sizes, especially for high-resolution 3D shapes.

Purpose of the Study:

• To develop a mesh representation learning method that reduces model size independently of 3D shape resolution.
• To improve the efficiency of 3D deep learning models by addressing parameter bloat in mesh processing.
• To achieve state-of-the-art performance in 3D tasks with a more compact model architecture.

Main Methods:

• Introduced spectral dictionaries (bases) for weighting matrices, making model size resolution-independent.
• Employed weight-sharing for learning weighting matrix coefficients from spectral features across hierarchical levels.
• Developed an adaptive sampling method to learn hierarchical mapping matrices, enhancing performance without increasing inference-stage model size.

Main Results:

• Achieved state-of-the-art results on various 3D tasks.
• Demonstrated a significantly smaller model size compared to previous methods.
• The proposed method's performance is independent of the 3D shape's resolution.

Conclusions:

• The spectral dictionary approach effectively reduces model size for mesh representation learning.
• The adaptive sampling method further enhances performance without compromising model efficiency.
• This work offers a more practical and scalable solution for deep learning on 3D meshes.