Learning on 3D Meshes With Laplacian Encoding and Pooling.

Area of Science:

• Computer Vision and Graphics
• Geometric Deep Learning
• Computational Geometry

Background:

• 3D models are crucial in computer vision and graphics.
• Processing 3D mesh data with deep learning presents challenges due to irregular connectivity.
• Existing methods struggle with topological variations and efficiency.

Purpose of the Study:

• To develop an efficient and intrinsic deep learning approach for 3D mesh processing.
• To effectively capture relational information within irregular mesh structures.
• To create a method robust to different triangulations and isometric transformations.

Main Methods:

• Encoding mesh connectivity using Laplacian spectral analysis.
• Employing mesh feature aggregation blocks (MFABs) for local and global information aggregation.
• Building a mesh hierarchy via Laplacian spectral clustering and using a Correlation Net for global feature aggregation.

Main Results:

• The proposed network architecture is flexible for meshes with varying vertex counts.
• Achieved state-of-the-art performance in shape segmentation and classification tasks.
• Demonstrated superior results on the ShapeNet and COSEG datasets.

Conclusions:

• The developed deep learning method effectively processes 3D meshes by leveraging spectral analysis and hierarchical aggregation.
• The approach offers robustness and flexibility, outperforming existing methods in key 3D vision tasks.
• This work provides a significant advancement for intrinsic deep learning on 3D mesh data.