Mesh Convolution With Continuous Filters for 3-D Surface Parsing.

Area of Science:

• Computer Graphics
• 3-D Computer Vision
• Geometric Deep Learning

Background:

• Deep learning for 3-D surfaces faces challenges in hierarchical modeling due to a lack of efficient operations.
• Existing methods struggle with effective geometric feature extraction from complex 3-D mesh data.

Purpose of the Study:

• To propose novel, modular operations for enhanced geometric feature learning from 3-D triangle meshes.
• To develop a hierarchical neural network for perceptual parsing of 3-D surfaces.
• To provide an open-source implementation for broader research accessibility.

Main Methods:

• Developed novel mesh convolutions utilizing spherical harmonics for continuous filters.
• Implemented GPU-accelerated mesh decimation for on-the-fly processing of batched meshes.
• Introduced mesh (un)pooling operations for handling upsampled/downsampled mesh features.
• Integrated these operations into a hierarchical neural network, PicassoNet++.

Main Results:

• Picasso operations enable effective hierarchical modeling of 3-D surfaces.
• PicassoNet++ demonstrates highly competitive performance on 3-D shape analysis benchmarks.
• The system achieves state-of-the-art results in 3-D scene segmentation tasks.

Conclusions:

• The proposed Picasso operations and PicassoNet++ significantly advance deep learning capabilities for 3-D surface analysis.
• The open-source toolkit facilitates future research in geometric deep learning and 3-D computer vision.
• This work addresses key limitations in hierarchical 3-D mesh processing for computer graphics and vision applications.