Geometric Deep Learning for 3D Meshes and Shapes

The field of geometric deep learning is rapidly advancing, with a focus on developing novel architectures and techniques for processing and analyzing 3D meshes and shapes. Recent developments have centered around improving the ability of graph convolutional networks (GCNs) to capture both local and global features of complex geometric shapes, enabling more accurate shape reconstruction and analysis. Another key area of research has been the development of new smoothing operators and diffusion-like processes for irregular data such as point clouds and meshes, which has far-reaching implications for applications in shape analysis, matching, and reconstruction. Additionally, there has been significant progress in learning the spectrum of the Laplace-Beltrami operator, a fundamental problem in geometric deep learning, using graph neural networks and other machine learning approaches. Noteworthy papers in this area include:

  • The introduction of the 3D Geometric Mesh Network (3DGeoMeshNet), a novel GCN-based framework for 3D mesh reconstruction.
  • The development of a broad class of smoothing operators derived from general similarity or adjacency matrices, which can be normalized into diffusion-like operators.
  • The proposal of a geometric deep learning framework to predict the Laplace-Beltrami spectrum efficiently given the CAD mesh of a part, achieving significant computational savings without sacrificing accuracy.

Sources

Self-Attention Based Multi-Scale Graph Auto-Encoder Network of 3D Meshes

Normalizing Diffusion Kernels with Optimal Transport

Prevention of Overfitting on Mesh-Structured Data Regressions with a Modified Laplace Operator

An AI Approach for Learning the Spectrum of the Laplace-Beltrami Operator

Adaptive Particle-Based Shape Modeling for Anatomical Surface Correspondence

Identification of Violin Reduction via Contour Lines Classification

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