In 3D computer vision and geometric deep learning, I have come across the term “sphere matrix” (or spherical component) of a tensor.

Could anyone clarify:

  • Definition: How is the sphere matrix formally defined for a 2nd-order tensor in 3D applications? 2. Use in 3D Vision: How is this decomposition (spherical + deviatoric) leveraged in 3D CNNs, GNNs, or equivariant networks for tasks like point cloud classification, surface normal estimation, or shape analysis? 3. Practical Benefits: Does using the sphere matrix help enforce rotation/scale invariance or improve geometric feature stability in 3D representations? 4. References: Are there published works or implementations (e.g., in PyTorch Geometric, MinkowskiEngine, or SE(3)-equivariant networks) that explicitly use spherical tensor components for 3D perception?
  • I am exploring whether using spherical tensor representations could improve robustness and invariance in 3D vision pipelines (point cloud, mesh, or voxel-based).

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