Concentric Spherical GNN for 3D Representation Learning

James S Fox, Bo Zhao, Beatriz Gonzalez Del Rio, Siva Rajamanickam, Rampi Ramprasad, Le Song

Keywords: spherical cnn, CNN, point cloud, graph convolution, rotation, equivariance, 3D, molecular, volumetric

Abstract:

Learning 3D representations of point clouds that generalize well to arbitrary orientations is a challenge of practical importance in problems ranging from computer vision to molecular modeling.
The proposed approach is based on a concentric spherical representation of 3D space, formed by nesting spatially-sampled spheres resulting from the highly regular icosahedral discretization.
We propose separate intra-sphere and inter-sphere convolutions over the resulting concentric spherical grid, which are combined into a convolutional framework for learning volumetric and rotationally equivariant representations over point clouds.
We demonstrate the effectiveness of our approach for 3D object classification, and towards resolving the electronic structure of atomistic systems.

One-sentence Summary: We propose a concentric spherical convolutional approach learning rotationally equivariant representations of 3D point cloud data, with application to computer vision and molecular modeling.