  Learning 3D representations that generalize well to arbitrarily oriented
inputs is a challenge of practical importance in applications varying from
computer vision to physics and chemistry. We propose a novel multi-resolution
convolutional architecture for learning over concentric spherical feature maps,
of which the single sphere representation is a special case. Our hierarchical
architecture is based on alternatively learning to incorporate both
intra-sphere and inter-sphere information. We show the applicability of our
method for two different types of 3D inputs, mesh objects, which can be
regularly sampled, and point clouds, which are irregularly distributed. We also
propose an efficient mapping of point clouds to concentric spherical images,
thereby bridging spherical convolutions on grids with general point clouds. We
demonstrate the effectiveness of our approach in improving state-of-the-art
performance on 3D classification tasks with rotated data.
