SpinWeighted Spherical CNNs
Abstract
Learning equivariant representations is a promising way to reduce sample and model complexity and improve the generalization performance of deep neural networks. The spherical CNNs are successful examples, producing SO(3)equivariant representations of spherical inputs. There are two main types of spherical CNNs. The first type lifts the inputs to functions on the rotation group SO(3) and applies convolutions on the group, which are computationally expensive since SO(3) has one extra dimension. The second type applies convolutions directly on the sphere, which are limited to zonal (isotropic) filters, and thus have limited expressivity. In this paper, we present a new type of spherical CNN that allows anisotropic filters in an efficient way, without ever leaving the spherical domain. The key idea is to consider spinweighted spherical functions, which were introduced in physics in the study of gravitational waves. These are complexvalued functions on the sphere whose phases change upon rotation. We define a convolution between spinweighted functions and build a CNN based on it. The spinweighted functions can also be interpreted as spherical vector fields, allowing applications to tasks where the inputs or outputs are vector fields. Experiments show that our method outperforms previous methods on tasks like classification of spherical images, classification of 3D shapes and semantic segmentation of spherical panoramas.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.10731
 Bibcode:
 2020arXiv200610731E
 Keywords:

 Computer Science  Computer Vision and Pattern Recognition;
 Computer Science  Machine Learning
 EPrint:
 Accepted to NeurIPS'20