Spin-Weighted Spherical CNNs
This work addresses the need for more expressive and efficient equivariant representations in spherical deep learning, with applications in computer vision and physics, though it is incremental as it builds on existing spherical CNN frameworks.
The authors tackled the problem of limited expressivity and computational inefficiency in spherical CNNs by introducing spin-weighted spherical functions, which allow anisotropic filters efficiently on the sphere, leading to improved performance on tasks like spherical image classification, 3D shape classification, and semantic segmentation of spherical panoramas.
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 spin-weighted spherical functions, which were introduced in physics in the study of gravitational waves. These are complex-valued functions on the sphere whose phases change upon rotation. We define a convolution between spin-weighted functions and build a CNN based on it. The spin-weighted 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.