Spin-Weighted Spherical CNNs

• DOI: 10.48550/arxiv.2006.10731
• Publication Date: 2020-01-01
• Authors: Carlos Esteves; Ameesh Makadia; Kostas Daniilidis
• Keywords: Equivariant map; Rotation group SO; Convolution (computer science); Spherical mean; Tensor operator; Spherical Geometry

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