PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical CNNs

Spherical signals exist in many applications, e.g., planetary data, LiDAR scans and digitalization of 3D objects, calling for models that can process spherical data effectively. It does not perform well when simply projecting into the 2D plane then using planar convolution neural networks (CNNs), because distortion from projection ineffective translation equivariance. Actually, good principles designing CNNs are avoiding distortions converting shift equivariance property to rotation domain. In this work, we use partial differential operators (PDOs) design a equivariant CNN, PDO-eS2CNN, which is exactly continuous We discretize PDO-eS2CNNs, analyze error resulted discretization. This first time theoretically analyzed experiments, PDO-eS2CNNs show greater parameter efficiency outperform other significantly on several tasks.