Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs

TL;DR

This paper introduces spherical scattering networks that are scalable, rotationally equivariant, and invariant to isometries, enabling efficient analysis of high-resolution spherical data within the spherical CNN framework.

Contribution

It develops scattering networks on the sphere that enhance scalability and invariance, integrating them into spherical CNNs for high-resolution data processing.

Findings

Scattering networks on the sphere are computationally scalable.

They exhibit rotational equivariance and isometry invariance.

They enable spherical CNNs to handle high-resolution signals.

Abstract

Convolutional neural networks (CNNs) constructed natively on the sphere have been developed recently and shown to be highly effective for the analysis of spherical data. While an efficient framework has been formulated, spherical CNNs are nevertheless highly computationally demanding; typically they cannot scale beyond spherical signals of thousands of pixels. We develop scattering networks constructed natively on the sphere that provide a powerful representational space for spherical data. Spherical scattering networks are computationally scalable and exhibit rotational equivariance, while their representational space is invariant to isometries and provides efficient and stable signal representations. By integrating scattering networks as an additional type of layer in the generalized spherical CNN framework, we show how they can be leveraged to scale spherical CNNs to the high-resolution data typical of many practical applications, with spherical signals of many tens of megapixels and beyond.