Spherical CNNs

TL;DR

This paper introduces spherical CNNs that are rotation-equivariant and efficient, enabling improved analysis of spherical images for applications like 3D recognition and molecular energy prediction.

Contribution

The paper develops the foundational building blocks for spherical CNNs, including a new spherical cross-correlation and a generalized FFT for efficient computation.

Findings

Spherical CNNs are computationally efficient and numerically accurate.

They outperform traditional methods on 3D model recognition tasks.

Effective for atomization energy regression in molecular applications.

Abstract

Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined to fail, because the space-varying distortions introduced by such a projection will make translational weight sharing ineffective. In this paper we introduce the building blocks for constructing spherical CNNs. We propose a definition for the spherical cross-correlation that is both expressive and rotation-equivariant. The spherical correlation satisfies a generalized Fourier theorem, which allows us to compute it efficiently using a generalized (non-commutative) Fast Fourier Transform (FFT) algorithm. We demonstrate the computational efficiency, numerical accuracy, and effectiveness of spherical CNNs applied to 3D model recognition and atomization energy regression.