Spherical CNNs

Taco S. Cohen, Mario Geiger, Jonas Köhler, Max Welling

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.

TL;DR: We introduce Spherical CNNs, a convolutional network for spherical signals, and apply it to 3D model recognition and molecular energy regression.

Keywords: deep learning, equivariance, convolution, group convolution, 3D, vision, omnidirectional, shape recognition, molecular energy regression

Code: [ jonas-koehler/s2cnn](https://github.com/jonas-koehler/s2cnn) + [ 2 community implementations](https://paperswithcode.com/paper/?openreview=Hkbd5xZRb)

Data: [2D-3D Match Dataset](https://paperswithcode.com/dataset/2d-3d-match-dataset)

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:1801.10130/code)