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.
BibTeX
@inproceedings{
s.2018spherical,
title={Spherical {CNN}s},
author={Taco S. Cohen and Mario Geiger and Jonas Köhler and Max Welling},
booktitle={International Conference on Learning Representations},
year={2018},
url={https://openreview.net/forum?id=Hkbd5xZRb},
}