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.
Users
Please
log in to take part in the discussion (add own reviews or comments).