Rotation-Invariant Spherical Autoencoders

Anonymous

Keywords: equivariance, invariance, spherical images, autoencoders

TL;DR: An autoencoder architecture and loss function for spherical signals with SO(3)-invariant latent space and its applications

Abstract: Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and $SO(3)$ convolutions, researchers have recently developed deep learning methods that are equivariant to 3D rotations, and thus better suited to operate on such data. In this paper, we consider the problem of unsupervised learning of rotation-invariant representations for spherical images. In particular, we design an autoencoder architecture consisting of $S^2$ and $SO(3)$ convolutional layers. As 3D rotations are often a nuisance factor, the latent space is constrained to be exactly invariant to them. As the rotation information is discarded in the latent space, we craft a novel rotation-invariant loss function for training the network. Extensive experiments on multiple datasets demonstrate the usefulness of the learned representations on clustering, retrieval and classification applications.