Rotation-Invariant Autoencoders for Signals on Spheres
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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 better suited for classifying spherical images. These newly proposed convolutional layers naturally extend the notion of convolution to functions on the unit sphere S^2 and the group of rotations SO(3) and these layers are equivariant to 3D rotations. In this paper, we consider the problem of unsupervised learning of rotation-invariant representations for spherical images. In particular, we carefully 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 these input transformations. 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.
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