Rotation-Invariant Autoencoders for Signals on Spheres

• URL: http://arxiv.org/abs/2012.04474v1
• Date: Tue, 8 Dec 2020 15:15:03 GMT
• Title: Rotation-Invariant Autoencoders for Signals on Spheres
• Authors: Suhas Lohit, Shubhendu Trivedi
• Abstract summary: We study the problem of unsupervised learning of rotation-invariant representations for spherical images. In particular, we design an autoencoder architecture consisting of $S2$ and $SO(3)$ convolutional layers. Experiments on multiple datasets demonstrate the usefulness of the learned representations on clustering, retrieval and classification applications.
• Score: 10.406659081400354
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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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