Learning SO(3) Equivariant Representations with Spherical CNNs
This addresses the challenge of 3D rotations in 3D classification tasks, which typically require high capacity and data augmentation, by providing a more efficient solution.
The paper tackles the problem of 3D rotation equivariance in convolutional neural networks by proposing a spherical CNN that uses spherical harmonic convolutions and spectral pooling, resulting in networks with lower capacity and no data augmentation achieving performance comparable to state-of-the-art in retrieval and classification benchmarks.
We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.