Learning SO(3) Equivariant Representations with Spherical CNNs

• Published in: International journal of computer vision 2020-03, Vol.128 (3), p.588-600
• Main Authors: Esteves, Carlos, Allen-Blanchette, Christine, Makadia, Ameesh, Daniilidis, Kostas
• Format: Article
• Language: English
• Subjects: Analysis; Artificial Intelligence; Artificial neural networks; Classification; Computer Imaging; Computer Science; Data augmentation; Image Processing and Computer Vision; Neural networks; Pattern Recognition; Pattern Recognition and Graphics; Shape recognition; Spherical harmonics; Three dimensional models; Vision
• ISSN: 0920-5691; 1573-1405
• DOI: 10.1007/s11263-019-01220-1

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 3D shape retrieval and classification benchmarks.