Learning SO(3) Equivariant Representations with Spherical CNNs

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...

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Bibliographic Details
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
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Summary: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.
ISSN:0920-5691
1573-1405
DOI:10.1007/s11263-019-01220-1