Learning SO(3) Equivariant Representations with Spherical CNNs

TY - JOUR

T1 - Learning SO(3) Equivariant Representations with Spherical CNNs

AU - Esteves, Carlos

AU - Allen-Blanchette, Christine

AU - Makadia, Ameesh

AU - Daniilidis, Kostas

N1 - Publisher Copyright: © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - 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.

AB - 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.

KW - 3D vision

KW - Equivariance

KW - Sphere

KW - Spherical CNN

UR - http://www.scopus.com/inward/record.url?scp=85073982214&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073982214&partnerID=8YFLogxK

U2 - 10.1007/s11263-019-01220-1

DO - 10.1007/s11263-019-01220-1

M3 - Article

SN - 0920-5691

VL - 128

SP - 588

EP - 600

JO - International Journal of Computer Vision

JF - International Journal of Computer Vision

IS - 3

ER -