Learning SO(3) Equivariant Representations with Spherical CNNs

Carlos Esteves, Christine Allen-Blanchette, Ameesh Makadia, Kostas Daniilidis

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)588-600
Number of pages13
JournalInternational Journal of Computer Vision
Issue number3
StatePublished - Mar 1 2020

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


  • 3D vision
  • Equivariance
  • Sphere
  • Spherical CNN


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