Learning SO(3) Equivariant Representations with Spherical CNNs
Abstract
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.
Cite
Text
Esteves et al. "Learning SO(3) Equivariant Representations with Spherical CNNs." Proceedings of the European Conference on Computer Vision (ECCV), 2018. doi:10.1007/978-3-030-01261-8_4Markdown
[Esteves et al. "Learning SO(3) Equivariant Representations with Spherical CNNs." Proceedings of the European Conference on Computer Vision (ECCV), 2018.](https://mlanthology.org/eccv/2018/esteves2018eccv-learning/) doi:10.1007/978-3-030-01261-8_4BibTeX
@inproceedings{esteves2018eccv-learning,
title = {{Learning SO(3) Equivariant Representations with Spherical CNNs}},
author = {Esteves, Carlos and Allen-Blanchette, Christine and Makadia, Ameesh and Daniilidis, Kostas},
booktitle = {Proceedings of the European Conference on Computer Vision (ECCV)},
year = {2018},
doi = {10.1007/978-3-030-01261-8_4},
url = {https://mlanthology.org/eccv/2018/esteves2018eccv-learning/}
}