3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, Taco S Cohen
Abstract
We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a linear combination of a complete steerable kernel basis, which is derived analytically in this paper. We prove that equivariant convolutions are the most general equivariant linear maps between fields over R^3. Our experimental results confirm the effectiveness of 3D Steerable CNNs for the problem of amino acid propensity prediction and protein structure classification, both of which have inherent SE(3) symmetry.
BibTeX
@inproceedings{NEURIPS2018_488e4104,
author = {Weiler, Maurice and Geiger, Mario and Welling, Max and Boomsma, Wouter and Cohen, Taco S},
booktitle = {Advances in Neural Information Processing Systems},
editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data},
url = {https://proceedings.neurips.cc/paper_files/paper/2018/file/488e4104520c6aab692863cc1dba45af-Paper.pdf},
volume = {31},
year = {2018}
}