3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
Machine Learning
2018-10-30 v2 Machine Learning
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.
Cite
@article{arxiv.1807.02547,
title = {3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data},
author = {Maurice Weiler and Mario Geiger and Max Welling and Wouter Boomsma and Taco Cohen},
journal= {arXiv preprint arXiv:1807.02547},
year = {2018}
}