3D Steerable CNNs: Learning Rotationally Equivariant Features In Volumetric Data

Authors:
Maurice Weiler University of Amsterdam
Wouter Boomsma University of Copenhagen
Mario Geiger EPFL
Max Welling University of Amsterdam / Qualcomm AI Research
Taco Cohen University of Amsterdam

Introduction:

The authors present a convolutional network that is equivariant to rigid body motions.

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.

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