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3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
Maurice Weiler · Wouter Boomsma · Mario Geiger · Max Welling · Taco S Cohen

Tue Dec 04 07:45 AM -- 09:45 AM (PST) @ Room 210 #45

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.

Author Information

Maurice Weiler (University of Amsterdam)
Wouter Boomsma (University of Copenhagen)
Mario Geiger (EPFL)
Max Welling (University of Amsterdam / Qualcomm AI Research)
Taco S Cohen (University of Amsterdam)

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