|Maurice Weiler||University of Amsterdam|
|Wouter Boomsma||University of Copenhagen|
|Max Welling||University of Amsterdam / Qualcomm AI Research|
|Taco Cohen||University of Amsterdam|
The authors present a convolutional network that is equivariant to rigid body motions.
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.