  Regular group convolutional neural networks (G-CNNs) have been shown to
increase model performance and improve equivariance to different geometrical
symmetries. This work addresses the problem of SE(3), i.e., roto-translation
equivariance, on volumetric data. Volumetric image data is prevalent in many
medical settings. Motivated by the recent work on separable group convolutions,
we devise a SE(3) group convolution kernel separated into a continuous SO(3)
(rotation) kernel and a spatial kernel. We approximate equivariance to the
continuous setting by sampling uniform SO(3) grids. Our continuous SO(3) kernel
is parameterized via RBF interpolation on similarly uniform grids. We
demonstrate the advantages of our approach in volumetric medical image
analysis. Our SE(3) equivariant models consistently outperform CNNs and regular
discrete G-CNNs on challenging medical classification tasks and show
significantly improved generalization capabilities. Our approach achieves up to
a 16.5% gain in accuracy over regular CNNs.
