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.

本文通过分离一个连续的 SO（3）（旋转）内核和一个连续的空间内核来设计一个 SE（3）群卷积核，通过在均匀的 SO (3) 网格上进行 RBF 插值来参数化连续的 SO (3) 内核，对临床任务的分析显示，我们的 SE（3）等变模型在挑战性医学分类任务上始终优于 CNN 和定期离散 G-CNN，并显示显着改进的泛化能力；我们的方法比定期 CNN 的正确率提高了高达 16.5％。