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.

翻译：正则群卷积神经网络（G-CNNs）已被证明能够提升模型性能并增强对不同几何对称性的等变性。本文研究了体积数据上的SE(3)（即旋转-平移等变性）问题。体积图像数据在众多医学场景中普遍存在。受近期关于可分离群卷积工作的启发，我们设计了一种SE(3)群卷积核，它被分解为连续SO(3)（旋转）核与空间核两部分。我们通过采样均匀SO(3)网格来近似连续情况下的等变性。我们的连续SO(3)核采用基于相似均匀网格的径向基函数（RBF）插值进行参数化。我们在体积医学图像分析中展示了该方法的优势。在具有挑战性的医学分类任务中，我们的SE(3)等变模型始终优于CNN和常规离散G-CNN，并展现出显著增强的泛化能力。相较于常规CNN，我们的方法准确率提升高达16.5%。