Convolutional neural networks (CNNs) allow for parameter sharing and translational equivariance by using convolutional kernels in their linear layers. By restricting these kernels to be SO(3)-steerable, CNNs can further improve parameter sharing and equivariance. These equivariant convolutional layers have several advantages over standard convolutional layers, including increased robustness to unseen poses, smaller network size, and improved sample efficiency. Despite this, most segmentation networks used in medical image analysis continue to rely on standard convolutional kernels. In this paper, we present a new family of segmentation networks that use equivariant voxel convolutions based on spherical harmonics, as well as equivariant pooling and normalization operations. These SE(3)-equivariant volumetric segmentation networks, which are robust to data poses not seen during training, do not require rotation-based data augmentation during training. In addition, we demonstrate improved segmentation performance in MRI brain tumor and healthy brain structure segmentation tasks, with enhanced robustness to reduced amounts of training data and improved parameter efficiency. Code to reproduce our results, and to implement the equivariant segmentation networks for other tasks is available at http://github.com/SCAN-NRAD/e3nn_Unet

翻译：卷积神经网络（CNN）通过在线性层中使用卷积核实现参数共享和平移等变性。通过将这些核限制为SO(3)可操控的，CNN可以进一步改善参数共享和等变性。这些等变卷积层相比标准卷积层具有多项优势，包括对未见姿态的鲁棒性增强、网络规模更小以及样本效率提升。尽管如此，医学图像分析中使用的大多数分割网络仍依赖标准卷积核。本文提出了一类新的分割网络，使用基于球谐函数的等变体素卷积，以及等变池化和归一化操作。这些SE(3)等变体积分割网络对训练中未见的姿态具有鲁棒性，在训练过程中无需基于旋转的数据增强。此外，我们在MRI脑肿瘤和健康脑结构分割任务中展示了更优的分割性能，对减少训练数据量具有更强的鲁棒性，并提升了参数效率。复现结果及将等变分割网络应用于其他任务的代码可在http://github.com/SCAN-NRAD/e3nn_Unet获取。