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~\url{http://github.com/SCAN-NRAD/e3nn_Unet}.

翻译：尽管如此,医学图像分析中使用的大多数分解网络仍然依赖标准的共生内核。在本文件中,我们介绍了一个新的分化网络组合,这些网络使用基于球形共振的静态 voxel 共生网络,以及等离子共生和常规操作。这些SE(3)-Qevarial 体积分解网络,对培训期间没有看到的数据具有很强的力度,因此不需要在培训期间进行基于轮换的数据增强。此外,我们展示了MRI肿瘤和健康大脑结构分化任务的分解性能的改善,同时降低了基于球形共振的静态 voxel 共生网络的强度,并改进了我们现有数据分流/变异性网络的效率。</s>