Rigid motion tracking is paramount in many medical imaging applications where movements need to be detected, corrected, or accounted for. Modern strategies rely on convolutional neural networks (CNN) and pose this problem as rigid registration. Yet, CNNs do not exploit natural symmetries in this task, as they are equivariant to translations (their outputs shift with their inputs) but not to rotations. Here we propose EquiTrack, the first method that uses recent steerable SE(3)-equivariant CNNs (E-CNN) for motion tracking. While steerable E-CNNs can extract corresponding features across different poses, testing them on noisy medical images reveals that they do not have enough learning capacity to learn noise invariance. Thus, we introduce a hybrid architecture that pairs a denoiser with an E-CNN to decouple the processing of anatomically irrelevant intensity features from the extraction of equivariant spatial features. Rigid transforms are then estimated in closed-form. EquiTrack outperforms state-of-the-art learning and optimisation methods for motion tracking in adult brain MRI and fetal MRI time series. Our code is available at https://github.com/BBillot/EquiTrack.

翻译：刚体运动跟踪在诸多需要检测、校正或解释运动的医学成像应用中至关重要。现代策略依赖卷积神经网络，并将此问题视为刚体配准。然而，卷积神经网络并未利用该任务中的自然对称性——它们对平移是等变的（输出随输入平移而平移），但对旋转并非如此。本文提出EquiTrack，这是首个利用最近发展的可转向SE(3)-等变卷积神经网络进行运动跟踪的方法。尽管可转向SE(3)-等变卷积神经网络能够提取不同姿态下的对应特征，但在含噪医学图像上的测试表明，其学习能力不足以实现噪声不变性。为此，我们引入一种混合架构，将去噪器与SE(3)-等变卷积神经网络配对，以解耦解剖无关的强度特征处理与等变空间特征提取。随后以闭式解估计刚体变换。在成人大脑MRI及胎儿MRI时间序列的运动跟踪任务中，EquiTrack显著优于当前最优的学习与优化方法。我们的代码开源在https://github.com/BBillot/EquiTrack。