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Rigid motion tracking is paramount in many medical imaging applications wheremovements need to be detected, corrected, or accounted for. Modern strategiesrely on convolutional neural networks (CNN) and pose this problem as rigidregistration. Yet, CNNs do not exploit natural symmetries in this task, as theyare equivariant to translations (their outputs shift with their inputs) but notto rotations. Here we propose EquiTrack, the first method that uses recentsteerable SE(3)-equivariant CNNs (E-CNN) for motion tracking. While steerableE-CNNs can extract corresponding features across different poses, testing themon noisy medical images reveals that they do not have enough learning capacityto learn noise invariance. Thus, we introduce a hybrid architecture that pairsa denoiser with an E-CNN to decouple the processing of anatomically irrelevantintensity features from the extraction of equivariant spatial features. Rigidtransforms are then estimated in closed-form. EquiTrack outperformsstate-of-the-art learning and optimisation methods for motion tracking in adultbrain MRI and fetal MRI time series. Our code is available atgithub.com/BBillot/equitrack.

SE(3)-Equivariant and Noise-Invariant 3D Motion Tracking in Medical Images