SE(3)-Equivariant and Noise-Invariant 3D Rigid Motion Tracking in Brain MRI
This addresses motion tracking in medical imaging, which is crucial for applications like movement detection and correction, but it is incremental as it builds on existing equivariant CNN techniques.
The paper tackles the problem of rigid motion tracking in brain MRI by proposing EquiTrack, a hybrid method that combines a denoiser with SE(3)-equivariant CNNs to handle noise and exploit symmetries, outperforming state-of-the-art methods in adult and fetal MRI time series.
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.