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

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 github.com/BBillot/equitrack.

Fetal Pose Estimation in Volumetric MRI using a 3D Convolution Neural Network

The performance and diagnostic utility of magnetic resonance imaging (MRI) in pregnancy is fundamentally constrained by fetal motion. Motion of the fetus, which is unpredictable and rapid on the scale of conventional imaging times, limits the set of viable acquisition techniques to single-shot imaging with severe compromises in signal-to-noise ratio and diagnostic contrast, and frequently results in unacceptable image quality. Surprisingly little is known about the characteristics of fetal motion during MRI and here we propose and demonstrate methods that exploit a growing repository of MRI observations of the gravid abdomen that are acquired at low spatial resolution but relatively high temporal resolution and over long durations (10-30 minutes). We estimate fetal pose per frame in MRI volumes of the pregnant abdomen via deep learning algorithms that detect key fetal landmarks. Evaluation of the proposed method shows that our framework achieves quantitatively an average error of 4.47 mm and 96.4\% accuracy (with error less than 10 mm). Fetal pose estimation in MRI time series yields novel means of quantifying fetal movements in health and disease, and enables the learning of kinematic models that may enhance prospective mitigation of fetal motion artifacts during MRI acquisition.

Temporal Registration in In-Utero Volumetric MRI Time Series

We present a robust method to correct for motion and deformations for in-utero volumetric MRI time series. Spatio-temporal analysis of dynamic MRI requires robust alignment across time in the presence of substantial and unpredictable motion. We make a Markov assumption on the nature of deformations to take advantage of the temporal structure in the image data. Forward message passing in the corresponding hidden Markov model (HMM) yields an estimation algorithm that only has to account for relatively small motion between consecutive frames. We demonstrate the utility of the temporal model by showing that its use improves the accuracy of the segmentation propagation through temporal registration. Our results suggest that the proposed model captures accurately the temporal dynamics of deformations in in-utero MRI time series.