SE(3)-Equivariant and Noise-Invariant 3D Rigid Motion Tracking in Brain MRI

TL;DR

This paper introduces EquiTrack, a novel SE(3)-equivariant CNN-based method for 3D rigid motion tracking in brain MRI, effectively handling noise and outperforming existing techniques.

Contribution

It presents the first use of steerable SE(3)-equivariant CNNs for medical motion tracking and introduces a hybrid denoising architecture to improve noise invariance.

Findings

Outperforms state-of-the-art methods in brain MRI motion tracking

Effectively handles noisy medical images with the hybrid architecture

Provides a closed-form solution for rigid transform estimation

Abstract

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.