MomentaMorph: Unsupervised Spatial-Temporal Registration with Momenta, Shooting, and Correction
This addresses motion estimation errors in medical imaging for tissue deformation analysis, but it is incremental as it builds on existing registration methods with a novel correction step.
The paper tackles the problem of motion estimation from tagged MRI images with large motion and repetitive patterns, which causes registration methods to get trapped in local optima. It introduces a 'momenta, shooting, and correction' framework that achieves accurate, dense, and diffeomorphic 2D/3D motion fields, as demonstrated on synthetic and real datasets.
Tagged magnetic resonance imaging (tMRI) has been employed for decades to measure the motion of tissue undergoing deformation. However, registration-based motion estimation from tMRI is difficult due to the periodic patterns in these images, particularly when the motion is large. With a larger motion the registration approach gets trapped in a local optima, leading to motion estimation errors. We introduce a novel "momenta, shooting, and correction" framework for Lagrangian motion estimation in the presence of repetitive patterns and large motion. This framework, grounded in Lie algebra and Lie group principles, accumulates momenta in the tangent vector space and employs exponential mapping in the diffeomorphic space for rapid approximation towards true optima, circumventing local optima. A subsequent correction step ensures convergence to true optima. The results on a 2D synthetic dataset and a real 3D tMRI dataset demonstrate our method's efficiency in estimating accurate, dense, and diffeomorphic 2D/3D motion fields amidst large motion and repetitive patterns.