# MomentaMorph: Unsupervised Spatial-Temporal Registration with Momenta, Shooting, and Correction

arXiv: https://arxiv.org/abs/2308.02949 · HTML: https://mlsanity.com/paper/2308.02949/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 5 Aug 2023.

## Builds on (most cited first, 15 of 15)

- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [What Matters in Unsupervised Optical Flow](https://mlsanity.com/paper/2006.04902/) (2020)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [SMURF: Self-Teaching Multi-Frame Unsupervised RAFT with Full-Image Warping](https://mlsanity.com/paper/2105.07014/) (2021)
- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [U-Net vs Transformer: Is U-Net Outdated in Medical Image Registration?](https://mlsanity.com/paper/2208.04939/) (2022)
- [Learning Pixel Trajectories with Multiscale Contrastive Random Walks](https://mlsanity.com/paper/2201.08379/) (2022)
- [CNN-based Lung CT Registration with Multiple Anatomical Constraints](https://mlsanity.com/paper/2011.14372/) (2020)
- [DeepTag: An Unsupervised Deep Learning Method for Motion Tracking on Cardiac Tagging Magnetic Resonance Images](https://mlsanity.com/paper/2103.02772/) (2021)
- [Dense Unsupervised Learning for Video Segmentation](https://mlsanity.com/paper/2111.06265/) (2021)
- [Coordinate Translator for Learning Deformable Medical Image Registration](https://mlsanity.com/paper/2203.03626/) (2022)
- [Motion Pyramid Networks for Accurate and Efficient Cardiac Motion Estimation](https://mlsanity.com/paper/2006.15710/) (2020)
- [New starting point registration method for tagged MRI tongue motion estimation](https://mlsanity.com/paper/2302.04330/) (2023)
- [DRIMET: Deep Registration for 3D Incompressible Motion Estimation in Tagged-MRI with Application to the Tongue](https://mlsanity.com/paper/2301.07234/) (2023)

## Built on by (most cited first, 2 of 2)

- [Is Registering Raw Tagged-MR Enough for Strain Estimation in the Era of Deep Learning?](https://mlsanity.com/paper/2401.17571/) (2024)
- [Solving a Nonlinear Blind Inverse Problem for Tagged MRI with Physics and Deep Generative Priors](https://mlsanity.com/paper/2603.00882/) (2026)

## Abstract (arXiv)

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.