# Bidirectional Recurrence for Cardiac Motion Tracking with Gaussian Process Latent Coding

arXiv: https://arxiv.org/abs/2410.20752 · HTML: https://mlsanity.com/paper/2410.20752/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 64 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [FlowFormer: A Transformer Architecture for Optical Flow](https://mlsanity.com/paper/2203.16194/) (2022)
- [Deep Learning for Segmentation using an Open Large-Scale Dataset in 2D Echocardiography](https://mlsanity.com/paper/1908.06948/) (2019)
- [UnFlow: Unsupervised Learning of Optical Flow with a Bidirectional Census Loss](https://mlsanity.com/paper/1711.07837/) (2017)
- [An Unsupervised Learning Model for Deformable Medical Image Registration](https://mlsanity.com/paper/1802.02604/) (2018)
- [Iterative Residual Refinement for Joint Optical Flow and Occlusion Estimation](https://mlsanity.com/paper/1904.05290/) (2019)
- [SelFlow: Self-Supervised Learning of Optical Flow](https://mlsanity.com/paper/1904.09117/) (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)
- [FlowFormer++: Masked Cost Volume Autoencoding for Pretraining Optical Flow Estimation](https://mlsanity.com/paper/2303.01237/) (2023)
- [Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks](https://mlsanity.com/paper/2003.09514/) (2020)
- [End-to-End Unsupervised Deformable Image Registration with a Convolutional Neural Network](https://mlsanity.com/paper/1704.06065/) (2017)
- [DiffuseMorph: Unsupervised Deformable Image Registration Using Diffusion Model](https://mlsanity.com/paper/2112.05149/) (2021)
- [Correlation-aware Coarse-to-fine MLPs for Deformable Medical Image Registration](https://mlsanity.com/paper/2406.00123/) (2024)
- [DeepTag: An Unsupervised Deep Learning Method for Motion Tracking on Cardiac Tagging Magnetic Resonance Images](https://mlsanity.com/paper/2103.02772/) (2021)
- [Region-specific Diffeomorphic Metric Mapping](https://mlsanity.com/paper/1906.00139/) (2019)
- [Biomechanics-informed Neural Networks for Myocardial Motion Tracking in MRI](https://mlsanity.com/paper/2006.04725/) (2020)
- [Generative Myocardial Motion Tracking via Latent Space Exploration with Biomechanics-informed Prior](https://mlsanity.com/paper/2206.03830/) (2022)
- [GraphEcho: Graph-Driven Unsupervised Domain Adaptation for Echocardiogram Video Segmentation](https://mlsanity.com/paper/2309.11145/) (2023)
- [FOAL: Fast Online Adaptive Learning for Cardiac Motion Estimation](https://mlsanity.com/paper/2003.04492/) (2020)
- [Non-iterative Coarse-to-fine Transformer Networks for Joint Affine and Deformable Image Registration](https://mlsanity.com/paper/2307.03421/) (2023)
- [FSDiffReg: Feature-wise and Score-wise Diffusion-guided Unsupervised Deformable Image Registration for Cardiac Images](https://mlsanity.com/paper/2307.12035/) (2023)
- [Unsupervised Deformable Image Registration with Absent Correspondences in Pre-operative and Post-Recurrence Brain Tumor MRI Scans](https://mlsanity.com/paper/2206.03900/) (2022)
- [GL-Fusion: Global-Local Fusion Network for Multi-view Echocardiogram Video Segmentation](https://mlsanity.com/paper/2309.11144/) (2023)
- [Flow Network Tracking for Spatiotemporal and Periodic Point Matching: Applied to Cardiac Motion Analysis](https://mlsanity.com/paper/1807.02951/) (2018)

## Built on by (most cited first, 5 of 5)

- [Dyna3DGR: 4D Cardiac Motion Tracking with Dynamic 3D Gaussian Representation](https://mlsanity.com/paper/2507.16608/) (2025)
- [BOTM: Echocardiography Segmentation via Bi-directional Optimal Token Matching](https://mlsanity.com/paper/2505.18052/) (2025)
- [FAMSeg: Fetal Femur and Cranial Ultrasound Segmentation Using Feature-Aware Attention and Mamba Enhancement](https://mlsanity.com/paper/2506.07431/) (2025)
- [CardiacCLIP: Video-based CLIP Adaptation for LVEF Prediction in a Few-shot Manner](https://mlsanity.com/paper/2509.17065/) (2025)
- [Learning to Beat: Phenotype-Guided Latent Flow with Regional Motion Priors for Biventricular Motion Synthesis](https://mlsanity.com/paper/2608.19738/) (2026)

## Abstract (arXiv)

Quantitative analysis of cardiac motion is crucial for assessing cardiac function. This analysis typically uses imaging modalities such as MRI and Echocardiograms that capture detailed image sequences throughout the heartbeat cycle. Previous methods predominantly focused on the analysis of image pairs lacking consideration of the motion dynamics and spatial variability. Consequently, these methods often overlook the long-term relationships and regional motion characteristic of cardiac. To overcome these limitations, we introduce the GPTrack, a novel unsupervised framework crafted to fully explore the temporal and spatial dynamics of cardiac motion. The GPTrack enhances motion tracking by employing the sequential Gaussian Process in the latent space and encoding statistics by spatial information at each time stamp, which robustly promotes temporal consistency and spatial variability of cardiac dynamics. Also, we innovatively aggregate sequential information in a bidirectional recursive manner, mimicking the behavior of diffeomorphic registration to better capture consistent long-term relationships of motions across cardiac regions such as the ventricles and atria. Our GPTrack significantly improves the precision of motion tracking in both 3D and 4D medical images while maintaining computational efficiency. The code is available at: https://github.com/xmed-lab/GPTrack