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Bidirectional Recurrence for Cardiac Motion Tracking with Gaussian Process Latent Coding
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Proposes GPTrack, an unsupervised cardiac motion tracking framework that places a Gaussian process prior over latent codes in a bidirectional recurrent transformer-based diffeomorphic registration network, evaluated on echocardiogram (CardiacUDA, CAMUS) and cardiac MRI (ACDC).
Problem
Unsupervised cardiac motion tracking across long image sequences (3D echocardiogram videos and 4D cardiac MRI) struggles with long-term temporal consistency, regional motion variability, and error accumulation in Lagrangian displacement integration, while being computationally efficient.
Approach
Combine a bidirectional forward-backward recurrent transformer cell (mimicking diffeomorphic forward-backward registration) with a Gaussian process prior over latent velocity codes, solved efficiently as a Kalman-filtered state-space model (Matern 3/2 kernel) with position-based distances, to produce temporally consistent diffeomorphic motion fields.
Key results
- On CardiacUDA, GPTrack-XL reaches 82.37% average Dice (vs. 79.41% for DeepTag) with PSNR 32.03 and SSIM 80.04.
- On ACDC, GPTrack-XL achieves 82.65% average Dice, above FSDiffReg (82.30%), with PSNR 35.52 and SSIM 86.19.
- Ablation on CardiacUDA shows bidirectional recursion plus GP raises average Dice from 79.83 (neither) to 82.37 while reducing det(J)<=0 from 0.048% to 0.027%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use GPTrack-XL instead of DeepTag | Cardiac motion tracking · CardiacUDA | Avg. Dice (%): 79.41 -> 82.37 | Helped |
| use GPTrack-XL instead of FSDiffReg | Cardiac motion tracking · ACDC | Avg. Dice: 82.30 -> 82.65 | Helped |
| use GPTrack-XL instead of DeepTag | Cardiac motion tracking · CAMUS | Avg. Dice (%): 84.80 -> 85.29 | Helped |
| add Gaussian Process while leaving out bidirectional recurrence (ablation) | GPTrack-XL · GPTrack-XL ablation | Dice.Avg: 79.83 -> 80.81 | Helped |
| add bidirectional recurrence while leaving out Gaussian Process (ablation) | GPTrack-XL · GPTrack-XL ablation | Dice.Avg: 79.83 -> 81.21 | Helped |
| add Gaussian Process to the bidirectional method (ablation) | GPTrack-XL · GPTrack-XL ablation | Dice.Avg: 81.21 -> 82.37 | Helped |
| add bidirectional recurrence to the GP method (ablation) | GPTrack-XL · GPTrack-XL ablation | Dice.Avg: 80.81 -> 82.37 | Helped |
Limitations
- Uses positional encoding as the cardiac motion prior, which may degrade performance on out-of-domain datasets.
- Lightweight GPTrack-XL on CardiacUDA has more parameters (7.5M) and TFlops than some baselines such as DeepTag and VM-DIF.
- Evaluated only on echocardiogram (A4C/A2C) and cardiac MRI datasets.
Experimental setup
Datasets: CardiacUDA CAMUS ACDC
Benchmarks: CardiacUDA CAMUS ACDC
Metrics: Dice PSNR SSIM Hausdorff distance det(J) <= 0 percentage ||J|-1|| inference time parameters TFlops
Baselines: LDDMM RDMM ANTs (SyN) VM-SSD VM-NCC SYMNet VM-DIF DiffuseMorph DeepTag FSDiffReg CorrMLP NICE-Trans
Builds on: VoxelMorph DeepTag diffeomorphic registration (LDDMM) Matern kernel GP to state-space conversion RWKV-style recurrent transformer
Closest papers by meaning
- From Heartbeat to Cardiochoreography: A Mechanics Foundation Model for Individualized 4D Cardiac Motion Generation Conditioned on Electrophysiology (NeurIPS 2026 · similarity 0.88)
- EchoXFlow: A Beamspace Echocardiography Dataset for Cardiac Motion, Flow, and Function (NeurIPS 2026 · similarity 0.84)
- Cylindrical Geodesic Flow Matching for Quasiperiodic Physiological Signal Transformation (NeurIPS 2026 · similarity 0.83)
- EchoWorld: Learning Motion-Aware World Models for Echocardiography Probe Guidance (CVPR 2025 · similarity 0.82)
- MotionTTT: 2D Test-Time-Training Motion Estimation for 3D Motion Corrected MRI (NeurIPS 2024 · similarity 0.82)
- PhysDiff: Physiology-based Dynamicity Disentangled Diffusion Model for Remote Physiological Measurement (AAAI 2025 · similarity 0.82)
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