Low-Rank Velocity Fields as a Structural Prior for Unsupervised 4D Medical Image Interpolation

4D medical image interpolation aims to recover missing volumes from sparsely observed time points and is important for dynamic anatomical analysis in applications such as cardiac MRI and thoracic CT, where motion is often repetitive or near-periodic over clinically relevant intervals. A key challenge is that this structure is not always encoded directly in deformation representations for interpolation. In addition, physiological motion is often non-uniform, so equal temporal intervals do not necessarily correspond to equal amounts of anatomical change. To address these issues, we formulate interpolation as learning a continuous deformation process with a phase-structured prior. Given two endpoint volumes, we parameterize a phase-conditioned velocity field with a finite Fourier basis, which embeds near-periodic motion patterns directly into the deformation space and supports continuous querying at arbitrary target times. We further introduce a phase-aligned temporal reparameterization that maps normalized within-interval time to a latent motion phase according to deformation variation intensity, thereby better modeling non-uniform motion progression. Intermediate volumes are then synthesized by continuously warping both endpoints, followed by bidirectional fusion and lightweight residual refinement. Experiments on ACDC and 4D-Lung show that the proposed method achieves state-of-the-art performance over existing baselines while producing anatomically plausible and coherent intermediate volumes from sparse observations.

Developing robust artificial intelligence models for 4D (3D + time) medical imaging is constrained by limited annotated data, inter-device domain shifts, and privacy restrictions. To address this, we propose a 4D controllable generative framework for anatomically consistent data augmentation. A semi-supervised variational autoencoder learns a compact latent representation of anatomical volumes while jointly predicting aligned segmentation masks in a unified framework. Anatomical structure is then disentangled from temporal dynamics through a cascaded latent diffusion model (LDM). A static LDM generates subject-specific anatomy conditioned on clinical priors (diagnosis and volumes measures) and a subsequent motion LDM estimates residual latent motions, ensuring strict temporal coherence across the 4D sequence. The proposed approach was evaluated on cine cardiac MRI as a representative 4D imaging application. Experiments across multiple datasets demonstrate high controllability of static anatomy (Pearson r > 0.8) and strong temporal coherence (FVD = 288.08). In cross-vendor generalization experiments, augmenting training sets with synthetic 4D sequences significantly improves downstream segmentation performance. Using nnU-Net, the proposed augmentation strategy improves the average Dice score by 1.4% and reduces the Hausdorff Distance by 3.0mm compared to training on real data alone, for the left ventricle, Dice improves by 2.8% with a 5.4mm reduction in boundary error. Overall, this framework provides a scalable and controllable solution for 4D medical image synthesis, supporting the development of more robust models with limited annotations and cross-vendor variability. Code available on https://github.com/cyiheng/4DCardiacMRISynthesis.

Existing unified 4D reconstruction and point tracking approaches typically rely on heuristic interpolations or just predict at integer timestamps, lacking kinematic coherence and failing to model dynamics at any arbitrary timestamp. In this paper, we propose Uni4R, a framework that unifies these tasks by learning continuous velocity fields through the synergy of Optimal Transport (OT) and Ordinary Differential Equation (ODE). Importantly, this continuous velocity field acts as a kinematic prior that mutually benefits both 4D reconstruction and point tracking. Specifically, we propose the Flow Matching Guided Decoder (FMGD). A global velocity branch first extracts anchor features that capture the global dynamic state of the sequence. Then, FMGD leverages Flow Matching (FM) theory to formulate a probability path defined by OT on the anchor feature manifold, instantiating it as FM-guided velocity features for velocity prediction. This establishes a robust kinematic inductive bias. Meanwhile, a point reconstruction branch provides geometric features. The local velocity prediction module then joint above features and time embeddings, to decode velocities at arbitrary timestamps. To overcome the absence of high-quality ground-truth velocities in fractional frames, we propose an integral-consistency training strategy. This strategy uses an ODE solver to integrate velocities to recover target pointmaps, enabling the model to be supervised end-to-end directly from integer timestamps. Experimental results demonstrate that Uni4R achieves SOTA performance in both 4D reconstruction and point tracking, and achieves SOTA in our new kinematics-aware benchmark at continuous time.