# Phase-Aligned Finite-Fourier Periodic Deformation for 4D Medical Image Interpolation

arXiv: https://arxiv.org/abs/2608.24027 · HTML: https://mlsanity.com/paper/2608.24027/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 46 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 18 of 18)

- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [AMT: All-Pairs Multi-Field Transforms for Efficient Frame Interpolation](https://mlsanity.com/paper/2304.09790/) (2023)
- [IFRNet: Intermediate Feature Refine Network for Efficient Frame Interpolation](https://mlsanity.com/paper/2205.14620/) (2022)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [Diffusion Deformable Model for 4D Temporal Medical Image Generation](https://mlsanity.com/paper/2206.13295/) (2022)
- [Representation Learning via Global Temporal Alignment and Cycle-Consistency](https://mlsanity.com/paper/2105.05217/) (2021)
- [TimeReplayer: Unlocking the Potential of Event Cameras for Video Interpolation](https://mlsanity.com/paper/2203.13859/) (2022)
- [Medical Image Registration via Neural Fields](https://mlsanity.com/paper/2206.03111/) (2022)
- [FLD: Fourier Latent Dynamics for Structured Motion Representation and Learning](https://mlsanity.com/paper/2402.13820/) (2024)
- [A Spatiotemporal Volumetric Interpolation Network for 4D Dynamic Medical Image](https://mlsanity.com/paper/2002.12680/) (2020)
- [Data-Efficient Unsupervised Interpolation Without Any Intermediate Frame for 4D Medical Images](https://mlsanity.com/paper/2404.01464/) (2024)
- [Ultrasound Image-to-Video Synthesis via Latent Dynamic Diffusion Models](https://mlsanity.com/paper/2503.14966/) (2025)
- [CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences](https://mlsanity.com/paper/2406.18582/) (2024)
- [FB-Diff: Fourier Basis-guided Diffusion for Temporal Interpolation of 4D Medical Imaging](https://mlsanity.com/paper/2507.04547/) (2025)
- [Latent Motion Profiling for Annotation-free Cardiac Phase Detection in Adult and Fetal Echocardiography Videos](https://mlsanity.com/paper/2507.05154/) (2025)
- [Continuous 3D Myocardial Motion Tracking via Echocardiography](https://mlsanity.com/paper/2310.02792/) (2023)
- [CPT-Interp: Continuous sPatial and Temporal Motion Modeling for 4D Medical Image Interpolation](https://mlsanity.com/paper/2405.15385/) (2024)

## Abstract (arXiv)

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.