# CPT-Interp: Continuous sPatial and Temporal Motion Modeling for 4D Medical Image Interpolation

arXiv: https://arxiv.org/abs/2405.15385 · HTML: https://mlsanity.com/paper/2405.15385/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 67 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 25 of 25)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Softmax Splatting for Video Frame Interpolation](https://mlsanity.com/paper/2003.05534/) (2020)
- [A Deep Learning Framework for Unsupervised Affine and Deformable Image Registration](https://mlsanity.com/paper/1809.06130/) (2018)
- [SynthMorph: learning contrast-invariant registration without acquired images](https://mlsanity.com/paper/2004.10282/) (2020)
- [VideoINR: Learning Video Implicit Neural Representation for Continuous Space-Time Super-Resolution](https://mlsanity.com/paper/2206.04647/) (2022)
- [Deep Learning in Medical Image Registration: A Review](https://mlsanity.com/paper/1912.12318/) (2019)
- [Zooming Slow-Mo: Fast and Accurate One-Stage Space-Time Video Super-Resolution](https://mlsanity.com/paper/2002.11616/) (2020)
- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [Diffusion Deformable Model for 4D Temporal Medical Image Generation](https://mlsanity.com/paper/2206.13295/) (2022)
- [A Unified Pyramid Recurrent Network for Video Frame Interpolation](https://mlsanity.com/paper/2211.03456/) (2022)
- [NODEO: A Neural Ordinary Differential Equation Based Optimization Framework for Deformable Image Registration](https://mlsanity.com/paper/2108.03443/) (2021)
- [BiFormer: Learning Bilateral Motion Estimation via Bilateral Transformer for 4K Video Frame Interpolation](https://mlsanity.com/paper/2304.02225/) (2023)
- [4DFlowNet: Super-Resolution 4D Flow MRI using Deep Learning and Computational Fluid Dynamics](https://mlsanity.com/paper/2004.07035/) (2020)
- [Multi-scale Neural ODEs for 3D Medical Image Registration](https://mlsanity.com/paper/2106.08493/) (2021)
- [Exploring Motion Ambiguity and Alignment for High-Quality Video Frame Interpolation](https://mlsanity.com/paper/2203.10291/) (2022)
- [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)
- [Robust deformable image registration using cycle-consistent implicit representations](https://mlsanity.com/paper/2310.01934/) (2023)
- [Ground Truth Or Dare: Factors Affecting The Creation Of Medical Datasets For Training AI](https://mlsanity.com/paper/2309.12327/) (2023)
- [Unsupervised Landmark Detection Based Spatiotemporal Motion Estimation for 4D Dynamic Medical Images](https://mlsanity.com/paper/2109.14805/) (2021)
- [Frame Interpolation with Multi-Scale Deep Loss Functions and Generative Adversarial Networks](https://mlsanity.com/paper/1711.06045/) (2017)
- [Fourier-Net+: Leveraging Band-Limited Representation for Efficient 3D Medical Image Registration](https://mlsanity.com/paper/2307.02997/) (2023)
- [ORRN: An ODE-based Recursive Registration Network for Deformable Respiratory Motion Estimation with Lung 4DCT Images](https://mlsanity.com/paper/2305.14673/) (2023)

## Built on by (most cited first, 3 of 3)

- [AceVFI: A Comprehensive Survey of Advances in Video Frame Interpolation](https://mlsanity.com/paper/2506.01061/) (2025)
- [FB-Diff: Fourier Basis-guided Diffusion for Temporal Interpolation of 4D Medical Imaging](https://mlsanity.com/paper/2507.04547/) (2025)
- [Phase-Aligned Finite-Fourier Periodic Deformation for 4D Medical Image Interpolation](https://mlsanity.com/paper/2608.24027/) (2026)

## Abstract (arXiv)

Motion information from 4D medical imaging offers critical insights into dynamic changes in patient anatomy for clinical assessments and radiotherapy planning and, thereby, enhances the capabilities of 3D image analysis. However, inherent physical and technical constraints of imaging hardware often necessitate a compromise between temporal resolution and image quality. Frame interpolation emerges as a pivotal solution to this challenge. Previous methods often suffer from discretion when they estimate the intermediate motion and execute the forward warping. In this study, we draw inspiration from fluid mechanics to propose a novel approach for continuously modeling patient anatomic motion using implicit neural representation. It ensures both spatial and temporal continuity, effectively bridging Eulerian and Lagrangian specifications together to naturally facilitate continuous frame interpolation. Our experiments across multiple datasets underscore the method's superior accuracy and speed. Furthermore, as a case-specific optimization (training-free) approach, it circumvents the need for extensive datasets and addresses model generalization issues.