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NODER: Image Sequence Regression Based on Neural Ordinary Differential Equations

Hao Bai, Yi Hong

TL;DR

The paper tackles regression on 3D medical image sequences under missing data and high-dimensional constraints by introducing NODER, an optimization-based framework that uses Neural ODEs to model non-linear temporal dynamics of voxel clouds. To manage computational cost, dynamics are solved in a latent space via an Encoder–Decoder pair, with a memory-efficient Adjoint Sensitivity Method for training and diffeomorphic regularization to preserve topology. The approach yields state-of-the-art results on ADNI and ACDC datasets, outperforming diffusion and geodesic-based methods in 3D image regression while offering practical predictions from limited time points. This has important clinical implications for longitudinal analysis where complete time-series data are often unavailable, and the authors provide code to facilitate adoption.

Abstract

Regression on medical image sequences can capture temporal image pattern changes and predict images at missing or future time points. However, existing geodesic regression methods limit their regression performance by a strong underlying assumption of linear dynamics, while diffusion-based methods have high computational costs and lack constraints to preserve image topology. In this paper, we propose an optimization-based new framework called NODER, which leverages neural ordinary differential equations to capture complex underlying dynamics and reduces its high computational cost of handling high-dimensional image volumes by introducing the latent space. We compare our NODER with two recent regression methods, and the experimental results on ADNI and ACDC datasets demonstrate that our method achieves the state-of-the-art performance in 3D image regression. Our model needs only a couple of images in a sequence for prediction, which is practical, especially for clinical situations where extremely limited image time series are available for analysis. Our source code is available at https://github.com/ZedKing12138/NODER-pytorch.

NODER: Image Sequence Regression Based on Neural Ordinary Differential Equations

TL;DR

The paper tackles regression on 3D medical image sequences under missing data and high-dimensional constraints by introducing NODER, an optimization-based framework that uses Neural ODEs to model non-linear temporal dynamics of voxel clouds. To manage computational cost, dynamics are solved in a latent space via an Encoder–Decoder pair, with a memory-efficient Adjoint Sensitivity Method for training and diffeomorphic regularization to preserve topology. The approach yields state-of-the-art results on ADNI and ACDC datasets, outperforming diffusion and geodesic-based methods in 3D image regression while offering practical predictions from limited time points. This has important clinical implications for longitudinal analysis where complete time-series data are often unavailable, and the authors provide code to facilitate adoption.

Abstract

Regression on medical image sequences can capture temporal image pattern changes and predict images at missing or future time points. However, existing geodesic regression methods limit their regression performance by a strong underlying assumption of linear dynamics, while diffusion-based methods have high computational costs and lack constraints to preserve image topology. In this paper, we propose an optimization-based new framework called NODER, which leverages neural ordinary differential equations to capture complex underlying dynamics and reduces its high computational cost of handling high-dimensional image volumes by introducing the latent space. We compare our NODER with two recent regression methods, and the experimental results on ADNI and ACDC datasets demonstrate that our method achieves the state-of-the-art performance in 3D image regression. Our model needs only a couple of images in a sequence for prediction, which is practical, especially for clinical situations where extremely limited image time series are available for analysis. Our source code is available at https://github.com/ZedKing12138/NODER-pytorch.
Paper Structure (6 sections, 7 equations, 5 figures, 1 table)

This paper contains 6 sections, 7 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Method
  3. Background and Definitions
  4. Formulation of Image Regression in Neural ODEs
  5. Experiments
  6. Conclusion and Discussion

Figures (5)

  • Figure 1: Overview of our proposed NODER framework.
  • Figure 2: Visualization of the regression results on the ADNI dataset. Top to bottom rows: 1) image sequence of a subject, 2) our prediction, 3) image difference of original sequence w.r.t. the first baseline image, and 4) image difference between generated and original corresponding images.
  • Figure 3: Visualization of the regression results on the ACDC dataset. Top to bottom rows: 1) image sequence of a subject, 2) our prediction, 3) image difference of original sequence w.r.t. the first baseline image, and 4) image difference between generated and original corresponding images.
  • Figure 4: Visualization of using (2nd row) and not using (3rd row) the smoothness constraints on regression the image sequence (1st row).
  • Figure 5: Visualization of deformation fields without (left) and with the boundary condition (right).