Deformable image registration (DIR), aiming to find spatial correspondence between images, is one of the most critical problems in the domain of medical image analysis. In this paper, we present a novel, generic, and accurate diffeomorphic image registration framework that utilizes neural ordinary differential equations (NODEs). We model each voxel as a moving particle and consider the set of all voxels in a 3D image as a high-dimensional dynamical system whose trajectory determines the targeted deformation field. Our method leverages deep neural networks for their expressive power in modeling dynamical systems, and simultaneously optimizes for a dynamical system between the image pairs and the corresponding transformation. Our formulation allows various constraints to be imposed along the transformation to maintain desired regularities. Our experiment results show that our method outperforms the benchmarks under various metrics. Additionally, we demonstrate the feasibility to expand our framework to register multiple image sets using a unified form of transformation,which could possibly serve a wider range of applications.

翻译：形变图像配准（DIR）旨在寻找图像间的空间对应关系，是医学图像分析领域最关键的问题之一。本文提出了一种新颖、通用且精确的微分同胚图像配准框架，该框架利用神经常微分方程（NODEs）。我们将每个体素建模为运动粒子，并将三维图像中的所有体素集合视为一个高维动力系统，其轨迹决定了目标形变场。该方法利用深度神经网络在动力系统建模中的强大表达能力，同时优化图像对之间的动力系统及其对应的变换。我们的公式允许在变换过程中施加各种约束以保持期望的正则性。实验结果表明，我们的方法在各种评价指标上均优于基准方法。此外，我们证明了将该框架扩展为使用统一变换形式配准多个图像集的可行性，这将可能服务于更广泛的应用场景。