Deformable Image Registration using Neural ODEs Yifan Wu * Tom Z.Jiahao * Jiancong Wang * Paul A. Yushkevich James C. Gee M. Ani Hsieh University of Pennsylvania, Philadelphia, PA, USA {yfwu, zjh}@seas.upenn.edu {jiancong.wang, pauly2}@pennmedicine.upenn.edu gee@upenn.edu mya@seas.upenn.edu I J J  a b c d e f g h i j |D| Figure 1: 2D image registration using our framework. The rows show (J ) the moving images, (I ) fixed images, (J ψ ) warped moving images, (|D ψ |) Jacobian determinants of the transformation ψ, and (ψ) grid visualization of ψ respectively. The columns (b)(d)(f)(h)(j) incorporate a fixed boundary constraints while (a)(c)(e)(g)(i) do not. Abstract Deformable image registration, aiming to find spatial correspondence between a given image pair, is one of the most critical problems in the domain of medical image anal- ysis. In this paper, we present a generic, fast, and accurate diffeomorphic image registration framework that leverages 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 sys- tem whose trajectory determines the targeted deformation field. Compared with traditional optimization based meth- ods, our framework reduces the running time from tens of minutes to tens of seconds. Compared with recent data- driven deep learning methods, our framework is more ac- cessible since it does not require large amounts of training data. Our experiments show that the registration results of *Equal contribution. our method outperform the-state-of-arts under various met- rics, indicating that our modeling approach is well fitted for the task of deformable image registration. 1. Introduction Deformable image registration (DIR) is a well-studied problem in modern medical image analysis, because of its broad range of applications including normalization of pop- ulation studies, quantifying changes in longitudinal imag- ing, accounting for motions of organ, and as a building block of other image analysis algorithms. DIR is a pro- cess for establishing spatial correspondence between image pairs, and the term “deformable” points to the nonlinear and dense nature of the required transformation [21]. The wide range of applications of DIR have sparked developments in several directions. One body of work searches for a mapping/deformation field by optimizing a 1 arXiv:2108.03443v2 [cs.CV] 27 Aug 2021