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Deformable Image Registration (DIR) plays a significant role in quantifyingdeformation in medical data. Recent Deep Learning methods have shown promisingaccuracy and speedup for registering a pair of medical images. However, in 4D(3D + time) medical data, organ motion, such as respiratory motion and heartbeating, can not be effectively modeled by pair-wise methods as they wereoptimized for image pairs but did not consider the organ motion patternsnecessary when considering 4D data. This paper presents ORRN, an OrdinaryDifferential Equations (ODE)-based recursive image registration network. Ournetwork learns to estimate time-varying voxel velocities for an ODE that modelsdeformation in 4D image data. It adopts a recursive registration strategy toprogressively estimate a deformation field through ODE integration of voxelvelocities. We evaluate the proposed method on two publicly available lung 4DCTdatasets, DIRLab and CREATIS, for two tasks: 1) registering all images to theextreme inhale image for 3D+t deformation tracking and 2) registering extremeexhale to inhale phase images. Our method outperforms other learning-basedmethods in both tasks, producing the smallest Target Registration Error of1.24mm and 1.26mm, respectively. Additionally, it produces less than 0.001\%unrealistic image folding, and the computation speed is less than 1 second foreach CT volume. ORRN demonstrates promising registration accuracy, deformationplausibility, and computation efficiency on group-wise and pair-wiseregistration tasks. It has significant implications in enabling fast andaccurate respiratory motion estimation for treatment planning in radiationtherapy or robot motion planning in thoracic needle insertion.

ORRN: An ODE-based Recursive Registration Network for Deformable Respiratory Motion Estimation with Lung 4DCT Images