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

arXiv: https://arxiv.org/abs/2305.14673 · HTML: https://mlsanity.com/paper/2305.14673/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 60 references that are in the map.
- First posted on arXiv 24 May 2023.

## Builds on (most cited first, 23 of 23)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [TorchIO: A Python library for efficient loading, preprocessing, augmentation and patch-based sampling of medical images in deep learning](https://mlsanity.com/paper/2003.04696/) (2020)
- [Delving Deeper into Convolutional Networks for Learning Video Representations](https://mlsanity.com/paper/1511.06432/) (2015)
- [What Matters in Unsupervised Optical Flow](https://mlsanity.com/paper/2006.04902/) (2020)
- [Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks](https://mlsanity.com/paper/2003.09514/) (2020)
- [Recursive Cascaded Networks for Unsupervised Medical Image Registration](https://mlsanity.com/paper/1907.12353/) (2019)
- [Deep Learning in Medical Image Registration: A Review](https://mlsanity.com/paper/1912.12318/) (2019)
- [NODEO: A Neural Ordinary Differential Equation Based Optimization Framework for Deformable Image Registration](https://mlsanity.com/paper/2108.03443/) (2021)
- [CNN-based Lung CT Registration with Multiple Anatomical Constraints](https://mlsanity.com/paper/2011.14372/) (2020)
- [mlVIRNET: Multilevel Variational Image Registration Network](https://mlsanity.com/paper/1909.10084/) (2019)
- [One Shot Learning for Deformable Medical Image Registration and Periodic Motion Tracking](https://mlsanity.com/paper/1907.04641/) (2019)
- [Multi-scale Neural ODEs for 3D Medical Image Registration](https://mlsanity.com/paper/2106.08493/) (2021)
- [3D Convolutional Neural Networks Image Registration Based on Efficient Supervised Learning from Artificial Deformations](https://mlsanity.com/paper/1908.10235/) (2019)
- [GroupRegNet: A Groupwise One-shot Deep Learning-based 4D Image Registration Method](https://mlsanity.com/paper/2009.02613/) (2020)
- [Recurrent Registration Neural Networks for Deformable Image Registration](https://mlsanity.com/paper/1906.09988/) (2019)
- [Real-to-Sim Registration of Deformable Soft Tissue with Position-Based Dynamics for Surgical Robot Autonomy](https://mlsanity.com/paper/2011.00800/) (2020)
- [Recursive Deformable Image Registration Network with Mutual Attention](https://mlsanity.com/paper/2206.01863/) (2022)
- [Model-Predictive Control of Blood Suction for Surgical Hemostasis using Differentiable Fluid Simulations](https://mlsanity.com/paper/2102.01436/) (2021)
- [Recursive Refinement Network for Deformable Lung Registration between Exhale and Inhale CT Scans](https://mlsanity.com/paper/2106.07608/) (2021)
- [CRANE: a 10 Degree-of-Freedom, Tele-surgical System for Dexterous Manipulation within Imaging Bores](https://mlsanity.com/paper/2109.13407/) (2021)

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

- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [CPT-Interp: Continuous sPatial and Temporal Motion Modeling for 4D Medical Image Interpolation](https://mlsanity.com/paper/2405.15385/) (2024)
- [Continuous sPatial-Temporal Deformable Image Registration (CPT-DIR) for motion modelling in radiotherapy: beyond classic voxel-based methods](https://mlsanity.com/paper/2405.00430/) (2024)

## Abstract (arXiv)

Deformable Image Registration (DIR) plays a significant role in quantifying deformation in medical data. Recent Deep Learning methods have shown promising accuracy and speedup for registering a pair of medical images. However, in 4D (3D + time) medical data, organ motion, such as respiratory motion and heart beating, can not be effectively modeled by pair-wise methods as they were optimized for image pairs but did not consider the organ motion patterns necessary when considering 4D data. This paper presents ORRN, an Ordinary Differential Equations (ODE)-based recursive image registration network. Our network learns to estimate time-varying voxel velocities for an ODE that models deformation in 4D image data. It adopts a recursive registration strategy to progressively estimate a deformation field through ODE integration of voxel velocities. We evaluate the proposed method on two publicly available lung 4DCT datasets, DIRLab and CREATIS, for two tasks: 1) registering all images to the extreme inhale image for 3D+t deformation tracking and 2) registering extreme exhale to inhale phase images. Our method outperforms other learning-based methods in both tasks, producing the smallest Target Registration Error of 1.24mm and 1.26mm, respectively. Additionally, it produces less than 0.001% unrealistic image folding, and the computation speed is less than 1 second for each CT volume. ORRN demonstrates promising registration accuracy, deformation plausibility, and computation efficiency on group-wise and pair-wise registration tasks. It has significant implications in enabling fast and accurate respiratory motion estimation for treatment planning in radiation therapy or robot motion planning in thoracic needle insertion.