# Robust deformable image registration using cycle-consistent implicit representations

arXiv: https://arxiv.org/abs/2310.01934 · HTML: https://mlsanity.com/paper/2310.01934/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [A Deep Learning Framework for Unsupervised Affine and Deformable Image Registration](https://mlsanity.com/paper/1809.06130/) (2018)
- [Learn2Reg: comprehensive multi-task medical image registration challenge, dataset and evaluation in the era of deep learning](https://mlsanity.com/paper/2112.04489/) (2021)
- [Deep Learning in Medical Image Registration: A Survey](https://mlsanity.com/paper/1903.02026/) (2019)
- [CycleMorph: Cycle Consistent Unsupervised Deformable Image Registration](https://mlsanity.com/paper/2008.05772/) (2020)
- [CNN-based Lung CT Registration with Multiple Anatomical Constraints](https://mlsanity.com/paper/2011.14372/) (2020)
- [Estimation of Large Motion in Lung CT by Integrating Regularized Keypoint Correspondences into Dense Deformable Registration](https://mlsanity.com/paper/1807.00467/) (2018)
- [Unsupervised Deformable Image Registration Using Cycle-Consistent CNN](https://mlsanity.com/paper/1907.01319/) (2019)
- [Test-Time Training for Deformable Multi-Scale Image Registration](https://mlsanity.com/paper/2103.13578/) (2021)
- [Meta-Registration: Learning Test-Time Optimization for Single-Pair Image Registration](https://mlsanity.com/paper/2207.10996/) (2022)

## Built on by (most cited first, 13 of 13)

- [CPT-Interp: Continuous sPatial and Temporal Motion Modeling for 4D Medical Image Interpolation](https://mlsanity.com/paper/2405.15385/) (2024)
- [Neural Fields for Continuous Periodic Motion Estimation in 4D Cardiovascular Imaging](https://mlsanity.com/paper/2407.20728/) (2024)
- [Capturing Longitudinal Changes in Brain Morphology Using Temporally Parameterized Neural Displacement Fields](https://mlsanity.com/paper/2504.09514/) (2025)
- [Deformable Image Registration with Stochastically Regularized Biomechanical Equilibrium](https://mlsanity.com/paper/2312.14987/) (2023)
- [Gaussian Primitives for Deformable Image Registration](https://mlsanity.com/paper/2406.03394/) (2024)
- [ST-NeRP: Spatial-Temporal Neural Representation Learning with Prior Embedding for Patient-specific Imaging Study](https://mlsanity.com/paper/2410.19283/) (2024)
- [VoxelOpt: Voxel-Adaptive Message Passing for Discrete Optimization in Deformable Abdominal CT Registration](https://mlsanity.com/paper/2506.19975/) (2025)
- [Implicit Neural Representations for Registration of Left Ventricle Myocardium During a Cardiac Cycle](https://mlsanity.com/paper/2501.07248/) (2025)
- [Neural Graphics Primitives-based Deformable Image Registration for On-the-fly Motion Extraction](https://mlsanity.com/paper/2402.05568/) (2024)
- [CPT-4DMR: Continuous sPatial-Temporal Representation for 4D-MRI Reconstruction](https://mlsanity.com/paper/2509.18427/) (2025)
- [Deformable Medical Image Registration with KAN-based Implicit Neural Representations](https://mlsanity.com/paper/2509.22874/) (2025)
- [MGRegBench: A Novel Benchmark Dataset with Anatomical Landmarks for Mammography Image Registration](https://mlsanity.com/paper/2512.17605/) (2025)
- [Don't Mind the Gaps: Implicit Neural Representations for Resolution-Agnostic Retinal OCT Analysis](https://mlsanity.com/paper/2601.02447/) (2026)

## Abstract (arXiv)

Recent works in medical image registration have proposed the use of Implicit Neural Representations, demonstrating performance that rivals state-of-the-art learning-based methods. However, these implicit representations need to be optimized for each new image pair, which is a stochastic process that may fail to converge to a global minimum. To improve robustness, we propose a deformable registration method using pairs of cycle-consistent Implicit Neural Representations: each implicit representation is linked to a second implicit representation that estimates the opposite transformation, causing each network to act as a regularizer for its paired opposite. During inference, we generate multiple deformation estimates by numerically inverting the paired backward transformation and evaluating the consensus of the optimized pair. This consensus improves registration accuracy over using a single representation and results in a robust uncertainty metric that can be used for automatic quality control. We evaluate our method with a 4D lung CT dataset. The proposed cycle-consistent optimization method reduces the optimization failure rate from 2.4% to 0.0% compared to the current state-of-the-art. The proposed inference method improves landmark accuracy by 4.5% and the proposed uncertainty metric detects all instances where the registration method fails to converge to a correct solution. We verify the generalizability of these results to other data using a centerline propagation task in abdominal 4D MRI, where our method achieves a 46% improvement in propagation consistency compared with single-INR registration and demonstrates a strong correlation between the proposed uncertainty metric and registration accuracy.