# textttGradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency

arXiv: https://arxiv.org/abs/2206.05897 · HTML: https://mlsanity.com/paper/2206.05897/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 72 references that are in the map.
- First posted on arXiv 13 Jun 2022.

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

- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [Unsupervised Monocular Depth Estimation with Left-Right Consistency](https://mlsanity.com/paper/1609.03677/) (2016)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [GeoNet: Unsupervised Learning of Dense Depth, Optical Flow and Camera Pose](https://mlsanity.com/paper/1803.02276/) (2018)
- [FlowFormer: A Transformer Architecture for Optical Flow](https://mlsanity.com/paper/2203.16194/) (2022)
- [Learning Correspondence from the Cycle-Consistency of Time](https://mlsanity.com/paper/1903.07593/) (2019)
- [A Deep Learning Framework for Unsupervised Affine and Deformable Image Registration](https://mlsanity.com/paper/1809.06130/) (2018)
- [SynthMorph: learning contrast-invariant registration without acquired images](https://mlsanity.com/paper/2004.10282/) (2020)
- [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach](https://mlsanity.com/paper/1703.10908/) (2017)
- [Recursive Cascaded Networks for Unsupervised Medical Image Registration](https://mlsanity.com/paper/1907.12353/) (2019)
- [Networks for Joint Affine and Non-parametric Image Registration](https://mlsanity.com/paper/1903.08811/) (2019)
- [Accurate Point Cloud Registration with Robust Optimal Transport](https://mlsanity.com/paper/2111.00648/) (2021)
- [Learning Pixel Trajectories with Multiscale Contrastive Random Walks](https://mlsanity.com/paper/2201.08379/) (2022)
- [CNN-based Lung CT Registration with Multiple Anatomical Constraints](https://mlsanity.com/paper/2011.14372/) (2020)
- [ICON: Learning Regular Maps Through Inverse Consistency](https://mlsanity.com/paper/2105.04459/) (2021)
- [mlVIRNET: Multilevel Variational Image Registration Network](https://mlsanity.com/paper/1909.10084/) (2019)
- [Constrained H1-regularization schemes for diffeomorphic image registration](https://mlsanity.com/paper/1503.00757/) (2015)
- [Recursive Refinement Network for Deformable Lung Registration between Exhale and Inhale CT Scans](https://mlsanity.com/paper/2106.07608/) (2021)

## Built on by (most cited first, 30 of 41)

- [uniGradICON: A Foundation Model for Medical Image Registration](https://mlsanity.com/paper/2403.05780/) (2024)
- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [Deep Learning in Medical Image Registration: Magic or Mirage?](https://mlsanity.com/paper/2408.05839/) (2024)
- [multiGradICON: A Foundation Model for Multimodal Medical Image Registration](https://mlsanity.com/paper/2408.00221/) (2024)
- [SAMConvex: Fast Discrete Optimization for CT Registration using Self-supervised Anatomical Embedding and Correlation Pyramid](https://mlsanity.com/paper/2307.09727/) (2023)
- [Inverse Consistency by Construction for Multistep Deep Registration](https://mlsanity.com/paper/2305.00087/) (2023)
- [LesionLocator: Zero-Shot Universal Tumor Segmentation and Tracking in 3D Whole-Body Imaging](https://mlsanity.com/paper/2502.20985/) (2025)
- [Beyond the LUMIR challenge: The pathway to foundational registration models](https://mlsanity.com/paper/2505.24160/) (2025)
- [SAME++: A Self-supervised Anatomical eMbeddings Enhanced medical image registration framework using stable sampling and regularized transformation](https://mlsanity.com/paper/2311.14986/) (2023)
- [textttNePhi: Neural Deformation Fields for Approximately Diffeomorphic Medical Image Registration](https://mlsanity.com/paper/2309.07322/) (2023)
- [NAISR: A 3D Neural Additive Model for Interpretable Shape Representation](https://mlsanity.com/paper/2303.09234/) (2023)
- [Improving Generalization of Medical Image Registration Foundation Model](https://mlsanity.com/paper/2505.06527/) (2025)
- [Exploring Cycle Consistency Learning in Interactive Volume Segmentation](https://mlsanity.com/paper/2303.06493/) (2023)
- [EfficientMorph: Parameter-Efficient Transformer-Based Architecture for 3D Image Registration](https://mlsanity.com/paper/2403.11026/) (2024)
- [TimeFlow: Temporal Conditioning for Longitudinal Brain MRI Registration and Aging Analysis](https://mlsanity.com/paper/2501.08667/) (2025)
- [Gaussian Primitives for Deformable Image Registration](https://mlsanity.com/paper/2406.03394/) (2024)
- [SAMReg: SAM-enabled Image Registration with ROI-based Correspondence](https://mlsanity.com/paper/2410.14083/) (2024)
- [SACB-Net: Spatial-awareness Convolutions for Medical Image Registration](https://mlsanity.com/paper/2503.19592/) (2025)
- [Self-supervised Landmark Learning with Deformation Reconstruction and Cross-subject Consistency Objectives](https://mlsanity.com/paper/2308.04987/) (2023)
- [CARL: A Framework for Equivariant Image Registration](https://mlsanity.com/paper/2405.16738/) (2024)
- [Improving Instance Optimization in Deformable Image Registration with Gradient Projection](https://mlsanity.com/paper/2410.15767/) (2024)
- [LEDA: Log-Euclidean Diffeomorphism Autoencoder for Efficient Statistical Analysis of Diffeomorphisms](https://mlsanity.com/paper/2412.16129/) (2024)
- [Mono-Modalizing Extremely Heterogeneous Multi-Modal Medical Image Registration](https://mlsanity.com/paper/2506.15596/) (2025)
- [Community-Level Modeling of Gyral Folding Patterns for Robust and Anatomically Informed Individualized Brain Mapping](https://mlsanity.com/paper/2602.01482/) (2026)
- [NOIR: Neural Operator mapping for Implicit Representations](https://mlsanity.com/paper/2603.13118/) (2026)
- [Stop Holding Your Breath: CT-Informed Gaussian Splatting for Dynamic Bronchoscopy](https://mlsanity.com/paper/2604.28179/) (2026)
- [A Self-Supervised Image Registration Approach for Measuring Local Response Patterns in Metastatic Ovarian Cancer](https://mlsanity.com/paper/2407.17114/) (2024)
- [MORPH-LER: Log-Euclidean Regularization for Population-Aware Image Registration](https://mlsanity.com/paper/2502.02029/) (2025)
- [Reference-Free 3D Reconstruction of Brain Dissection Slabs via Learned Atlas Coordinates](https://mlsanity.com/paper/2503.09963/) (2025)
- [Downstream Analysis of Foundational Medical Vision Models for Disease Progression](https://mlsanity.com/paper/2503.16842/) (2025)

## Abstract (arXiv)

We present an approach to learning regular spatial transformations between image pairs in the context of medical image registration. Contrary to optimization-based registration techniques and many modern learning-based methods, we do not directly penalize transformation irregularities but instead promote transformation regularity via an inverse consistency penalty. We use a neural network to predict a map between a source and a target image as well as the map when swapping the source and target images. Different from existing approaches, we compose these two resulting maps and regularize deviations of the bfJacobian of this composition from the identity matrix. This regularizer -- textttGradICON -- results in much better convergence when training registration models compared to promoting inverse consistency of the composition of maps directly while retaining the desirable implicit regularization effects of the latter. We achieve state-of-the-art registration performance on a variety of real-world medical image datasets using a single set of hyperparameters and a single non-dataset-specific training protocol.