# Inverse Consistency by Construction for Multistep Deep Registration

arXiv: https://arxiv.org/abs/2305.00087 · HTML: https://mlsanity.com/paper/2305.00087/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 10 of 10)

- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (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)
- [Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks](https://mlsanity.com/paper/2003.09514/) (2020)
- [Networks for Joint Affine and Non-parametric Image Registration](https://mlsanity.com/paper/1903.08811/) (2019)
- [textttGradICON: Approximate Diffeomorphisms via Gradient Inverse Consistency](https://mlsanity.com/paper/2206.05897/) (2022)
- [Learning the Effect of Registration Hyperparameters with HyperMorph](https://mlsanity.com/paper/2203.16680/) (2022)
- [Inverse-Consistent Deep Networks for Unsupervised Deformable Image Registration](https://mlsanity.com/paper/1809.03443/) (2018)
- [ICON: Learning Regular Maps Through Inverse Consistency](https://mlsanity.com/paper/2105.04459/) (2021)
- [A Multiple Decoder CNN for Inverse Consistent 3D Image Registration](https://mlsanity.com/paper/2002.06468/) (2020)

## Built on by (most cited first, 12 of 12)

- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [Beyond the LUMIR challenge: The pathway to foundational registration models](https://mlsanity.com/paper/2505.24160/) (2025)
- [Guiding Registration with Emergent Similarity from Pre-Trained Diffusion Models](https://mlsanity.com/paper/2506.02419/) (2025)
- [Disentangling Progress in Medical Image Registration: Beyond Trend-Driven Architectures towards Domain-Specific Strategies](https://mlsanity.com/paper/2512.01913/) (2025)
- [Gaussian Primitives for Deformable Image Registration](https://mlsanity.com/paper/2406.03394/) (2024)
- [Deformation-aware GAN for Medical Image Synthesis with Substantially Misaligned Pairs](https://mlsanity.com/paper/2408.09432/) (2024)
- [CARL: A Framework for Equivariant Image Registration](https://mlsanity.com/paper/2405.16738/) (2024)
- [PointVoxelFormer -- Reviving point cloud networks for 3D medical imaging](https://mlsanity.com/paper/2412.17390/) (2024)
- [Reliability-Aware CT-MRI Registration: A Quality Engineering Framework with Stability Analysis and Risk Classification](https://mlsanity.com/paper/2607.02585/) (2026)
- [Downstream Analysis of Foundational Medical Vision Models for Disease Progression](https://mlsanity.com/paper/2503.16842/) (2025)
- [OncoReg: Medical Image Registration for Oncological Challenges](https://mlsanity.com/paper/2503.23179/) (2025)
- [Biomechanical Constraints Assimilation in Deep-Learning Image Registration: Application to sliding and locally rigid deformations](https://mlsanity.com/paper/2504.05444/) (2025)

## Abstract (arXiv)

Inverse consistency is a desirable property for image registration. We propose a simple technique to make a neural registration network inverse consistent by construction, as a consequence of its structure, as long as it parameterizes its output transform by a Lie group. We extend this technique to multi-step neural registration by composing many such networks in a way that preserves inverse consistency. This multi-step approach also allows for inverse-consistent coarse to fine registration. We evaluate our technique on synthetic 2-D data and four 3-D medical image registration tasks and obtain excellent registration accuracy while assuring inverse consistency.