# Spatially-varying Regularization with Conditional Transformer for Unsupervised Image Registration

arXiv: https://arxiv.org/abs/2303.06168 · HTML: https://mlsanity.com/paper/2303.06168/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 10 Mar 2023.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [Learn2Reg: comprehensive multi-task medical image registration challenge, dataset and evaluation in the era of deep learning](https://mlsanity.com/paper/2112.04489/) (2021)
- [ViT-V-Net: Vision Transformer for Unsupervised Volumetric Medical Image Registration](https://mlsanity.com/paper/2104.06468/) (2021)
- [HyperMorph: Amortized Hyperparameter Learning for Image Registration](https://mlsanity.com/paper/2101.01035/) (2021)
- [CycleMorph: Cycle Consistent Unsupervised Deformable Image Registration](https://mlsanity.com/paper/2008.05772/) (2020)
- [End-to-End Unsupervised Deformable Image Registration with a Convolutional Neural Network](https://mlsanity.com/paper/1704.06065/) (2017)
- [Learning Conditional Deformable Templates with Convolutional Networks](https://mlsanity.com/paper/1908.02738/) (2019)
- [Conditional Deformable Image Registration with Convolutional Neural Network](https://mlsanity.com/paper/2106.12673/) (2021)
- [Fast 3D registration with accurate optimisation and little learning for Learn2Reg 2021](https://mlsanity.com/paper/2112.03053/) (2021)
- [Metric Learning for Image Registration](https://mlsanity.com/paper/1904.09524/) (2019)
- [Region-specific Diffeomorphic Metric Mapping](https://mlsanity.com/paper/1906.00139/) (2019)
- [On Finite Difference Jacobian Computation in Deformable Image Registration](https://mlsanity.com/paper/2212.06060/) (2022)
- [Coordinate Translator for Learning Deformable Medical Image Registration](https://mlsanity.com/paper/2203.03626/) (2022)

## 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)
- [Multimodal Diffeomorphic Registration with Neural ODEs and Structural Descriptors](https://mlsanity.com/paper/2512.22689/) (2025)
- [CT-Guided Spatially-varying Regularization for Voxel-Wise Deformable Whole-Body PET Registration](https://mlsanity.com/paper/2604.22905/) (2026)

## Abstract (arXiv)

In the past, optimization-based registration models have used spatially-varying regularization to account for deformation variations in different image regions. However, deep learning-based registration models have mostly relied on spatially-invariant regularization. Here, we introduce an end-to-end framework that uses neural networks to learn a spatially-varying deformation regularizer directly from data. The hyperparameter of the proposed regularizer is conditioned into the network, enabling easy tuning of the regularization strength. The proposed method is built upon a Transformer-based model, but it can be readily adapted to any network architecture. We thoroughly evaluated the proposed approach using publicly available datasets and observed a significant performance improvement while maintaining smooth deformation. The source code of this work will be made available after publication.