# Unsupervised Deformable Image Registration with Structural Nonparametric Smoothing

arXiv: https://arxiv.org/abs/2506.10813 · HTML: https://mlsanity.com/paper/2506.10813/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 80 references that are in the map.
- First posted on arXiv 12 Jun 2025.

## Builds on (most cited first, 30 of 49)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [LoFTR: Detector-Free Local Feature Matching with Transformers](https://mlsanity.com/paper/2104.00680/) (2021)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [LightGlue: Local Feature Matching at Light Speed](https://mlsanity.com/paper/2306.13643/) (2023)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [RepVGG: Making VGG-style ConvNets Great Again](https://mlsanity.com/paper/2101.03697/) (2021)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [DISK: Learning local features with policy gradient](https://mlsanity.com/paper/2006.13566/) (2020)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [DKM: Dense Kernelized Feature Matching for Geometry Estimation](https://mlsanity.com/paper/2202.00667/) (2022)
- [ASpanFormer: Detector-Free Image Matching with Adaptive Span Transformer](https://mlsanity.com/paper/2208.14201/) (2022)
- [Large Deformation Diffeomorphic Image Registration with Laplacian Pyramid Networks](https://mlsanity.com/paper/2006.16148/) (2020)
- [Anti-Oversmoothing in Deep Vision Transformers via the Fourier Domain Analysis: From Theory to Practice](https://mlsanity.com/paper/2203.05962/) (2022)
- [XFeat: Accelerated Features for Lightweight Image Matching](https://mlsanity.com/paper/2404.19174/) (2024)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [HyperMorph: Amortized Hyperparameter Learning for Image Registration](https://mlsanity.com/paper/2101.01035/) (2021)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Conditional Deformable Image Registration with Convolutional Neural Network](https://mlsanity.com/paper/2106.12673/) (2021)
- [SiLK -- Simple Learned Keypoints](https://mlsanity.com/paper/2304.06194/) (2023)
- [XMorpher: Full Transformer for Deformable Medical Image Registration via Cross Attention](https://mlsanity.com/paper/2206.07349/) (2022)
- [Closing the Gap between Deep and Conventional Image Registration using Probabilistic Dense Displacement Networks](https://mlsanity.com/paper/1907.10931/) (2019)

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

- [Encoder-Only Image Registration](https://mlsanity.com/paper/2509.00451/) (2025)
- [VoxelOpt: Voxel-Adaptive Message Passing for Discrete Optimization in Deformable Abdominal CT Registration](https://mlsanity.com/paper/2506.19975/) (2025)
- [Gaussian Primitive Optimized Deformable Retinal Image Registration](https://mlsanity.com/paper/2508.16852/) (2025)

## Abstract (arXiv)

Learning-based deformable image registration (DIR) accelerates alignment by amortizing traditional optimization via neural networks. Label supervision further enhances accuracy, enabling efficient and precise nonlinear alignment of unseen scans. However, images with sparse features amid large smooth regions, such as retinal vessels, introduce aperture and large-displacement challenges that unsupervised DIR methods struggle to address. This limitation occurs because neural networks predict deformation fields in a single forward pass, leaving fields unconstrained post-training and shifting the regularization burden entirely to network weights. To address these issues, we introduce SmoothProper, a plug-and-play neural module enforcing smoothness and promoting message passing within the network's forward pass. By integrating a duality-based optimization layer with tailored interaction terms, SmoothProper efficiently propagates flow signals across spatial locations, enforces smoothness, and preserves structural consistency. It is model-agnostic, seamlessly integrates into existing registration frameworks with minimal parameter overhead, and eliminates regularizer hyperparameter tuning. Preliminary results on a retinal vessel dataset exhibiting aperture and large-displacement challenges demonstrate our method reduces registration error to 1.88 pixels on 2912x2912 images, marking the first unsupervised DIR approach to effectively address both challenges. The source code will be available at https://github.com/tinymilky/SmoothProper.