# Region-specific Diffeomorphic Metric Mapping

arXiv: https://arxiv.org/abs/1906.00139 · HTML: https://mlsanity.com/paper/1906.00139/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2019.

## Built on by (most cited first, 24 of 24)

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- [NODEO: A Neural Ordinary Differential Equation Based Optimization Framework for Deformable Image Registration](https://mlsanity.com/paper/2108.03443/) (2021)
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- [ICON: Learning Regular Maps Through Inverse Consistency](https://mlsanity.com/paper/2105.04459/) (2021)
- [Diffeomorphic Image Registration with Neural Velocity Field](https://mlsanity.com/paper/2202.12498/) (2022)
- [ResNet-LDDMM: Advancing the LDDMM Framework using Deep Residual Networks](https://mlsanity.com/paper/2102.07951/) (2021)
- [Light-weight Deformable Registration using Adversarial Learning with Distilling Knowledge](https://mlsanity.com/paper/2110.01293/) (2021)
- [Deep Learning for Medical Image Registration: A Comprehensive Review](https://mlsanity.com/paper/2204.11341/) (2022)
- [SITReg: Multi-resolution architecture for symmetric, inverse consistent, and topology preserving image registration](https://mlsanity.com/paper/2303.10211/) (2023)
- [CorticalFlow: A Diffeomorphic Mesh Deformation Module for Cortical Surface Reconstruction](https://mlsanity.com/paper/2206.02374/) (2022)
- [Bidirectional Recurrence for Cardiac Motion Tracking with Gaussian Process Latent Coding](https://mlsanity.com/paper/2410.20752/) (2024)
- [Fluid registration between lung CT and stationary chest tomosynthesis images](https://mlsanity.com/paper/2203.04958/) (2022)
- [Uncertainty quantification in non-rigid image registration via stochastic gradient Markov chain Monte Carlo](https://mlsanity.com/paper/2110.13289/) (2021)
- [Spatially-varying Regularization with Conditional Transformer for Unsupervised Image Registration](https://mlsanity.com/paper/2303.06168/) (2023)
- [Towards Saner Deep Image Registration](https://mlsanity.com/paper/2307.09696/) (2023)
- [Unsupervised learning of spatially varying regularization for diffeomorphic image registration](https://mlsanity.com/paper/2412.17982/) (2024)
- [On-the-Fly Guidance Training for Medical Image Registration](https://mlsanity.com/paper/2308.15216/) (2023)
- [MRUCT: Mixed Reality Assistance for Acupuncture Guided by Ultrasonic Computed Tomography](https://mlsanity.com/paper/2502.08786/) (2025)
- [Dyna3DGR: 4D Cardiac Motion Tracking with Dynamic 3D Gaussian Representation](https://mlsanity.com/paper/2507.16608/) (2025)
- [Moment evolution equations and moment matching for stochastic image EPDiff](https://mlsanity.com/paper/2110.03337/) (2021)
- [SearchMorph:Multi-scale Correlation Iterative Network for Deformable Registration](https://mlsanity.com/paper/2206.13076/) (2022)
- [CT-Guided Spatially-varying Regularization for Voxel-Wise Deformable Whole-Body PET Registration](https://mlsanity.com/paper/2604.22905/) (2026)

## Abstract (arXiv)

We introduce a region-specific diffeomorphic metric mapping (RDMM) registration approach. RDMM is non-parametric, estimating spatio-temporal velocity fields which parameterize the sought-for spatial transformation. Regularization of these velocity fields is necessary. However, while existing non-parametric registration approaches, e.g., the large displacement diffeomorphic metric mapping (LDDMM) model, use a fixed spatially-invariant regularization our model advects a spatially-varying regularizer with the estimated velocity field, thereby naturally attaching a spatio-temporal regularizer to deforming objects. We explore a family of RDMM registration approaches: 1) a registration model where regions with separate regularizations are pre-defined (e.g., in an atlas space), 2) a registration model where a general spatially-varying regularizer is estimated, and 3) a registration model where the spatially-varying regularizer is obtained via an end-to-end trained deep learning (DL) model. We provide a variational derivation of RDMM, show that the model can assure diffeomorphic transformations in the continuum, and that LDDMM is a particular instance of RDMM. To evaluate RDMM performance we experiment 1) on synthetic 2D data and 2) on two 3D datasets: knee magnetic resonance images (MRIs) of the Osteoarthritis Initiative (OAI) and computed tomography images (CT) of the lung. Results show that our framework achieves state-of-the-art image registration performance, while providing additional information via a learned spatio-temoporal regularizer. Further, our deep learning approach allows for very fast RDMM and LDDMM estimations. Our code will be open-sourced. Code is available at https://github.com/uncbiag/registration.