# VPREG: An Optimal Control Formulation for Diffeomorphic Image Registration Based on the Variational Principle Grid Generation Method

arXiv: https://arxiv.org/abs/2510.13109 · HTML: https://mlsanity.com/paper/2510.13109/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 74 references that are in the map.
- First posted on arXiv 15 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [SynthMorph: learning contrast-invariant registration without acquired images](https://mlsanity.com/paper/2004.10282/) (2020)
- [Learning a Probabilistic Model for Diffeomorphic Registration](https://mlsanity.com/paper/1812.07460/) (2018)
- [Accurate Point Cloud Registration with Robust Optimal Transport](https://mlsanity.com/paper/2111.00648/) (2021)
- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [A Lagrangian Gauss-Newton-Krylov Solver for Mass- and Intensity-Preserving Diffeomorphic Image Registration](https://mlsanity.com/paper/1703.04446/) (2017)
- [CLAIRE: A distributed-memory solver for constrained large deformation diffeomorphic image registration](https://mlsanity.com/paper/1808.04487/) (2018)
- [Metamorphic image registration using a semi-Lagrangian scheme](https://mlsanity.com/paper/2106.08817/) (2021)
- [An inexact Newton-Krylov algorithm for constrained diffeomorphic image registration](https://mlsanity.com/paper/1408.6299/) (2014)
- [Constrained H1-regularization schemes for diffeomorphic image registration](https://mlsanity.com/paper/1503.00757/) (2015)
- [Fast GPU 3D Diffeomorphic Image Registration](https://mlsanity.com/paper/2004.08893/) (2020)
- [A Semi-Lagrangian two-level preconditioned Newton-Krylov solver for constrained diffeomorphic image registration](https://mlsanity.com/paper/1604.02153/) (2016)
- [Distributed-memory large deformation diffeomorphic 3D image registration](https://mlsanity.com/paper/1608.03630/) (2016)
- [Multi-Node Multi-GPU Diffeomorphic Image Registration for Large-Scale Imaging Problems](https://mlsanity.com/paper/2008.12820/) (2020)
- [CLAIRE: Scalable GPU-Accelerated Algorithms for Diffeomorphic Image Registration in 3D](https://mlsanity.com/paper/2401.17493/) (2024)
- [Recent insights on the Uniqueness Problem of Diffeomorphisms determined by Prescribed Jacobian Determinant and Curl](https://mlsanity.com/paper/2207.13053/) (2022)

## Abstract (arXiv)

This paper introduces VPreg, a novel diffeomorphic image registration method. This work provides several improvements to our past work on mesh generation and diffeomorphic image registration. VPreg aims to achieve excellent registration accuracy while controlling the quality of the registration transformations. It ensures a positive Jacobian determinant of the spatial transformation and provides an accurate approximation of the inverse of the registration, a crucial property for many neuroimaging workflows. Unlike conventional methods, VPreg generates this inverse transformation within the group of diffeomorphisms rather than operating on the image space. The core of VPreg is a grid generation approach, referred to as Variational Principle (VP), which constructs non-folding grids with prescribed Jacobian determinant and curl. These VP-generated grids guarantee diffeomorphic spatial transformations essential for computational anatomy and morphometry, and provide a more accurate inverse than existing methods. To assess the potential of the proposed approach, we conduct a performance analysis for 150 registrations of brain scans from the OASIS-1 dataset. Performance evaluation based on Dice scores for 35 regions of interest, along with an empirical analysis of the properties of the computed spatial transformations, demonstrates that VPreg outperforms state-of-the-art methods in terms of Dice scores, regularity properties of the computed transformation, and accuracy and consistency of the provided inverse map. We compare our results to ANTs-SyN, Freesurfer-Easyreg, and FSL-Fnirt.