Beyond the LUMIR challenge: The pathway to foundational registration models

Medical image challenges have played a transformative role in advancing the field, catalyzing algorithmic innovation and establishing new performance standards across diverse clinical applications. Image registration, a foundational task in neuroimaging pipelines, has similarly benefited from the Learn2Reg initiative. Building on this foundation, we introduce the Large-scale Unsupervised Brain MRI Image Registration (LUMIR) challenge, a next-generation benchmark designed to assess and advance unsupervised brain MRI registration. Distinct from prior challenges that leveraged anatomical label maps for supervision, LUMIR removes this dependency by providing over 4,000 preprocessed T1-weighted brain MRIs for training without any label maps, encouraging biologically plausible deformation modeling through self-supervision. In addition to evaluating performance on 590 held-out test subjects, LUMIR introduces a rigorous suite of zero-shot generalization tasks, spanning out-of-domain imaging modalities (e.g., FLAIR, T2-weighted, T2*-weighted), disease populations (e.g., Alzheimer's disease), acquisition protocols (e.g., 9.4T MRI), and species (e.g., macaque brains). A total of 1,158 subjects and over 4,000 image pairs were included for evaluation. Performance was assessed using both segmentation-based metrics (Dice coefficient, 95th percentile Hausdorff distance) and landmark-based registration accuracy (target registration error). Across both in-domain and zero-shot tasks, deep learning-based methods consistently achieved state-of-the-art accuracy while producing anatomically plausible deformation fields. The top-performing deep learning-based models demonstrated diffeomorphic properties and inverse consistency, outperforming several leading optimization-based methods, and showing strong robustness to most domain shifts, the exception being a drop in performance on out-of-domain contrasts.

MORPH-LER: Log-Euclidean Regularization for Population-Aware Image Registration

Spatial transformations that capture population-level morphological statistics are critical for medical image analysis. Commonly used smoothness regularizers for image registration fail to integrate population statistics, leading to anatomically inconsistent transformations. Inverse consistency regularizers promote geometric consistency but lack population morphometrics integration. Regularizers that constrain deformation to low-dimensional manifold methods address this. However, they prioritize reconstruction over interpretability and neglect diffeomorphic properties, such as group composition and inverse consistency. We introduce MORPH-LER, a Log-Euclidean regularization framework for population-aware unsupervised image registration. MORPH-LER learns population morphometrics from spatial transformations to guide and regularize registration networks, ensuring anatomically plausible deformations. It features a bottleneck autoencoder that computes the principal logarithm of deformation fields via iterative square-root predictions. It creates a linearized latent space that respects diffeomorphic properties and enforces inverse consistency. By integrating a registration network with a diffeomorphic autoencoder, MORPH-LER produces smooth, meaningful deformation fields. The framework offers two main contributions: (1) a data-driven regularization strategy that incorporates population-level anatomical statistics to enhance transformation validity and (2) a linearized latent space that enables compact and interpretable deformation fields for efficient population morphometrics analysis. We validate MORPH-LER across two families of deep learning-based registration networks, demonstrating its ability to produce anatomically accurate, computationally efficient, and statistically meaningful transformations on the OASIS-1 brain imaging dataset.

A Symmetric Dynamic Learning Framework for Diffeomorphic Medical Image Registration

Diffeomorphic image registration is crucial for various medical imaging applications because it can preserve the topology of the transformation. This study introduces DCCNN-LSTM-Reg, a learning framework that evolves dynamically and learns a symmetrical registration path by satisfying a specified control increment system. This framework aims to obtain symmetric diffeomorphic deformations between moving and fixed images. To achieve this, we combine deep learning networks with diffeomorphic mathematical mechanisms to create a continuous and dynamic registration architecture, which consists of multiple Symmetric Registration (SR) modules cascaded on five different scales. Specifically, our method first uses two U-nets with shared parameters to extract multiscale feature pyramids from the images. We then develop an SR-module comprising a sequential CNN-LSTM architecture to progressively correct the forward and reverse multiscale deformation fields using control increment learning and the homotopy continuation technique. Through extensive experiments on three 3D registration tasks, we demonstrate that our method outperforms existing approaches in both quantitative and qualitative evaluations.

A Steerable Deep Network for Model-Free Diffusion MRI Registration

Nonrigid registration is vital to medical image analysis but remains challenging for diffusion MRI (dMRI) due to its high-dimensional, orientation-dependent nature. While classical methods are accurate, they are computationally demanding, and deep neural networks, though efficient, have been underexplored for nonrigid dMRI registration compared to structural imaging. We present a novel, deep learning framework for model-free, nonrigid registration of raw diffusion MRI data that does not require explicit reorientation. Unlike previous methods relying on derived representations such as diffusion tensors or fiber orientation distribution functions, in our approach, we formulate the registration as an equivariant diffeomorphism of position-and-orientation space. Central to our method is an $\mathsf{SE}(3)$-equivariant UNet that generates velocity fields while preserving the geometric properties of a raw dMRI's domain. We introduce a new loss function based on the maximum mean discrepancy in Fourier space, implicitly matching ensemble average propagators across images. Experimental results on Human Connectome Project dMRI data demonstrate competitive performance compared to state-of-the-art approaches, with the added advantage of bypassing the overhead for estimating derived representations. This work establishes a foundation for data-driven, geometry-aware dMRI registration directly in the acquisition space.

Bidirectional Recurrence for Cardiac Motion Tracking with Gaussian Process Latent Coding

Quantitative analysis of cardiac motion is crucial for assessing cardiac function. This analysis typically uses imaging modalities such as MRI and Echocardiograms that capture detailed image sequences throughout the heartbeat cycle. Previous methods predominantly focused on the analysis of image pairs lacking consideration of the motion dynamics and spatial variability. Consequently, these methods often overlook the long-term relationships and regional motion characteristic of cardiac. To overcome these limitations, we introduce the \textbf{GPTrack}, a novel unsupervised framework crafted to fully explore the temporal and spatial dynamics of cardiac motion. The GPTrack enhances motion tracking by employing the sequential Gaussian Process in the latent space and encoding statistics by spatial information at each time stamp, which robustly promotes temporal consistency and spatial variability of cardiac dynamics. Also, we innovatively aggregate sequential information in a bidirectional recursive manner, mimicking the behavior of diffeomorphic registration to better capture consistent long-term relationships of motions across cardiac regions such as the ventricles and atria. Our GPTrack significantly improves the precision of motion tracking in both 3D and 4D medical images while maintaining computational efficiency. The code is available at: https://github.com/xmed-lab/GPTrack

Learning Diffeomorphism for Image Registration with Time-Continuous Networks using Semigroup Regularization

Diffeomorphic image registration (DIR) is a critical task in 3D medical image analysis, aimed at finding topology preserving deformations between pairs of images. Focusing on the solution of the flow map differential equation as the diffeomorphic deformation, recent methods use discrete timesteps along with various regularization terms to penalize the negative determinant of Jacobian and impose smoothness of the solution vector field. In this paper, we propose a novel learning-based approach for diffeomorphic 3D-image registration which finds the diffeomorphisms in the time continuum with fewer regularization terms and no additional integration. As one of the fundamental properties of flow maps, we exploit the semigroup property as the only form of regularization, ensuring temporally continuous diffeomorphic flows between pairs of images. Leveraging this property, our method alleviates the need for additional regularization terms and scaling and squaring integration during both training and evaluation. To achieve time-continuous diffeomorphisms, we employ time-embedded UNets, a technique commonly utilized in diffusion models. The proposed method reveals that ensuring diffeomorphism in a continuous time interval leads to better registration results. Experimental results on two public datasets (OASIS and CANDI) demonstrate the superiority of our model over both learning-based and optimization-based methods.

$\texttt{NePhi}$: Neural Deformation Fields for Approximately Diffeomorphic Medical Image Registration

This work proposes $\texttt{NePhi}$, a neural deformation model which results in approximately diffeomorphic transformations. In contrast to the predominant voxel-based approaches, $\texttt{NePhi}$ represents deformations functionally which allows for memory-efficient training and inference. This is of particular importance for large volumetric registrations. Further, while medical image registration approaches representing transformation maps via multi-layer perceptrons have been proposed, $\texttt{NePhi}$ facilitates both pairwise optimization-based registration $\textit{as well as}$ learning-based registration via predicted or optimized global and local latent codes. Lastly, as deformation regularity is a highly desirable property for most medical image registration tasks, $\texttt{NePhi}$ makes use of gradient inverse consistency regularization which empirically results in approximately diffeomorphic transformations. We show the performance of $\texttt{NePhi}$ on two 2D synthetic datasets as well as on real 3D lung registration. Our results show that $\texttt{NePhi}$ can achieve similar accuracies as voxel-based representations in a single-resolution registration setting while using less memory and allowing for faster instance-optimization.

Decoder-Only Image Registration

In unsupervised medical image registration, the predominant approaches involve the utilization of a encoder-decoder network architecture, allowing for precise prediction of dense, full-resolution displacement fields from given paired images. Despite its widespread use in the literature, we argue for the necessity of making both the encoder and decoder learnable in such an architecture. For this, we propose a novel network architecture, termed LessNet in this paper, which contains only a learnable decoder, while entirely omitting the utilization of a learnable encoder. LessNet substitutes the learnable encoder with simple, handcrafted features, eliminating the need to learn (optimize) network parameters in the encoder altogether. Consequently, this leads to a compact, efficient, and decoder-only architecture for 3D medical image registration. Evaluated on two publicly available brain MRI datasets, we demonstrate that our decoder-only LessNet can effectively and efficiently learn both dense displacement and diffeomorphic deformation fields in 3D. Furthermore, our decoder-only LessNet can achieve comparable registration performance to state-of-the-art methods such as VoxelMorph and TransMorph, while requiring significantly fewer computational resources. Our code and pre-trained models are available at https://github.com/xi-jia/LessNet.

INR-LDDMM: Fluid-based Medical Image Registration Integrating Implicit Neural Representation and Large Deformation Diffeomorphic Metric Mapping

We propose a flow-based registration framework of medical images based on implicit neural representation. By integrating implicit neural representation and Large Deformable Diffeomorphic Metric Mapping (LDDMM), we employ a Multilayer Perceptron (MLP) as a velocity generator while optimizing velocity and image similarity. Moreover, we adopt a coarse-to-fine approach to address the challenge of deformable-based registration methods dropping into local optimal solutions, thus aiding the management of significant deformations in medical image registration. Our algorithm has been validated on a paired CT-CBCT dataset of 50 patients,taking the dice coefficient of transferred annotations as an evaluation metric. Compared to existing methods, our approach achieves the state-of-the-art performance.

AutoCT: Automated CT registration, segmentation, and quantification

The processing and analysis of computed tomography (CT) imaging is important for both basic scientific development and clinical applications. In AutoCT, we provide a comprehensive pipeline that integrates an end-to-end automatic preprocessing, registration, segmentation, and quantitative analysis of 3D CT scans. The engineered pipeline enables atlas-based CT segmentation and quantification leveraging diffeomorphic transformations through efficient forward and inverse mappings. The extracted localized features from the deformation field allow for downstream statistical learning that may facilitate medical diagnostics. On a lightweight and portable software platform, AutoCT provides a new toolkit for the CT imaging community to underpin the deployment of artificial intelligence-driven applications.