From Model Based to Learned Regularization in Medical Image Registration: A Comprehensive Review

TL;DR

This paper presents a comprehensive taxonomy of regularization in medical image registration, separating methods into model-based, problem-specific, and learned approaches to address the ill-posed deformation estimation. It surveys explicit and implicit regularization, inverse-/cycle-consistency, and topology-preserving strategies, and discusses their transfer from conventional to learning-based registration. The review highlights learned regularization, including learned smoothness, deformation spaces, and test-time adaptation, as a promising but data- and compute-intensive direction. It also identifies open challenges—notably gaps in physics-inspired transfer, evaluation diversity, and clinical translation—and outlines future directions such as physics-informed networks, segmentation-driven priors, and foundation-model-like adaptability to improve realism and applicability of registration in practice.

Abstract

Image registration is fundamental in medical imaging applications, such as disease progression analysis or radiation therapy planning. The primary objective of image registration is to precisely capture the deformation between two or more images, typically achieved by minimizing an optimization problem. Due to its inherent ill-posedness, regularization is a key component in driving the solution toward anatomically meaningful deformations. A wide range of regularization methods has been proposed for both conventional and deep learning-based registration. However, the appropriate application of regularization techniques often depends on the specific registration problem, and no one-fits-all method exists. Despite its importance, regularization is often overlooked or addressed with default approaches, assuming existing methods are sufficient. A comprehensive and structured review remains missing. This review addresses this gap by introducing a novel taxonomy that systematically categorizes the diverse range of proposed regularization methods. It highlights the emerging field of learned regularization, which leverages data-driven techniques to automatically derive deformation properties from the data. Moreover, this review examines the transfer of regularization methods from conventional to learning-based registration, identifies open challenges, and outlines future research directions. By emphasizing the critical role of regularization in image registration, we hope to inspire the research community to reconsider regularization strategies in modern registration algorithms and to explore this rapidly evolving field further.

Figures (7)

• Figure 1: Regularization is an essential building block of successful registration algorithms. We identify three main categories of regularization methods: (I) Model based regularization that imposes prior assumptions on the deformation; (II) problem specific regularization that takes into account additional knowledge about the data, such as spatial information in the form of segmentation maps or physiological information; and (III) Learned regularization, which derives deformation properties from training data with a machine or deep learning model. The amount of prior information included in the regularization increases from category I to III. Most problem specific and learned regularization methods have their origin in model based regularization.
• Figure 2: Explicit vs. implicit regularization: Overview of approaches to integrating regularization in conventional (left) and learning-based (right) medical image registration. In both, regularization can be achieved explicitly with a regularizing loss term (dark blue) or implicitly with the parameterization of the transformation model (light blue). Additionally, guiding loss terms (green) can drive the registration toward a desired solution. For learning-based registration, the regularization applied during training is inherently captured in the network parameters at inference time.
• Figure 3: Model based regularization: Smoothness and folding: Different levels of smoothness regularization, controlled with the regularization parameter $\alpha$ (see Eq. \ref{['eq:opt']}). The pink arrows indicate regions of folding. With increasing $\alpha$, more smoothing is applied and less folding is observed.
• Figure 4: Model based regularization -- Inverse- vs. cycle-consistency: Inverse-consistency ensures that the forward and backward deformations are inverses of each other. Cycle-consistency ensures that a forward-backward deformed image resembles the original image.
• Figure 5: Problem specific regularization: Depending on the registration problem and data, different deformation properties may arise. With data-specific information, such as segmentation maps, regularization can locally account for suitable deformation properties. Images are taken from the Learn2Reg abdominal CT abdCT, NLST nlst, BraTS brats, and ACDC acdc datasets.