DARE: A Deformable Adaptive Regularization Estimator for Learning-Based Medical Image Registration

TL;DR

DARE tackles the problem of non-physically plausible deformations in learned deformable image registration by introducing gradient-norm–driven adaptive elastic regularization that modulates strain and shear energies, along with a folding-prevention mechanism. The method defines $R_{DARE}(u)$ and adaptive components $\hat{\lambda}(u)$, $\hat{\mu}(u)$, and $\hat{\alpha}(u)$ as functions of $\|\nabla u\|$, enabling context-aware regularization, and adds a Jacobian-based folding penalty to enforce invertibility. Empirically, DARE achieves higher Dice scores and substantially lower folding rates across IXI, OASIS, and MUI-P datasets compared to both variational regularizers and contemporary DL-based registration methods, demonstrating robust accuracy and anatomical plausibility. This physics-informed, adaptive framework has practical implications for clinical workflows where precise and realistic deformations are essential, making it a strong candidate for safer and more reliable medical image registration.

Abstract

Deformable medical image registration is a fundamental task in medical image analysis. While deep learning-based methods have demonstrated superior accuracy and computational efficiency compared to traditional techniques, they often overlook the critical role of regularization in ensuring robustness and anatomical plausibility. We propose DARE (Deformable Adaptive Regularization Estimator), a novel registration framework that dynamically adjusts elastic regularization based on the gradient norm of the deformation field. Our approach integrates strain and shear energy terms, which are adaptively modulated to balance stability and flexibility. To ensure physically realistic transformations, DARE includes a folding-prevention mechanism that penalizes regions with negative deformation Jacobian. This strategy mitigates non-physical artifacts such as folding, avoids over-smoothing, and improves both registration accuracy and anatomical plausibility

Figures (1)

• Figure 1: Examples of dynamic adjustment of $\lambda_{\textnormal{strain}}$ (top), $\mu_{\textnormal{shear}}$ (middle), and $\alpha$ (bottom) during training in response to the gradient norm.