Multi-scale Lipschitz Neural Fields Incorporating Frequency Decoupling for medical image registration

Abstract

Deformable image registration is a pivotal task in medical image analysis, essential for applications such as surgical navigation, lesion localization, and treatment planning. However, the accuracy of registration is frequently constrained by the ability to analyze complex textural features, which impedes the capture of fine-grained deformations and elevates surgical risks. To overcome these limitations, we propose the Multi-Scale Lipschitz Neural Fields Incorporating Frequency Decoupling (MLNFFD) framework, which reformulates the registration task as the correction of high-frequency residuals based on a low-frequency coarse registration foundation. Specifically, we employ a dual-branch architecture, comprising a band-limited U-Net low-frequency branch for coarse deformation estimation, and a Multi-Scale Lipschitz Neural Fields (MLNF) high-frequency branch dedicated to refining fine-grained deformation residuals. Through a complementary joint optimization strategy, the low-frequency branch provides an initial estimation that accelerates the optimization of the high-frequency branch, while the high-frequency branch refines the deformation field and enhances local details, fostering mutual reinforcement and improving registration accuracy. Additionally, the MLNF branch incorporates a Multi-Scale Implicit Dual-Domain Feature Representation (MIDFR), a deep similarity prior, and Lipschitz continuity constraints, enhancing the representation of complex textural features while ensuring the smoothness of the deformation field. Extensive experimental results on brain MRIs and cine cardiac MRIs datasets show that our proposed approach outperforms existing methods in terms of both registration accuracy and deformation field smoothness.