A hilbert analytic multi-scale deformable framework for robust multimodal medical image registration

Non-linear intensity variations and the possibility of producing anatomically inconsistent outputs pose a fundamental challenge to deformable registration of multimodal medical images, including CT and MRI. In this work, a multi-scale feature descriptor based on the 2D Hilbert analytic signal is used to present a new, diffeomorphic registration framework. Complementary amplitude and phase information are provided by this signal decomposition, resulting in a strong feature set that is independent of modality contrast. The presented approach integrates a stationary velocity field (SVF) through scaling and squaring to model deformations and guarantee smooth and topology-preserving transformations. A composite loss function combining Jacobian regularization, smoothness, and similarity balances deformation regularity and registration accuracy. A paired CT-MRI dataset is used to assess the proposed algorithm, which shows superior performance by attaining near zero negative Jacobians, better DSC up to 0.93, and consistent sub-pixel geometric accuracy (TRE mean ≈ 1.12 px). Additionally, ablation studies validated the significance of regularization, hierarchical optimization, and amplitude and phase encoding. The findings show that the proposed Hilbert-SVF technique is a reliable choice for multimodal registration in clinical and research applications as it achieves anatomically consistent and accurate registration across different modalities.