VoxelMorph-Based Non-Rigid Chest CT Registration With Multi-Frequency Encoding and Curriculum Learning

VoxelMorph, a widely adopted deep learning framework for non-rigid image registration, often encounters challenges in precisely aligning lung regions in chest computed tomography (CT) due to limited soft-tissue contrast, a scarcity of stable anatomical landmarks, and substantial inter-scan pose variations. To overcome these challenges, we introduce an enhanced VoxelMorph-based framework that integrates a wavelet-based multi-frequency encoder with curriculum learning. The encoder employs a non-decimated two-channel filter bank to decompose input CT volumes into low- and high-frequency components, facilitating parallel extraction of global lung morphology and fine vascular or pleural details before decoding them into a dense deformation vector field (DVF). During training, a curriculum based on synthetically generated DVFs incrementally increases deformation amplitude, stabilizing model optimization and enhancing robustness to substantial anatomical variations. Our dataset consists of chest CT scans from 501 patients; 400 were allocated for curriculum-based training with synthetic deformations, and 101 with longitudinal scan pairs were reserved for evaluation. On this test set, the proposed method achieved a root-mean-square error (RMSE) of 126.37 HU, a multi-scale structural similarity index measure (MS-SSIM) of 0.990, and a Dice coefficient of 0.974, significantly surpassing the baseline VoxelMorph model (RMSE: 140.29, MS-SSIM: 0.987, Dice: 0.970; Holm–Bonferroni–corrected plung) and reduced folding, indicating more anatomically plausible deformations. These findings indicate that the combined use of multi-frequency encoding and curriculum learning markedly enhances non-rigid registration accuracy in chest CT, particularly within low-contrast pulmonary regions that lack reliable anatomical landmarks.