Dual-metric Bayesian optimization of B-spline mesh size for 4DCT lung registration

Objectives: We aim to optimize the patient-specific mesh size (N) in the B-spline deformable image registration method, enhancing the computational efficiency of 4DCT lung image registration. Methods: This study included 37 subjects (10 from the DIRLAB public dataset and 27 from a private 4DCT cohort), each consisting of 10 respiratory phases. A Bayesian optimization (BO) framework was proposed to determine patient-specific N within [2, 50]. Registration accuracy was evaluated using the Dice Similarity Coefficient (DSC) and Hausdorff Distance (HD). To further validate registration robustness, extreme-phase registrations were additionally tested, and inverse consistency error (ICE) was calculated to assess deformation invertibility. A global evaluation approach was also applied across the full respiratory cycle, and the computational cost of the traditional grid search (GS) was analyzed for comparison. Results: BO efficiently determined patient-specific N, with optimal values ranging from 6 to 15 (overall mean = 10.4 ± 2.6), achieving DSC = 0.976 and HD = 0.814. In the extreme-phase tests, registration performance remained stable between forward and reverse directions, with DSC > 0.94, HD95< 3 mm, and small ICE differences (ICE95 = 0.467 ± 0.230 mm), indicating strong inverse consistency and deformation stability. Compared with GS, BO achieved 50.7 %–99.4 % time savings, while GS showed a power-law increase in runtime (exponent = 2.53). Conclusions: The proposed BO framework efficiently optimized patient-specific mesh sizes, achieving high registration accuracy and significantly reduced computation time, thereby offering a promising tool to improve efficiency in adaptive radiotherapy and motion-compensated treatment planning.