Progressive surface representation and refinement for rigid ultrasound-CT registration: a phantom study

Rigid ultrasound (US) and computed tomography (CT) registration remains challenging in computer assisted knee surgery because intraoperative US provides incomplete bone-surface observations that may contain outliers and spatially extended echo bands. This study presents and evaluates Progressive Surface Representation and Refinement (PSRR), a staged covariance-aware framework for rigid US-CT registration. PSRR constructs confidence-weighted local representative points and anisotropic covariance descriptors from segmented US bone-surface observations. It then estimates the rigid US-CT transformation using progressively gated correspondences, with CT-normal-guided dynamic updates of target points and their covariances during iterative refinement. PSRR was evaluated against five representative baseline methods in 120 controlled water-tank phantom registration trials spanning different effective overlap ratios and initial-pose perturbation levels. Across the 120 registration trials, PSRR achieved the lowest overall mean value of the average surface distance (ASD), at 2.51 ± 2.77 mm, and the highest 5-mm ASD threshold-attainment rate of 89.2% at the 5-mm ASD threshold among the compared methods. Compared with ICP and G-ICP, PSRR reduced all-case ASD by 48.6% and 35.8%, respectively. PSRR also achieved the lowest ASD under low overlap (2.57 ± 3.00 mm) and high perturbations (4.18 ± 4.21 mm) conditions. In landmark-based evaluation, PSRR yielded a mean target registration error (TRE) of 2.09 mm, lower than those of ICP and G-ICP. Ablation analyses further supported the contributions of confidence-weighted local representative construction, CT-normal-guided target refinement, and dynamic covariance updating. In controlled water-tank phantom experiments, PSRR improved surface-distance and landmark-based registration accuracy under reduced-overlap and perturbed-initialization conditions. Further evaluation in tissue-mimicking, cadaveric, or clinical settings is required to establish its intraoperative applicability.