Performance Comparison of CPD, NRICP, and Spherical Parameterization on Femoral Statistical Shape Model

Purpose: The aim of this study is to evaluate and compare the performance of three non-rigid registration methods—coherent point drift (CPD), non-rigid iterative closest point (NRICP), and spherical parameterization—in building statistical shape models (SSMs) of femurs for identifying morphological features in patients with knee osteoarthritis (OA). Method: A simplified femur template was selected. Non-rigid registration algorithms (CPD, NRICP, spherical parameterization) were applied to align the template surface to all other femur samples. The registration methods were assessed using multiple evaluation criteria: root mean square error (RMSE), Hausdorff distance (HD), computational efficiency, local deformation capability, outlier sensitivity, compactness, generalization, and specificity. Results: The results showed that all deformable algorithms exhibited reasonable registration results. Among them, CPD performed best in RMSE, HD, local deformation, and specificity. Spherical parameterization balanced all these metrics but was unsuitable for handling abnormal structures and could occasionally result in severe reconstruction errors in complex anatomical structures. NRICP was the fastest technique with the lowest generalization reconstruction error but achieved the lowest registration accuracy. Conclusion: CPD is the most suitable method for accurate femur registration in SSMs, especially for detecting OA-related morphological variations. Spherical parameterization is a promising approach if it can mitigate extreme errors. NRICP favors efficiency over accuracy, suitable for real-time tasks.