Smoothing the Undersampled Carpal Bone Model with Small Volume and Large Curvature: A Feasibility Study

The carpal bones are eight small bones with irregularities and high curvature on their surfaces. The 3D model of the carpal bone serves as the foundation of further clinical applications, e.g., wrist kinematic behavior. However, due to the limitation of the Magnetic Resonance Imaging (MRI) technique, reconstructed carpal bone models are discretely undersampled, which has dramatic stair-step effects and leads to abnormal meshes on edges or surfaces, etc. Our study focuses on determining the viability of various smoothing techniques for a carpal model reconstructed by in vivo gathered MR images. Five algorithms, namely the Laplacian smoothing algorithm, the Laplacian smoothing algorithm with pre-dilation, the scale-dependent Laplacian algorithm, the curvature flow algorithm, and the inverse distance algorithm, were chosen for evaluation. The assessment took into account the Relative Volume Difference and the Hausdorff Distance as well as the surface quality and the preservation of morphological and morphometric properties. For the five algorithms, we analyzed the Relative Volume Difference and the Hausdorff Distance for all eight carpal bones. Among all the algorithms, the scale-dependent Laplacian method processed the best result regarding surface quality and the preservation of morphological and morphometric properties. Based on our extensive examinations, the scale-dependent Laplacian algorithm is suitable for the undersampled carpal bone model with small volume and large curvature.