Ellipsoid-constrained robust fitting of quadrics with application to the 3D morphological characterization of articular surfaces

This paper addresses the ellipsoid-type-specified fitting of quadratic surfaces, in the scope of model-based global feature extraction within scattered 3D point clouds. At characterizing articular bone surfaces, the quadrics estimated indicate useful overall-symmetry-related intrinsic centers and axes in joints. A constrained weighted least-squares minimization of algebraic residuals is used, with a robust and bias-corrected metric. With only one quadratic constraint involved, every step produces closed-form eigenvector solutions. To guarantee that an ellipsoid is output, we originally exploit a 2D representation called the Quadric Shape Map (QSM) by carrying out a visual study of the influence of shape constraints. The identified ellipsoid guarantee is needed to extract the center and axes in a wrist joint data stemming from 3D medical images.