Robust Quadric Fitting and Mensuration Comparison in a Mapping Space Applied to 3d Morphological Characterization of Articular Surfaces

Ellipsoid-Constrained Robust Fitting of Quadrics with Application to the 3D Morphological Characterization of Articular Surfaces

“…It is similar to what was performed in the 2D case of ellipses by R. Halíř [4]. Previously, we have proposed a novel bi-dimensional diagram called the Quadric Shape Map (QSM) to analyze and compare the output primitives of the fitting procedure [1]. In section III, the QSM meaningfully justifies the ellipsoid guarantee.…”

“…Yet, global characteristics accounting for kinematic functionalities, such as centers and axes of joints are also important to the orthopedists. Their location is estimated by fitting specific surface primitives: spheres at the hip and the shoulder, and circular cylinders at the knee (see references in [1]). Most methods still use mere least squares.…”

“…Most methods still use mere least squares. We have more widely addressed the generic shape characterization based on global symmetries within all articular surfaces [1]. To this end, the use of a common quadratic model has been proposed.…”

“…To this respect, generic non-typologically constrained quadric fitting might be successful, provided the data shape is already close enough to an ellipsoid, such as in the hip [1]. Other help, yet without guarantee either on the type of quadric [2], [7].…”

“…Griffiths [8] is revisited. In addition, the constraint blends into the constrained robust fitting framework using Iterative Reweighted Least Squares (IRLS) that we retained [1], as described in section II. It is similar to what was performed in the 2D case of ellipses by R. Halíř [4].…”