Ball-and-socket joint motion description using spherical medial representation

The close inter-relationship between shape and functionality of osteo-articular complexes is fundamental for understanding, modeling, and imaging. It is thus desirable to put forward theoretical and methodological principles that take benefit of this relationship. In this paper, we propose a new representation of spherical motions that is applied to ball-and-socket joint such as hip and shoulder. We have been developing Spherical Medial Representation (SM-Rep) based on skeletonisation over the sphere. While M-Rep provides a paradigm for 3D surface and image analysis, the resulting surface remains in a 3D vector space. Since the geometry of the unit sphere is quite different, especially geodesies, SM-Rep supplies consistent elements to overcome this issue. Example of application of this framework to hip is given.