Parametrization of closed surfaces for 3-D shape description

A set of procedures for the explicit parametric representation and global description of surfaces of simply connected 3-D objects is presented. The proposed schemes overcome the shortcomings of earlier methods, such as constraints on positioning and shape of cross-sections. A continuous, one-to-one mapping from the surface of the original object to the surface of a unit sphere is used in the parametrization which is presented as an optimization problem. This approach allows the expansion of the object surface into a series of spherical harmonic functions, extending to 3-D the concept of elliptical Fourier descriptors for 2-D closed curves.