New 3D Fourier Descriptors for Genus-Zero Mesh Objects

Abstract

The 2D Fourier Descriptor is an elegant and powerful technique for 2D shape analysis. This paper intends to extend such technique to 3D. Though conceptually natural, such an extension is not trivial in that two critical problems, the spherical parametrization and invariants construction, must be solved. By using a newly developed surface parametrization method-the discrete conformal mapping (DCM) - we propose a 3D Fourier Descriptor (3D-FD) for representing and recognizing arbitrarily-complex genus-zero mesh objects. A new DCM algorithm is suggested which solves the first problem efficiently. We also derive a method to construct a truly complete set of Spherical Harmonic invariants. The 3D-FD descriptors have been tested on different complex mesh objects. Experiment results for shape representation are satisfactory. Show more