Generalized Fourier descriptors for shape analysis of 3-dimensional closed curves
Abstract
A new method for shape characterization of 3-D space curves is presented. The proposed procedure based on the Fourier analysis techniques can be regarded as a generalization and further development of methods described in the literature. Its advantages are its simplicity and its ability to describe the shape of any closed space curves regardless of their nature. The space curve is parametrised by its arc length and characterized by a set of 3-D vector valued "shape functions”. The shape function is unambiguously defined for any closed space curve, and contains the complete 3-D information on the curve. The three components of the shape function (called partial shape functions) are periodic with the period 2Π, and can be expanded in Fourier series. Starting with the appropriately selected partial shape functions, shape descriptors generated from Fourier coefficients are defined for shape evaluation. They are invariant under translation, rotation and dilation. In order to verify the validity of the computational model and to analyse the efficiency of the proposed procedure, experimental study has been performed using different test curves.