FOURIER-SERIES EXPANSION OF IRREGULAR CURVES

Fourier theory provides an important approach to shape analyses; many methods for the analysis and synthesis of shapes use a description bas ed on the expansion of a curve in Fourier series. Most of these method s have centered on modeling regular shapes, although irregular shapes defined by fractal functions have also been considered by using spectr al synthesis. In this paper we propose a novel representation of irreg ular shapes based on Fourier analysis. We formulate a parametric descr iption of irregular curves by using a geometric composition defined vi a Fourier expansion. This description allows us to model a wide variet y of fractals which include not only fractal functions, but also fract als belonging to other families. The coefficients of the Fourier expan sion can be parametrized in time in order to produce sequences of frac tals useful for modeling chaotic dynamics. The aim of the novel charac terization is to extend the potential of shape analyses based on Fouri er theory by including a definition of irregular curves. The major adv antage of this new approach is that it provides a way of studying geom etric aspects useful for shape identification and extraction, such as symmetry and similarity as well as invariant features.