Reconstruction of two dimensional patterns by Fourier descriptors

Two kinds of Fourier shape descriptors (FDs) are considered: ZR defined by C.T. Zahn and R.S. Roskies (1972) and G defined by G.H. Granlund (1972). In the first part of the paper ZR descriptors are studied. Two modifications of ZR descriptors are proposed. The new descriptors are based on step signature and smoother signature. The amplitudes of FDs are invariant under rotations, translations, changes in size, mirror reflections, and shifts in the starting point. In all the cases the reconstruction accuracy in terms of the number of FDs is studied, resulting in approximation error bounds. An efficient reconstruction method not requiring numerical integration is proposed for polygonal shapes. In the second part of the work theoretical results are verified in numerical experiments involving handwritten characters. In the same experiments, the performances of ZR and G descriptors are compared