Reconstruction of two dimensional patterns by Fourier descriptors

摘要

Two kinds of Fourier shape descriptors (FDs) are considered: ZRdefined 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 arestudied. Two modifications of ZR descriptors are proposed. The newdescriptors are based on step signature and smoother signature. Theamplitudes of FDs are invariant under rotations, translations, changesin size, mirror reflections, and shifts in the starting point. In allthe cases the reconstruction accuracy in terms of the number of FDs isstudied, resulting in approximation error bounds. An efficientreconstruction method not requiring numerical integration is proposedfor polygonal shapes. In the second part of the work theoretical resultsare verified in numerical experiments involving handwritten characters.In the same experiments, the performances of ZR and G descriptors arecompared