An Improved Method for 2-D Self-Similar Image Synthesis

Abstract-In this paper, we propose a new method ealled incremental Fourier synthesis to generate 2-D self-similar images based on a 2-D fractional Browninan motion (mm) model. With this method, the stationary increments of fBm are created by a Fourier synthesis method and the increments are added up to generate the nonstationary 2-D fBm process. Since the new method takes advantage of the FFT, its computational complexity is only O ( N 2 log,(N)), and its memory requirement is only O ( N 2) for a self-similar image of size N x N. 1