Two dimensional stochastic fractional AR models with strong periodicities

An empirical study of many natural two dimensional textures with strong quasi periodicities show that their spectral density at the peak frequency behaves like (f-f1)^-β, where 0 < β< 1. In many of the available random field models like the simultaneous autoregressive models, the spectral density at the peak frequency varies only like (f-f1)^-2. We propose here a class of models whose spectral density behaves like (f-f1)^-β, 0 < β < 1. We discuss the synthesis of two dimensional images obeying these models. We will display the synthesized images and note their resemblance to the natural textures.