FRACTAL CHARACTERIZATION OF NON-GAUSSIAN CRITICAL MARKOV RANDOM FIELDS

摘要

In this paper we propose a fractal charade rization of a class of non-Gaussian Markov Random Fields (MRFs). In particular, we show that all order statistics of this class of MRFs are power-law functions. We then present a comparative study between the class of CMRFs and that of fractional Brownian motions (FBMs). Both of these classes of models can be used to describe self-similar phenomena. Their characteristics, namely the index of similarity of a FBM, and the critical exponents of a CMRF, are defined and contrasted. We argue that CMRFs provide a more flexible mechanism for generating self-similar patterns, since the parameters of a CMRF can be selected to generate non-Gaussian anisotropic patterns, while FBM models are Inherently Isotropic and Gaussian. This research was partially supported by Cynex Software.