Critical Markov random fields and fractional Brownian motion in texture synthesis

In this paper we study and compare critical Markov random fields (CMRFs) and 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 anisotropic patterns, while FBM models are inherently isotropic.<
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