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<p><it>Abstract</it>—The 2D fractional Brownian motion (fBm) model provides a useful tool to model textured surfaces whose roughness is scale-invariant. To represent textures whose roughness is scale-dependent, we generalize the fBm model to the extended self-similar (ESS) model in this research. We present an estimation algorithm to extract the model parameters from real texture data. Furthermore, a new incremental Fourier synthesis algorithm is proposed to generate the 2D realizations of the ESS model. Finally, the estimation and rendering methods are combined to synthesize real textured surfaces.</p>
Fractals, fractional Brownian motion, processes with stationary increments, terrain modeling, texture analysis, texture synthesis, random fields, roughness perception.

C. J. Kuo and L. M. Kaplan, "Texture Roughness Analysis and Synthesis via Extended Self-Similar (ESS) Model," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 17, no. , pp. 1043-1056, 1995.
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