Isotropic two-dimensional Fractional Brownian Motion and its application in Ultrasonic analysis

In this paper, we first present a new algorithm to generate an isotropic 2 dimensional discrete Fractional Brownian Motion, using the method of Cholesky decomposition. Secondly, we derive a two dimensional Maximum Likelihood Estimator to extract the fractal parameters from a given stochastic fractal image. Finally, this algorithm is applied to scale independently parameterize the textures displayed in Ultrasonic medical images. The application is to detect immune reactions in transplanted kidneys.