Fractal analysis of self-similar textures using a Fourier-domain maximum likelihood estimation method

Fractional Brownian motion has been used to model self-similar textures. While using the fractal model, the most important procedure is measuring the Hurst parameter H, which is directly related to the fractal dimension. A maximum likelihood estimator has been applied to estimate the Hurst parameter H on a self-similar texture image. Much of the work done so far has concentrated in the spatial domain. In this paper, we propose an approximate MLE method for estimating H in the Fourier domain. The proposed Fourier-domain MLE method saves computational time, as the spatial-domain MLE needs extensive computations to obtain an inverse matrix. We use synthetic fractal datasets and a human tibia image to study the performance of our method.