Wavelet based estimation of the fractal dimension in fBm images

Fractional Brownian Motion (fBm) has been successfully exploited to model an important number of physical phenomena and non-stationary processes such as medical images. These mathematical models closely describe essential properties of natural phenomena, such as self-similarity, scale invariance and fractal dimension (FD). The use of wavelet analysis combined with fBm analysis may provide an interesting approach to compute key values for fBm processes, such as the fractal dimension FD. We propose two models to calculate the Hurst Coefficient H (and hence FD) for both one-dimensional and two-dimensional signals. The first approach is based on statistical properties of the signals, while the second one is based on their spectral characteristics. A formal extension of these two models to 2D processes is developed and implemented, and a comparison of both is presented. The proposed algorithms are tested using tomographic brain tumor data. Our simulation experiments offer promising results in the identification of such lesions.