A power differentiation method of fractal dimension estimation for 2-D signals

Fractal dimension has been used for texture analysis as it is highly correlated with the human perception of surface roughness. Several methods have been proposed for the estimation of the fractal dimension of an image. One of the most popular is via its power spectrum density, provided that it is modeled as a fractional Brownian function, In this paper, a new method, called the power differentiation method (PDM), for estimating the fractal dimension of a two-variable signal from its power spectrum density is presented. The method is first applied to noise-free data of known fractal dimension. It is also tested with noise-corrupted and quantized data. Particularly, in the case of noise-corrupted data, the modified power differentiation method (MPDM) is developed, resulting in more accurate estimation of the fractal dimension. The results obtained by the PDM and the MPDM are compared directly to those obtained using four other well-known methods of fractal dimension. Finally, preliminary results for the classification of ultrasonic liver images, obtained by applying the new method, are presented. (C) 1998 Academic Press.