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

Fractal dimension has been used for texture analysis as it is highly correl ated with the human perception of surface roughness. Several methods have b een proposed for the estimation of the fractal dimension of an image. One o f the most popular is via its power spectrum density, provided that it is m odeled as a fractional Brownian function, In this paper, a new method, call ed the power differentiation method (PDM), for estimating the fractal dimen sion 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, i n the case of noise-corrupted data, the modified power differentiation meth od (MPDM) is developed, resulting in more accurate estimation of the fracta l dimension. The results obtained by the PDM and the MPDM are compared dire ctly to those obtained using four other well-known methods of fractal dimen sion. Finally, preliminary results for the classification of ultrasonic liv er images, obtained by applying the new method, are presented. (C) 1998 Aca demic Press.