Robust estimation of image fractal dimension based on pyramidal decomposition

An approach to calculate the fractal dimension of images comes from power spectra of fractional Brownian motions: the ratio between powers at different scales is related to the persistence parameter H and, thus, to the fractal dimension D=3-H. The signal-dependent nature of speckle noise, however, prevents a correct estimation of fractal dimension from synthetic aperture radar (SAR) images. Here, we propose and assess a novel method to obtain D based on the multi-scale decomposition provided by the normalized Laplacian pyramid (NLP), which is a bandpass representation obtained by dividing the layers of an LP by its expanded baseband and designed to yield noise that is signal-independent. Experiments on both synthetic and true SAR images corroborate the underlying assumptions.