Multi-resolution estimation of fractal dimension from noisy images

A well-suited approach to calculate the fractal dimension of digital images stems from the power spectrum of a fractional Brownian motion: the ratio b etween 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 the speckle noise, however, prevents a correct estimation of fractal dimens ion 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 (LP), which is a bandpass representati on obtained by dividing the layers of a LP by its expanded base band and is designed to force the noise to become signal independent Extensive experim ents on synthetic fractal textures, both noise free and noisy, corroborate the underlying assumptions and show the performances, in terms of both accu racy and confidence of estimation, of pyramid methods compared with the wel l-established method based on the wavelet transform. Preliminary results on true SAR images from ERS-1 look promising as well. (C) 2001 SPIE and IS&T.