Abstract: It is widely recognized that SAR images exhibit a fractal behavior represented by the concept of fractal dimension, which is related to an intuitive concept of surface 'roughness.' The most suited approach to compute the fractal dimension comes from the power spectra of a fractal Brownian motion: the ratio between energies at different scales is related to the persistence parameter H and, thus, to the fractal dimension D equals 3 - H. The signal-dependent nature of speckle, however, prevents from the exploitation of this property to estimate the fractal dimension of SAR images. In this paper, we propose and assess a novel method to obtain such a fractal signature, based on the multi-scale image decomposition provided by the normalized Laplacian pyramid (NLP), which is a bandpass representation obtained by dividing the layers of the LP by expanded versions of its baseband, designed to exhibit noise that is independent of the signal. Thus, by analyzing SAR image texture on multiple scale through the NLP, it is possible to highlight and assess fractal behaviors of the radar cross-section. Experiments on both synthetic and true SAR images corroborate the theoretical assumptions underlying the proposed approach. !17
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