Multiresolution estimation of fractal dimension from images affected by signal-dependent noise

Bruno Aiazzi; Luciano Alparone; Stefano Baronti; Andrea Garzelli

doi:10.1117/12.366785

26 October 1999 Multiresolution estimation of fractal dimension from images affected by signal-dependent noise

Bruno Aiazzi, Luciano Alparone, Stefano Baronti, Andrea Garzelli

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366785
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

A well-suited approach to calculate the fractal dimension of digital images stems from the power spectrum of a fractional Brownian motion: the ratio between powers 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 the speckle noise, however, prevents from 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 multiscale decomposition provided by the normalized Laplacian pyramid, which is a bandpass representation obtained by dividing the layers of an LP by its expanded baseband and is designed to force the noise to become signal-independent. Extensive experiments on synthetic fractal textures, both noise-free and noisy, corroborate the underlying assumptions and show the performances, in terms of both accuracy and confidence of estimation, of pyramid methods compared with the well- established method based on the wavelet transform. Preliminary results on true SAR images from ERS-1 look promising as well.

Citation Download Citation

Bruno Aiazzi, Luciano Alparone, Stefano Baronti, and Andrea Garzelli "Multiresolution estimation of fractal dimension from images affected by signal-dependent noise", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366785

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KEYWORDS

Fractal analysis

Interference (communication)

Synthetic aperture radar

Wavelets

Speckle

Image segmentation

Wavelet transforms

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