A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces |
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Authors: | A Arnéodo N Decoster SG Roux |
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Institution: | (1) Centre de Recherche Paul Pascal, avenue Schweitzer, 33600 Pessac, France, FR;(2) Climate & Radiation Branch, NASA's Goddard Space Flight Center, Greenbelt, Maryland 20771, USA, US |
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Abstract: | We generalize the so-called wavelet transform modulus maxima (WTMM) method to multifractal image analysis. We show that the
implementation of this method provides very efficient numerical techniques to characterize statistically the roughness fluctuations
of fractal surfaces. We emphasize the wide range of potential applications of this wavelet-based image processing method in
fundamental as well as applied sciences. This paper is the first one of a series of three articles. It is mainly devoted to
the methodology and to test applications on random self-affine surfaces (e.g., isotropic fractional Brownian surfaces and anisotropic monofractal rough surfaces). Besides its ability to characterize
point-wise regularity, the WTMM method is definitely a multiscale edge detection method which can be equally used for pattern
recognition, detection of contours and image denoising. Paper II (N. Decoster, S.G. Roux, A. Arnéodo, to be published in Eur.
Phys. J. B 15 (2000)) will be devoted to some applications of the WTMM method to synthetic multifractal rough surfaces. In paper III (S.G.
Roux, A. Arnéodo, N. Decoster, to be published in Eur. Phys. J. 15 (2000)), we will report the results of a comparative experimental analysis of high-resolution satellite images of cloudy
scenes.
Received 8 July 1999 |
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Keywords: | PACS 47 53 +n Fractals - 02 50 -r Probability theory stochastic processes and statistics - 05 40 -a Fluctuation phenomena random processes noise and Brownian motion - 68 35 Bs Surface structure and topography |
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