Random Self-affine Surfaces Research Articles

Near-field speckles produced by random self-affine surfaces and their contrast transitions.

By use of a numerical calculation based on Green's integral equation, we study the near-field speckles produced by the random self-affine fractal surfaces of a dielectric medium. The speckle intensities evolve considerably in the near-field region, and the local fluctuations in them disappear before they have traversed the distance of a wavelength. The transition of the speckle contrast either on the surface or in the near field and in the neighborhood non-near-field regions depends on lateral correlation length xi and roughness exponent alpha of the random surfaces.

Description of random Gaussian surfaces by a four-vertex model.

A lattice model of random self-affine surfaces is derived using the inverse order of applying the six-vertex model. The well-argued simplification of such an approach results in the four-vertex model. The high numerical efficiency of the four-vertex model is demonstrated by calculating the fractal dimension of contour loops (isolines) of fractional Brownian surfaces as the function of the roughness exponent.

A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces

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. Arneodo, 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. Arneodo, 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.

Wavelet Based Multifractal Analysis of Rough Surfaces: Application to Cloud Models and Satellite Data

The wavelet transform modulus maxima (WTMM) method is generalized to multifractal image analysis, providing a statistical characterization of the fluctuating roughness of fractal surfaces. This isotropic 2D version of WTMM methodology is calibrated on deterministic self-similar interfaces and random self-affine surfaces (fractional Brownian surfaces and multifractal counterparts). Applications to high-resolution satellite data and simulated radiance fields for stratocumulus clouds are presented. {copyright} {ital 1997} {ital The American Physical Society}