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

  • A. Arnéodo
  • N. Decoster
  • S.G. Roux
Article

DOI: 10.1007/s100510051161

Cite this article as:
Arnéodo, A., Decoster, N. & Roux, S. Eur. Phys. J. B (2000) 15: 567. doi:10.1007/s100510051161

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.

PACS. 47.53.+n Fractals - 02.50.-r Probability theory, stochastic processes, and statistics05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion68.35.Bs Surface structure and topography

Copyright information

© EDP Sciences, Springer-Verlag, Società Italiana di Fisica 2000

Authors and Affiliations

  • A. Arnéodo
    • 1
  • N. Decoster
    • 1
  • S.G. Roux
    • 1
  1. 1.Centre de Recherche Paul PascalPessacFrance
  2. 2.Climate & Radiation Branch,NASA's Goddard Space Flight CenterMarylandUSA