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Wavelet Decomposition of Measures: Application to Multifractal Analysis of Images

  • Patrice Abry
  • Stéphane Jaffard
  • Stéphane Roux
  • Béatrice Vedel
  • Herwig Wendt
Conference paper
Part of the NATO Science for Peace and Security Series B: Physics and Biophysics book series (NAPSB)

Abstract

We show the relevance of multifractal analysis for some problems in image processing. We relate it to the standard question of the determination of correct function space settings. We show why a scale-invariant analysis, such as the one provided by wavelets, is pertinent for this purpose. Since a good setting for images is provided by spaces of measures, we give some insight into the problem of multifractal analysis of measures using wavelet techniques.

Keywords

Fourier transform function spaces fractals fractional integration Hölder regularity image classification image processing measures multifractal analysis scaling function scale invariance spectrum of singularities wavelets wavelet leaders 

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Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  • Patrice Abry
    • 1
  • Stéphane Jaffard
    • 2
  • Stéphane Roux
    • 1
  • Béatrice Vedel
    • 1
  • Herwig Wendt
    • 1
  1. 1.CNRS UMR 5672 Laboratoire de PhysiqueENS de LyonLyon cedexFrance
  2. 2.Laboratoire d'Analyse et de Mathématiques AppliquéesCNRS UMR 8050, Université Paris EstCréteil CedexFrance

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