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Multifractal analysis of three-dimensional histogram from color images

Author

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  • Chauveau, Julien
  • Rousseau, David
  • Richard, Paul
  • Chapeau-Blondeau, François

Abstract

Natural images, especially color or multicomponent images, are complex information-carrying signals. To contribute to the characterization of this complexity, we investigate the possibility of multiscale organization in the colorimetric structure of natural images. This is realized by means of a multifractal analysis applied to the three-dimensional histogram from natural color images. The observed behaviors are confronted to those of reference models with known multifractal properties. We use for this purpose synthetic random images with trivial monofractal behavior, and multidimensional multiplicative cascades known for their actual multifractal behavior. The behaviors observed on natural images exhibit similarities with those of the multifractal multiplicative cascades and display the signature of elaborate multiscale organizations stemming from the histograms of natural color images. This type of characterization of colorimetric properties can be helpful to various tasks of digital image processing, as for instance modeling, classification, indexing.

Suggested Citation

  • Chauveau, Julien & Rousseau, David & Richard, Paul & Chapeau-Blondeau, François, 2010. "Multifractal analysis of three-dimensional histogram from color images," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 57-67.
    • Handle: RePEc:eee:chsofr:v:43:y:2010:i:1:p:57-67
    DOI: 10.1016/j.chaos.2010.08.003
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    References listed on IDEAS

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    1. Su, Zhi-Yuan & Wu, Tzuyin & Wang, Shu-Yin, 2009. "Local scaling and multifractal spectrum analyses of DNA sequences – GenBank data analysis," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1750-1765.
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    3. Chapeau-Blondeau, François & Chauveau, Julien & Rousseau, David & Richard, Paul, 2009. "Fractal structure in the color distribution of natural images," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 472-482.
    4. Stanley, H.E. & Amaral, L.A.N. & Goldberger, A.L. & Havlin, S. & Ivanov, P.Ch. & Peng, C.-K., 1999. "Statistical physics and physiology: Monofractal and multifractal approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 309-324.
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    Cited by:

    1. Chéné, Yann & Belin, Étienne & Rousseau, David & Chapeau-Blondeau, François, 2013. "Multiscale analysis of depth images from natural scenes: Scaling in the depth of the woods," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 135-149.
    2. Lahmiri, Salim, 2016. "Image characterization by fractal descriptors in variational mode decomposition domain: Application to brain magnetic resonance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 235-243.
    3. Martsepp, Merike & Laas, Tõnu & Laas, Katrin & Priimets, Jaanis & Tõkke, Siim & Mikli, Valdek, 2022. "Dependence of multifractal analysis parameters on the darkness of a processed image," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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