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Fractal structure in the color distribution of natural images

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

Abstract

The colorimetric organization of RGB color images is investigated through the computation of the correlation integral of their three-dimensional histogram. For natural color images, as a common behavior, the correlation integral is found to follow a power law, with a noninteger exponent characteristic of a given image. This behavior identifies a fractal or multiscale self-similar distribution of the colors contained in typical natural images. This finding of a possible fractal structure in the colorimetric organization of natural images complement other fractal properties previously observed in their spatial organization. Such fractal colorimetric properties may be helpful to the characterization and modeling of natural images, and may contribute to progress in vision.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:472-482
    DOI: 10.1016/j.chaos.2009.01.008
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    References listed on IDEAS

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    1. Wu, Ming-Sheng & Teng, Wei-Chih & Jeng, Jyh-Horng & Hsieh, Jer-Guang, 2006. "Spatial correlation genetic algorithm for fractal image compression," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 497-510.
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    1. 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.
    2. 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.

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