Fractal structure in the color distribution of natural images

Journal Title: Chaos, Solitons & Fractals
Article Title: Fractal structure in the color distribution of natural images
Volume: 42
Issue: 1
First Page: 472
Last Page: 482
Issue Cover Date: 2009-10-15
Authors: François Chapeau-Blondeau1, Julien Chauveau1, David Rousseau1 and Paul Richard1

  1. Laboratoire d’Ingénierie des Systèmes Automatisés (LISA),
    Université d’Angers, 62 avenue Notre Dame du Lac, 49000 Angers, France

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.

DOI: 10.1016/j.chaos.2009.01.008