Pair Correlation Integral for Fractal Characterization of Three-Dimensional Histograms from Color Images

  • Julien Chauveau
  • David Rousseau
  • François Chapeau-Blondeau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5099)

Abstract

The pair correlation integral is used to assess the intrinsic dimensionality of the three-dimensional histogram of RGB color images. For application in the bounded colorimetric cube, this correlation measure is first calibrated on color histograms of reference constructed with integer dimensionality. The measure is then applied to natural color images. The results show that their color histogram tends to display a self-similar structure with noninteger fractal dimension. Such a fractal organization in the colorimetric space can have relevance for image segmentation or classification, or other areas of color image processing.

Keywords

Color image Color histogram Fractal Pair correlation integral Feature extraction and analysis 

References

  1. 1.
    Russ, J.C.: The Image Processing Handbook. CRC Press, Boca Raton (1995)Google Scholar
  2. 2.
    Landgrebe, D.: Hyperspectral image data analysis. IEEE Signal Processing Magazine 19(1), 17–28 (2002)CrossRefGoogle Scholar
  3. 3.
    Burton, G.J., Moorhead, I.R.: Color and spatial structure in natural scenes. Applied Optics 26, 157–170 (1987)CrossRefGoogle Scholar
  4. 4.
    Ruderman, D.L., Bialek, W.: Statistics of natural images: Scaling in the woods. Physical Review Letters 73, 814–817 (1994)CrossRefGoogle Scholar
  5. 5.
    Ruderman, D.L.: Origins of scaling in natural images. Vision Research 37, 3385–3398 (1997)CrossRefGoogle Scholar
  6. 6.
    Turiel, A., Parga, N., Ruderman, D.L., Cronin, T.W.: Multiscaling and information content of natural color images. Physical Review E 62, 1138–1148 (2000)Google Scholar
  7. 7.
    Hsiao, W.H., Millane, R.P.: Effects of occlusion, edges, and scaling on the power spectra of natural images. Journal of the Optical Society of America A 22, 1789–1797 (2005)Google Scholar
  8. 8.
    Grassberger, P., Procaccia, I.: Characterization of strange attractors. Physical Review Letters 50, 346–349 (1983)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Camastra, F.: Data dimensionality estimation methods: A survey. Pattern Recognition 36, 2945–2954 (2003)MATHCrossRefGoogle Scholar
  10. 10.
    Mandelbrot, B.B.: The Fractal Geometry of Nature. Freeman, San Francisco (1983)Google Scholar
  11. 11.
    Gouyet, J.F.: Physics and Fractal Structures. Springer, Berlin (1996)Google Scholar
  12. 12.
    Sharma, G. (ed.): Digital Color Imaging Handbook. CRC Press, Boca Raton (2003)Google Scholar
  13. 13.
    Turner, M.J., Andrews, P.R., Blackledge, J.M.: Fractal Geometry in Digital Imaging. Academic Press, New York (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Julien Chauveau
    • 1
  • David Rousseau
    • 1
  • François Chapeau-Blondeau
    • 1
  1. 1.Laboratoire d’Ingénierie des Systèmes Automatisés (LISA)Université d’AngersAngersFrance

Personalised recommendations