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.
Chapter PDF
Similar content being viewed by others
References
Russ, J.C.: The Image Processing Handbook. CRC Press, Boca Raton (1995)
Landgrebe, D.: Hyperspectral image data analysis. IEEE Signal Processing Magazine 19(1), 17–28 (2002)
Burton, G.J., Moorhead, I.R.: Color and spatial structure in natural scenes. Applied Optics 26, 157–170 (1987)
Ruderman, D.L., Bialek, W.: Statistics of natural images: Scaling in the woods. Physical Review Letters 73, 814–817 (1994)
Ruderman, D.L.: Origins of scaling in natural images. Vision Research 37, 3385–3398 (1997)
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)
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)
Grassberger, P., Procaccia, I.: Characterization of strange attractors. Physical Review Letters 50, 346–349 (1983)
Camastra, F.: Data dimensionality estimation methods: A survey. Pattern Recognition 36, 2945–2954 (2003)
Mandelbrot, B.B.: The Fractal Geometry of Nature. Freeman, San Francisco (1983)
Gouyet, J.F.: Physics and Fractal Structures. Springer, Berlin (1996)
Sharma, G. (ed.): Digital Color Imaging Handbook. CRC Press, Boca Raton (2003)
Turner, M.J., Andrews, P.R., Blackledge, J.M.: Fractal Geometry in Digital Imaging. Academic Press, New York (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chauveau, J., Rousseau, D., Chapeau-Blondeau, F. (2008). Pair Correlation Integral for Fractal Characterization of Three-Dimensional Histograms from Color Images. In: Elmoataz, A., Lezoray, O., Nouboud, F., Mammass, D. (eds) Image and Signal Processing. ICISP 2008. Lecture Notes in Computer Science, vol 5099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69905-7_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-69905-7_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69904-0
Online ISBN: 978-3-540-69905-7
eBook Packages: Computer ScienceComputer Science (R0)
