Power Law Dependencies to Detect Regions of Interest

  • Yves Caron
  • Harold Charpentier
  • Pascal Makris
  • Nicole Vincent
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)


This paper presents a novel approach to detect regions of interest in digital photographic grayscale images using power laws. The method is intended to find regions of interest in various types of unknown images. Either Zipf law or inverse Zipf law are used to achieve this detection. The detection method consists in dividing the image in several sub-images, computing the frequency of occurence of each different image pattern, representing this distribution by a power law model and classifying the sub-frames according to the power law characteristics. Both power laws models allow region of interest detection, however inverse Zipf law has better performances than Zipf law. The detection results are generally consistent with the human perception of regions of interest.


Segmentation region detection region of interest compression coding 


  1. 1.
    Beaver, P., Quirk, S.M., Sattler, J.P.: Object Identification in Greyscale Imagery using Fractal Dimension. In: Novak, M. (ed.) Fractal Reviews in the Natural and Applied Science, pp. 63–73. Chapman & Hall, London (1995)Google Scholar
  2. 2.
    Kadir, T., Brady, M.: Scale, Saliency and Image Description. International Journal of Computer Vision 45(2), 83–105 (2001)zbMATHCrossRefGoogle Scholar
  3. 3.
    Wang, J.Z., Li, J., Gray, R.M., Wiederhold, G.: Unsupervised Multiresolution Segmentation for Images with Low Depth of Field. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(1), 85–90 (2001)CrossRefGoogle Scholar
  4. 4.
    Zipf, G.K.: Human Behavior and the Principle of Least Effort. Addison-Wesley, New York (1949)Google Scholar
  5. 5.
    Miller, G.A., Newman, E.B.: Test of a Statistical Explanation of the Rank-Frequency Relation for Words in Written English. American Journal of Psychology 71, 209–218 (1958)CrossRefGoogle Scholar
  6. 6.
    Cohen, A., Mantegna, R.N., Havlin, S.: Numerical analysis of word frequencies in artificial and natural language texts. Fractals 5(1), 95–104 (1997)zbMATHCrossRefGoogle Scholar
  7. 7.
    Hill, B.M.: Zipf’s law and prior distributions for the composition of a population. Journal of the American Statistical Association 65, 1220–1232 (1970)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Makse, H.A., Havlin, S., Stanley, H.E.: Modelling urban growth patterns. Nature 377, 608–612 (1995)CrossRefGoogle Scholar
  9. 9.
    Mantegna, R.N., Buldyrev, S.V., Goldberger, A.L., Havlin, S., Peng, C.K., Simons, M., Stanley, H.E.: Linguistic Features of Noncoding DNA Sequences. Phys. Rev. Lett. 73, 3169 (1994)CrossRefGoogle Scholar
  10. 10.
    Breslau, L., Cao, P., Fan, L., Phillips, G., Shenker., S.: Web caching and Zipf-like distributions: Evidence and implications. In: Proceedings of IEEE Infocom, New York, pp. 126–134 (1999)Google Scholar
  11. 11.
    Huberman, B.A., Pirolli, P., Pitkow, J., Lukose, R.: Strong Regularities in World Wide Web Surfing. Science 280, 95–97 (1998)CrossRefGoogle Scholar
  12. 12.
    Vincent, N., Makris, P., Brodier, J.: Compressed Image Quality and Zipf’s Law. In: Proceedings of International Conference on Signal Processing (ICSP – IFIC-IAPRWCC2000), Beijing, China, pp. 1077–1084 (2002)Google Scholar
  13. 13.
    Caron, Y., Makris, P., Vincent, N.: A method for detecting artificial objects in natural environmements. In: International Conference on Pattern recognition (ICPR - IAPR), Québec, Canada, pp. 600–603 (2002)Google Scholar
  14. 14.
    Zipf, G.K. (ed.): The Psychology of Language, an Introduction to Dynamic Philology. M.I.T. Press, Cambridge (1965)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Yves Caron
    • 1
  • Harold Charpentier
    • 1
  • Pascal Makris
    • 1
  • Nicole Vincent
    • 1
  1. 1.Laboratoire d’InformatiqueUniversité François RabelaisToursFrance

Personalised recommendations