Statistics of natural and urban images

  • Christian Ziegaus
  • Elmar W. Lang
Part II: Cortical Maps and Receptive Fields
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1327)


We investigated ensembles of artificial and real-world grey-scale images to find different invariance properties: translation invariance, scale invariance and a new hierarchical invariance recently proposed by Ruderman [1]. We found that the assumption of translational invariance can be taken for granted. Our results concerning the scale invariance are qualitatively the same as those found by Ruderman [1] and others. The deviations of the distributions of the logarithmically transformed images from a Gaussian distribution cannot be seen as clearly as stated by Ruderman [1]. Depending on the preprocessing of the images the results concerning the hierarchical invariance differed widely. It seems that this new invariance can be confirmed only for logarithmically transformed images.


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  1. 1.
    Ruderman, D. L.: The statistics of natural images Network 5 (1994) 517–548Google Scholar
  2. 2.
    Ruderman, D. L.: Designing receptive fields for highest fidelity Network 5 (1994) 147–155Google Scholar
  3. 3.
    Field, D. J.: Relations between the statistics of natural images and the response properties of cortical cells J. Opt. Soc. Am. 4 (1987) 2379–2394Google Scholar
  4. 4.
    Field, D. J.: What is the goal of sensory coding? Neural Comput. 6 (1994) 559–601Google Scholar
  5. 5.
    Kadanoff, L. P.: Scaling laws for ising models near T c Physics 2 (1966) 263–273Google Scholar
  6. 6.
    Gardiner, C. W.: Handbook of Stochastic Methods (Berlin, Heidelberg: Springer) 1983Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Christian Ziegaus
    • 1
  • Elmar W. Lang
    • 1
  1. 1.Institute of BiophysicsUniversity of RegensburgRegensburgGermany

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