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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 1 — Jan. 1, 2003
  • pp: 56–66

Local correlations, information redundancy, and sufficient pixel depth in natural images

Yury Petrov and L. Zhaoping  »View Author Affiliations


JOSA A, Vol. 20, Issue 1, pp. 56-66 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000056


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Abstract

A mathematical framework that permits the factorization of a joint probability distribution into its localized components for a two-dimensional array of pixels is presented. The factorization was used to estimate the contribution to mutual information of two- (I2) and three-pixel (I3) luminance correlations for a large ensemble of natural images analyzed at various spatial scales and pixel depths b. It is shown that both I2 and I3 saturate at b ~ 6 bits per pixel. Three-pixel correlations are shown to produce only a marginal increase of information redundancy (4%) over two-pixel correlations (50%). Implications for neural representation in visual cortex are discussed.

© 2003 Optical Society of America

OCIS Codes
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(110.2960) Imaging systems : Image analysis
(200.3050) Optics in computing : Information processing
(330.4270) Vision, color, and visual optics : Vision system neurophysiology

Citation
Yury Petrov and L. Zhaoping, "Local correlations, information redundancy, and sufficient pixel depth in natural images," J. Opt. Soc. Am. A 20, 56-66 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-1-56


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References

  1. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J. 27, 379–423 (1948).
  2. E. R. Kretzmer, “Statistics of television signals,” Bell Syst. Tech. J. 31, 751–763 (1952).
  3. W. F. Schreiber, “The measurement of third-order probability distributions of television signals,” IRE Trans. Inf. Theory IT-2, 94–105 (1956).
  4. J. R. Parks, “Prediction and entropy of half-tone pictures,” Behav. Sci. 10, 436–445 (1965).
  5. N. S. Tzannes, R. V. Spencer, and A. J. Kaplan, “On estimating the entropy of random fields,” Inf. Control. 16, 1–6 (1970).
  6. F. Attneave, “Some information aspects of visual perception,” Psychol. Rev. 61, 183–193 (1954).
  7. H. B. Barlow, “Possible principles underlying the transformation of sensory messages,” in Sensory Communication, W. A. Rosenblith, ed. (MIT, Cambridge, Mass., 1961).
  8. J. J. Atick, “Could information theory provide an ecological theory of sensory processing?” Network 3, 213–251 (1992).
  9. H. B. Barlow and P. Foldiak, The Computing Neuron (Addison-Wesley, Reading, Mass., 1989).
  10. S. Watanabe, “Pattern recognition as a quest for minimum entropy,” Pattern Recognition 13, 381–387 (1981).
  11. S. Watanabe, Pattern Recognition: Human and Mechanical (Wiley, New York, 1985).
  12. S. B. Laughlin, “A simple coding procedure enhances a neuron’s information capacity,” Z. Naturforsch. 36, 910–912 (1981).
  13. J. J. Atick and A. N. Redlich, “Towards a theory of early visual processing,” Neural Comput. 2, 308–320 (1990).
  14. J. J. Atick, Z. Li, and A. N. Redlich, “Understanding retinal color coding from first principles,” Neural Comput. 4, 559–572 (1992).
  15. J. J. Atick and A. N. Redlich, “What does the retina know about the natural scenes?” Neural Comput. 4, 196–210 (1992).
  16. Zh. Li and J. J. Atick, “Towards a theory of the striate cortex,” Neural Comput. 6, 127–146 (1994).
  17. A. J. Bell and T. J. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
  18. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
  19. J. G. Daugman, “Entropy reduction and decorrelation in visual coding by oriented neural receptive fields,” IEEE Trans. Biomed. Eng. 36, 107–114 (1989).
  20. D. J. Field, “What is the goal of sensory coding?” Neural Comput. 6, 559–601 (1994).
  21. C. Jutten and J. Herault, “Blind separation of sources, part i: An adaptive algorithm based on neuromimetic architecture,” Signal Process. 24, 1–10 (1991).
  22. A. Hyvärinen and E. Oja, “Independent component analy- sis: algorithms and applications,” Neural Networks 13, 411–430 (2000).
  23. J. H. van Hateren and A. van der Schaaf, “Independent component filters of natural images compared with simple cells in primary visual cortex,” Proc. R. Soc. London Ser. B 265, 359–366 (1998).
  24. A. Hyvärinen and P. O. Hoyer, “Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces,” Neural Comput. 12, 1705–1720 (2000).
  25. B. A. Olshausen and D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature 381, 607–609 (1996).
  26. B. A Olshausen and D. J. Field, “Sparse coding with an overcomplete basis set: a strategy employed by V1?” Vision Res. 37, 3311–3325 (1997).
  27. M. G. A. Thomson, “Higher-order structure in natural scenes,” J. Opt. Soc. Am. A 16, 1549–1553 (1999).
  28. M. G. A. Thomson, “Beats, kurtosis and visual coding,” Network Comput. Neural Syst. 12, 271–287 (2001).
  29. A. B. Lee, K. S. Pedersen, and D. Mumford, “The complex statistics of high-contrast patches in natural images,” presented at the IEEE Workshop on Statistical and Computational Theories of Vision, Vancouver, Canada, 2001; http://www.cis.ohio-state.edu/szhu/SCTV2001.html
  30. N. G. Deriugin, “The power spectrum and the correlation function of the television signal,” Telecommunications 1, 1–12 (1957).
  31. D. J. Tolhurst, Y. Tadmor, and T. Chao, “Amplitude spectra of natural images,” Ophthalmic Physiol. Opt. 12, 229–232 (1992).
  32. D. L. Ruderman, “The statistics of natural images,” Network 5, 517–548 (1994).
  33. D. Kersten, “Predictability and redundancy in natural images,” J. Opt. Soc. Am. A 4, 2395–2400 (1987).

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