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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 7 — Jul. 1, 1999
  • pp: 1549–1553

Higher-order structure in natural scenes

Mitchell G. A. Thomson  »View Author Affiliations

JOSA A, Vol. 16, Issue 7, pp. 1549-1553 (1999)

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Real-world visual scenes display consistent first- and second-order statistical regularities to which visual neural representations may be perceptually matched, but these lower-order regularities stem from constraints on image power spectra, which appear to carry much less perceptual information than image phase spectra. Natural scenes are shown also to display consistent higher-order statistical regularities, and an analysis of these regularities in terms of fourth-order spectra shows that they are strongly dependent on spatial frequency. These findings have important consequences for the design of a visual system that aims to maximize sparseness in neural representations.

© 1999 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(110.2960) Imaging systems : Image analysis
(330.4060) Vision, color, and visual optics : Vision modeling
(330.6110) Vision, color, and visual optics : Spatial filtering

Original Manuscript: November 5, 1998
Revised Manuscript: March 11, 1999
Manuscript Accepted: March 11, 1999
Published: July 1, 1999

Mitchell G. A. Thomson, "Higher-order structure in natural scenes," J. Opt. Soc. Am. A 16, 1549-1553 (1999)

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  1. 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). [CrossRef] [PubMed]
  2. L. N. Piotrowski, F. W. Campbell, “A demonstration of the visual importance and flexibility of spatial-frequency amplitude and phase,” Perception 11, 337–346 (1982). [CrossRef] [PubMed]
  3. The term “conventional nth-order statistics” is used here to describe statistics derived from standard nth-order correlation functions; these are not the same as the statistics defined by Julesz and colleagues.4 This study deals only with the former, although the two are closely related.
  4. G. Julesz, E. N. Gilbert, L. A. Shepp, H. L. Frisch, “Inability of humans to discriminate between visual textures that agree in second-order statistics revisited,” Perception 2, 391–405 (1973). [CrossRef]
  5. H. B. Barlow, “What is the computational goal of the neocortex?” in Large-Scale Neuronal Theories of the Brain, C. Koch, ed. (MIT Press, Cambridge, Mass., 1994).
  6. D. J. Field, “What is the goal of sensory coding?” Neural Comput. 6, 559–601 (1994). [CrossRef]
  7. R. J. Baddeley, “Searching for filters with ‘interesting’ output distributions: an uninteresting direction to explore?” Network Comput. Neural Syst. 7, 409–421 (1996). [CrossRef]
  8. R. J. Baddeley, “An efficient code in V1?” Nature (London) 381, 560–561 (1996). [CrossRef]
  9. M. G. A. Thomson, D. H. Foster, “The role of second- and third-order statistics in the discriminability of natural images,” J. Opt. Soc. Am. A 14, 2081–2090 (1997). [CrossRef]
  10. Arguments are often made for incorporating some sort of spectral windowing into the whitening process such that low-amplitude components near the Nyquist limit are given relatively less power (for example, to avoid the effects of rectangular sampling in the frequency domain or to avoid boosting noise at high frequency). In analyses of coherence measures, however, the value of such windowing is unclear; windowing was therefore avoided here.
  11. C. Nikias, A. Petropolu, Higher-Order Spectra Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1996).
  12. C. Zetzsche, E. Barth, B. Wegmann, “The importance of intrinsically two-dimensional image features in biological vision and picture coding,” in Digital Images and Human Vision, A. B. Watson, ed. (MIT Press, Cambridge, Mass., 1993).
  13. J. J. Atick, N. A. Redlich, “What does the retina know about natural scenes?” Neural Comput. 4, 196–210 (1992). [CrossRef]
  14. E. Switkes, M. J. Mayer, J. A. Sloan, “Spatial-frequency analysis of the visual environment: anisotropy and the carpentered environment hypothesis,” Vision Res. 18, 1393–1399 (1978). [CrossRef]
  15. M. C. Morrone, D. C. Burr, “Feature detection in human vision: a phase-dependent energy model,” Proc. R. Soc. London, Ser. B 235, 221–24 (1988). [CrossRef]
  16. B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive-field properties by learning a sparse code for natural scenes,” Nature (London) 381, 607–609 (1996). [CrossRef]

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