OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 8 — Aug. 1, 1998
  • pp: 2036–2045

Statistics of cone responses to natural images: implications for visual coding

Daniel L. Ruderman, Thomas W. Cronin, and Chuan-Chin Chiao  »View Author Affiliations

JOSA A, Vol. 15, Issue 8, pp. 2036-2045 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (413 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We gathered hyperspectral images of natural, foliage-dominated scenes and converted them to human cone quantal catches to characterize the second-order redundancy present within the retinal photoreceptor array under natural conditions. The data are expressed most simply in a logarithmic response space, wherein an orthogonal decorrelation robustly produces three principal axes, one corresponding to simple changes in radiance and two that are reminiscent of the blue–yellow and red–green chromatic-opponent mechanisms found in the primate visual system. Further inclusion of spatial stimulus dimensions demonstrates a complete spatial decorrelation of these three cone-space axes in natural cone responses.

© 1998 Optical Society of America

OCIS Codes
(120.5630) Instrumentation, measurement, and metrology : Radiometry
(330.1720) Vision, color, and visual optics : Color vision
(330.4060) Vision, color, and visual optics : Vision modeling
(330.5310) Vision, color, and visual optics : Vision - photoreceptors

Original Manuscript: December 11, 1997
Revised Manuscript: April 7, 1998
Manuscript Accepted: April 9, 1998
Published: August 1, 1998

Daniel L. Ruderman, Thomas W. Cronin, and Chuan-Chin Chiao, "Statistics of cone responses to natural images: implications for visual coding," J. Opt. Soc. Am. A 15, 2036-2045 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Attneave, “Some informational aspects of visual perception,” Psychol. Rev. 61, 183–193 (1954). [CrossRef] [PubMed]
  2. H. B. Barlow, “Possible principles underlying the transformation of sensory messages,” in Sensory Communication, W. A. Rosenblith, ed. (MIT Press, Cambridge, Mass., 1961).
  3. M. V. Srinivasan, S. B. Laughlin, A. Dubs, “Predictive coding: a fresh view of inhibition in the retina,” Proc. R. Soc. London, Ser. B 216, 427–459 (1982). [CrossRef]
  4. J. J. Atick, N. Redlich, “Towards a theory of early visual processing,” Neural Comput. 2, 308–320 (1990). [CrossRef]
  5. B. A. Olshausen, D. J. Field, “Emergence of simple-cell receptive field properties by learning a sparse code for natural images,” Nature (London) 381, 607–609 (1996). [CrossRef]
  6. G. J. Burton, I. R. Moorhead, “Color and spatial structure in natural scenes,” Appl. Opt. 26, 157–170 (1987). [CrossRef] [PubMed]
  7. 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]
  8. J. H. van Hateren, “Theoretical predictions of spatiotemporal receptive fields of fly LMCs, and experimental validation,” J. Comp. Physiol. A 171, 157–170 (1992).
  9. D. L. Ruderman, W. Bialek, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994). [CrossRef] [PubMed]
  10. D. L. Ruderman, “The statistics of natural images,” Network 5, 517–548 (1994). [CrossRef]
  11. D. W. Dong, J. J. Atick, “Statistics of natural time-varying images,” Network 6, 345–358 (1995). [CrossRef]
  12. N. G. Nagle, D. Osorio, “The tuning of human photopigments may minimize red–green chromatic signals in natural conditions,” Proc. R. Soc. London, Ser. B 252, 209–213 (1993). [CrossRef]
  13. G. Brelstaff, A. Párraga, T. Troscianko, D. Carr, “Hyperspectral camera system: acquisition and analysis,” in Geographic Information Systems, Photogrammetry, and Geological/Geophysical Remote Sensing, J. B. Lurie, J. Pearson, E. Zilioli, eds., Proc. SPIE2587, 150–159 (1995). [CrossRef]
  14. M. A. Webster, J. D. Mollon, “Adaptation and the color statistics of natural images,” Vision Res. 37, 3283–3298 (1997). [CrossRef]
  15. C. A. Párraga, G. Brelstaff, T. Troscianko, “Color and luminance information in natural scenes,” J. Opt. Soc. Am. A 15, 563–569 (1998). [CrossRef]
  16. G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colour coding and optimum colour information transmission in the retina,” Proc. R. Soc. London, Ser. B 220, 89–113 (1983). [CrossRef]
  17. D. L. Ruderman, “Designing receptive fields for highest fidelity,” Network 5, 147–155 (1994). [CrossRef]
  18. A. Stockman, D. I. A. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993). [CrossRef]
  19. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).
  20. D. R. J. Laming, Sensory Analysis (Academic, London, 1986).
  21. D. L. Ruderman, “Origins of scaling in natural images,” Vision Res. 37, 3385–3398 (1997). [CrossRef]
  22. I. T. Jolliffe, Principal Component Analysis (Springer-Verlag, New York, 1986).
  23. P. Flanagan, P. Cavanagh, O. E. Favreau, “Independent orientation-selective mechanisms for the cardinal directions of colour space,” Vision Res. 30, 769–778 (1990). [CrossRef] [PubMed]
  24. F. M. DeMonasterio, P. Gouras, “Functional properties of ganglion cells of the rhesus monkey retina,” J. Physiol. (London) 251, 167–195 (1975).
  25. F. M. DeMonasterio, P. Gouras, D. J. Tolhurst, “Trichromatic colour opponency in ganglion cells of the rhesus monkey retina,” J. Physiol. (London) 251, 197–216 (1975).
  26. A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).
  27. R. C. Reid, R. M. Shapley, “Spatial structure of cone inputs to receptive fields in primate lateral geniculate nucleus,” Nature (London) 356, 716–718 (1992). [CrossRef]
  28. E. Hering, Outlines of a Theory of the Light Sense (Harvard U. Press, Cambridge, Mass., 1964).
  29. D. Jameson, L. M. Hurvich, “Some quantitative aspects of an opponent-colors theory. I. Chromatic responses and spectral saturation,” J. Opt. Soc. Am. 45, 546–552 (1955). [CrossRef]
  30. J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982). [CrossRef] [PubMed]
  31. M. A. Webster, “Human colour perception and its adaptation,” Network 7, 587–634 (1996). [CrossRef]
  32. P. Lennie, M. D’Zmura, “Mechanisms of color vision,” CRC Crit. Rev. Clin. Neurobiol. 3, 333–400 (1988).
  33. J. H. van Hateren, “Spatial, temporal and spectral pre-processing for colour vision,” Proc. R. Soc. London, Ser. B 251, 61–68 (1993). [CrossRef]
  34. Translation invariance implies that correlations depend only on pixel separations. From scale invariance the correlation matrix in the cone subspace is not a function of the pixel separation (up to an overall multiplicative factor). Thus the correlation matrix is of the form F(x)Cab, where x is the pixel separation vector and a and b are index cone-space directions. Such a correlation matrix can be diagonalized through a Fourier transform in the variable x and a separate diagonalization of the matrix C (yielding the l,α, and β directions). The associated eigenvalues will be a product of the F (spatial) eigenvalues and the C (cone-space) eigenvalues, as in Eq. (6). This is analogous to two decorrelated multiplicative processes, one in real space and the other in cone space.
  35. This invariance of the spectral shape is consistent with the hypothesis that spatial statistics in natural images are dominated by the size distribution of objects within the scenes.21
  36. J. J. Atick, Z. Li, A. N. Redlich, “Understanding retinal color coding from first principles,” Neural Comput. 4, 559–572 (1992). [CrossRef]
  37. J. B. Derrico, G. Buchsbaum, “A computational model of spatiochromatic image coding in early vision,” J. Visual Commun. Image Represent. 2, 31–38 (1991). [CrossRef]
  38. I. R. Moorhead, “Human color vision and natural images,” in Colour in Information Technology and Information Displays (Institution of Electronic and Radio Engineers, London, 1985).
  39. J. J. Vos, P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971). [CrossRef] [PubMed]
  40. W. S. Stiles, “Color vision: the approach through increment threshold sensitivity,” Proc. Natl. Acad. Sci. USA 45, 100–114 (1959). [CrossRef]
  41. D. R. Williams, D. I. A. MacLeod, M. M. Hayhoe, “Foveal tritanopia,” Vision Res. 21, 1341–1356 (1981). [CrossRef] [PubMed]
  42. D. Osorio, M. Vorobyev, “Colour vision as an adaptation to frugivory in primates,” Proc. R. Soc. London, Ser. B 263, 593–599 (1996). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited