Biological Cybernetics

, Volume 38, Issue 3, pp 171–178 | Cite as

A transducer function for threshold and suprathreshold human vision

  • Hugh R. Wilson


A nonlinear function is derived to describe the contrast transduction process for human visual mechanisms. This function is sigmoid in form, having an accelerating nonlinearity at low contrasts and a compressive nonlinearity at high contrasts. The resulting formulation is consistent with both signal detection theory and with Quick's (1974) equation for probability summation. Similarities between the present description of human vision and properties of complex cells in cat visual cortex are noted.


Visual Cortex Signal Detection Nonlinear Function Complex Cell Detection Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bergen, J.B., Wilson, H.R., Cowan, J.D.: Further evidence for four mechanisms mediating vision at threshold: sensitivities to complex gratings and aperiodic stimuli. J. Opt. Soc. Am. 69, 1580–1587 (1979)Google Scholar
  2. Fechner, G.: Elements of psychophysics. Adler, H.E. (ed.). New York: Holt, Rinehart, and Winston 1966Google Scholar
  3. Giese, S.C.: A model of suprathreshold contrast perception in the human visual system. Unpublished dissertation, University of Chicago 1977Google Scholar
  4. Green, D.M., Swets, J.A.: Signal detection theory and psychophysics. New York: John Wiley & Sons 1966Google Scholar
  5. Kelly, D.H.: Theory of flicker and transient responses. II. Counterphase gratings. J. Opt. Soc. Am. 61, 632–640 (1971)Google Scholar
  6. King-Smith, P.E., Kulikowski, J.J.: The detection of gratings by independent activation of line detectors. J. Physiol. (London) 247, 237–271 (1975)Google Scholar
  7. Kulikowski, J.J., Gorea, A.: Complete adaptation to patterned stimuli: a necessary and sufficient condition for Weber's law for contrast. Vision Res. 18, 1223–1228 (1978)Google Scholar
  8. Legge, G.E., Foley, J.M.: Contrast masking in human vision (submitted for publication) (1980)Google Scholar
  9. Legge, G.E.: Spatial frequency masking in human vision: binocular interactions. J. Opt. Soc. Am. 69, 838–847 (1979)Google Scholar
  10. Luce, R.D.: Detection and recognition. In: Handbook of mathematical psychology, Vol. 1, p. 103–189. Luce, R.D., Bush, R.R., Galanter, E. (eds.). New York: John Wiley & Sons 1963Google Scholar
  11. Maffei, L., Fiorentini, A.: The visual cortex as a spatial frequency analyser. Vision Res. 13, 1255–1268 (1973)Google Scholar
  12. Maudarbocus, A.Y., Ruddock, K.H.: Non-linearity of visual signals in relation to shape-sensitive adaptation responses. Vision Res. 13, 1713–1737 (1973)Google Scholar
  13. Movshon, J.A., Thompson, I.D., Tolhurst, K.J.: Receptive field organization of complex cells in the cat's striate cortex. J. Physiol. (London) 283, 79–99 (1978)Google Scholar
  14. Nachmias, J., Sansbury, R.V.: Grating contrast: discrimination may be better than detection. Vision Res. 14, 1039–1042 (1974)Google Scholar
  15. Nachmias, J.: Signal detection theory and its applications to problems in vision. In: Handbook of sensory physiology, Vol. VII/4: Visual psychophysics, pp. 56–78. Hurvich, L.M., Jameson, D. (eds.). Berlin, Heidelberg, New York: Springer 1972Google Scholar
  16. Nachmias, J.: On the psychometric function for contrast detection (submitted for publication) (1980)Google Scholar
  17. Quick, R.F.: A vector-magnitude model for contrast detection. Kybernetik 16, 65–67 (1974)Google Scholar
  18. Robson, J.G., Graham, N.: Probability summation and regional variation in sensitivity across the visual field. Suppl. to Investigative Ophthalmology and Visual Science: ARVO, 1978, p. 221Google Scholar
  19. Stromeyer, C.F., Klein, S.: Spatial frequency channels in human vision as asymmetric (edge) mechanisms. Vision Res. 14, 1409–1420 (1974)Google Scholar
  20. Stromeyer, C.F., Klein, S.: Evidence against narrow-band spatial frequency channels in human vision: the detectability of frequency modulated gratings. Vision Res. 15, 899–910 (1975)Google Scholar
  21. Swets, J.A. (ed.): Signal detection and recognition by human observers: contemporary readings. New York: John Wiley & Sons 1964Google Scholar
  22. Tanner, W.P.: Theory of recognition. In: Signal detection and recognition by human observers, pp. 413–430. Swets, J.A. (ed.). New York: John Wiley & Sons 1964Google Scholar
  23. Thomas, J.P., Barker, R.A., Gille, J.: A multidimensional space model for detection and discrimination of spatial patterns. Proceedings of the Tenths Annual Pittsburgh Conference on Modeling and Simulation. Vogt., W.G., Mickle, M.H. (eds.). Instrum. Soc. Am. 10, 201–207 (1978)Google Scholar
  24. Williams, D.W., Wilson, H.R.: Spatial frequency adaptation and spatial probability summation (manuscript in preparation) (1980)Google Scholar
  25. Williams, D.W., Wilson, H.R., Cowan, J.D.: Localized effects of spatial frequency adaptation (manuscript in preparation) (1980)Google Scholar
  26. Wilson, H.R.: Hysteresis in binocular grating perception: contrast effects. Vision Res. 17, 843–851 (1977)Google Scholar
  27. Wilson, H.R.: Quantitative characterization of two types of line spread function near the fovea. Vision Res. 18, 971–981 (1978)Google Scholar
  28. Wilson, H.R.: Nonlinear interactions in binocular vision. Proceedings of the Pittsburgh Conference on Modeling and Simulation, 1979Google Scholar
  29. Wilson, H.R.: Spatiotemporal characterization of a transient mechanism in the human visual system. Vision Res. 20, 443–452 (1980)Google Scholar
  30. Wilson, H.R., Bergen, J.: A four mechanism model for threshold spatial vision. Vision Res. 19, 19–32 (1979)Google Scholar
  31. Wilson, H.R., Cowan, J.D.: Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12, 1–24 (1972)Google Scholar
  32. Wilson, H.R., Cowan, J.D.: A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13, 55–80 (1973)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Hugh R. Wilson
    • 1
  1. 1.Department of Biophysics and Theoretical BiologyThe University of ChicagoChicagoUSA

Personalised recommendations