Abstract

The effect of contrast gain control mechanisms on discrimination between highly similar simple and complex stimuli is examined, with a focus on how discrimination accuracy changes as a function of the contrast of stimulus components. Two models of contrast gain control are evaluated. In both, the response of each pathway is attenuated by a factor determined by the total activity in a large pool of pathways. One model bases attenuation on the sum of linear filter responses within this pool; the other, based on Heeger’s contrast energy-driven model [J. Neurophysiol. 70, 1885 (1993)], uses squared filter responses. Predictions generated from the models are compared with data from experiments reported here and from the literature. Predictions are made for simple grating stimuli of different sizes and for stimuli to which a second grating component is added either as a second cue or as a mask. With one exception, predictions of the models agree closely with each other and with the data. The exception is a masking study that differentiates the models and supports the filter-driven model over the energy-driven model.

© 1997 Optical Society of America

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  1. D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
    [PubMed]
  2. D. J. Heeger, “Modeling simple-cell direction selectivity with normalized, half-squared, linear operators,” J. Neurophysiol. 70, 1885–1898 (1993).
    [PubMed]
  3. R. L. DeValois, K. K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).
  4. L. A. Olzak, J. P. Thomas, “Seeing spatial patterns,” in Handbook of Perception and Human Performance, Vol. 1: Sensory Processes and Perception, K. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), pp. 7-1– 7-56.
  5. D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
    [PubMed]
  6. W. S. Geisler, D. G. Albrecht, “Bayesian analysis of identification performance in monkey visual cortex: nonlinear mechanisms and stimulus certainty,” Vision Res. 35, 2723–2730 (1995).
    [CrossRef] [PubMed]
  7. M. W. Cannon, S. C. Fullenkamp, “Spatial interactions in apparent contrast: individual differences in enhancement and suppression effects,” Vision Res. 33, 1685–1695 (1993).
    [CrossRef] [PubMed]
  8. C. Chubb, G. Sperling, J. A. Solomon, “Texture interactions determine perceived contrast,” Proc. Natl. Acad. Sci. USA 86, 9631–9635 (1989).
    [CrossRef] [PubMed]
  9. B. Singer, M. D’Zmura, “Color contrast induction,” Vision Res. 34, 3111–3126 (1994).
    [CrossRef] [PubMed]
  10. J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2684 (1993).
    [CrossRef] [PubMed]
  11. C. Chubb, M. S. Landy, “Orthogonal distribution analysis: a new approach to the study of texture perception,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 291–301.
  12. L. A. Olzak, J. P. Thomas, “When orthogonal orientations are not processed independently,” Vision Res. 31, 51–57 (1991).
    [CrossRef] [PubMed]
  13. L. A. Olzak, J. P. Thomas, “Configural effects constrain Fourier models of pattern discrimination,” Vision Res. 32, 1885–1898 (1992).
    [CrossRef] [PubMed]
  14. J. P. Thomas, L. A. Olzak, “Uncertainty experiments support the roles of second-order mechanisms in spatial frequency and orientation discriminations,” J. Opt. Soc. Am. A 13, 689–696 (1996).
    [CrossRef]
  15. J. P. Thomas, “Underlying psychometric function for detecting gratings and identifying spatial frequency,” J. Opt. Soc. Am. 73, 751–758 (1983).
    [CrossRef] [PubMed]
  16. J. M. Foley, “Human luminance pattern-vision mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710–1719 (1994).
    [CrossRef]
  17. J. P. Thomas, L. A. Olzak, “Cue summation in spatial discriminations,” Vision Res. 30, 1865–1875 (1990).
    [CrossRef] [PubMed]
  18. B. G. Smith, J. P. Thomas, “Why are some spatial discriminations independent of contrast?” J. Opt. Soc. Am. A 6, 713–724 (1989).
    [CrossRef] [PubMed]
  19. M. G. Greenlee, “Spatial frequency discrimination of band-limited periodic targets: effects of stimulus contrast, bandwidth and retinal eccentricity,” Vision Res. 32, 275–283 (1992).
    [CrossRef] [PubMed]
  20. D. Regan, S. Bartol, T. J. Murray, K. I. Beverley, “Spatial frequency discrimination in normal vision and in patients with multiple sclerosis,” Brain 105, 735–754 (1982).
    [CrossRef] [PubMed]
  21. M. W. Greenlee, J. P. Thomas, “Effect of pattern adaptation on spatial frequency discrimination,” J. Opt. Soc. Am. A 9, 857–862 (1992).
    [CrossRef] [PubMed]
  22. D. Regan, K. I. Beverley, “Postadaptation orientation discrimination,” J. Opt. Soc. Am. A 2, 147–155 (1985).
    [CrossRef] [PubMed]
  23. S. F. Bowne, “Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination,” Vision Res. 30, 449–461 (1990).
    [CrossRef] [PubMed]
  24. E. L. Howard, “Perception of sinusoidal gratings as a function of Gaussian truncation,” Ph.D. dissertation (University of California, Los Angeles, Los Angeles, Calif., 1989).
  25. G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).
    [CrossRef] [PubMed]
  26. J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
    [CrossRef] [PubMed]
  27. J. P. Thomas, “Independent processing of suprathreshold spatial gratings as a function of their separation in spatial frequency,” J. Opt. Soc. Am. A 6, 1102–1111 (1989).
    [CrossRef] [PubMed]
  28. The derivation of Eq. (7) is sketched here for the energy-driven model. The derivation for the filter-driven model is exactly parallel. Given that test and mask components activate separate groups of pathways and that activity in the gain normalization pool is independent of which test stimulus is presented, and if we proceed from Eq. (6b), Eq. (4) can be factored and rewritten as follows: (8)Ri,j=1c22+∑testg(i)fi,t2+∑maskg(i)fi,m2×∑testwk(i)fi,t2+∑maskwk(i)fi,m2. Equation (5) then takes the following form: (9)d′=k1c22+∑testg(i)fi,t2+∑maskg(i)fi,m2-∑testwα(i)fi,A2+∑maskwα(i)fi,m2-∑testwβ(i)fi,A2+∑maskwβ(i)fi,m2∑testwα(i)fi,B2+∑maskwa(i)fi,m2-∑testwβ(i)fi,B2+∑maskwβ(i)fi,m2=k1c22+∑testg(i)fi,t2+∑maskg(i)fi,m2∑testwα(i)fi,A2-∑testwβ(i)fi,A2-∑testwα(i)fi,B2+∑testwβ(i)fi,B2.  The reciprocals of both sides of Eq. (9) are taken: (10)1d′=c22+∑testg(i)fi,t2+∑maskg(i)fi,m2k1∑testwα(i)fi,A2-∑testwβ(i)fi,A2-∑testwα(i)fi,B2+∑testwβ(i)fi,B2. Taking the difference between this expression when the mask is present and when it is absent yields (11)1dmask′-1dtest′=∑maskg(i)fi,m2k1∑testwα(i)fi,A2-∑testwβ(i)fi,A2-∑testwα(i)fi,B2+∑testwβ(i)fi,B2. Given that only the contrast of the mask component is varied, the variable fi,j can be replaced by the product si,mcmask, where si,m is the sensitivity of the filter in pathway i to the mask component and cmask is the contrast of the mask component. Equation (11) can then be factored and simplified to yield (12)1dmask′-1dtest′=cmask2∑maskg(i)Si,m2k1∑testwα(i)fi,A2-∑testwβ(i)fi,A2-∑testwα(i)fi,B2+∑testwβ(i)fi,B2=k3cmask2.  
  29. M. W. Cannon, S. C. Fullenkamp, “A model for lateral inhibitory interaction in perceived contrast,” Vision Res. 36, 1115–1125 (1996).
    [CrossRef] [PubMed]

1996 (2)

1995 (1)

W. S. Geisler, D. G. Albrecht, “Bayesian analysis of identification performance in monkey visual cortex: nonlinear mechanisms and stimulus certainty,” Vision Res. 35, 2723–2730 (1995).
[CrossRef] [PubMed]

1994 (2)

1993 (3)

J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2684 (1993).
[CrossRef] [PubMed]

M. W. Cannon, S. C. Fullenkamp, “Spatial interactions in apparent contrast: individual differences in enhancement and suppression effects,” Vision Res. 33, 1685–1695 (1993).
[CrossRef] [PubMed]

D. J. Heeger, “Modeling simple-cell direction selectivity with normalized, half-squared, linear operators,” J. Neurophysiol. 70, 1885–1898 (1993).
[PubMed]

1992 (3)

L. A. Olzak, J. P. Thomas, “Configural effects constrain Fourier models of pattern discrimination,” Vision Res. 32, 1885–1898 (1992).
[CrossRef] [PubMed]

M. G. Greenlee, “Spatial frequency discrimination of band-limited periodic targets: effects of stimulus contrast, bandwidth and retinal eccentricity,” Vision Res. 32, 275–283 (1992).
[CrossRef] [PubMed]

M. W. Greenlee, J. P. Thomas, “Effect of pattern adaptation on spatial frequency discrimination,” J. Opt. Soc. Am. A 9, 857–862 (1992).
[CrossRef] [PubMed]

1991 (2)

D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
[PubMed]

L. A. Olzak, J. P. Thomas, “When orthogonal orientations are not processed independently,” Vision Res. 31, 51–57 (1991).
[CrossRef] [PubMed]

1990 (2)

J. P. Thomas, L. A. Olzak, “Cue summation in spatial discriminations,” Vision Res. 30, 1865–1875 (1990).
[CrossRef] [PubMed]

S. F. Bowne, “Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination,” Vision Res. 30, 449–461 (1990).
[CrossRef] [PubMed]

1989 (3)

1985 (1)

1983 (1)

1982 (2)

D. Regan, S. Bartol, T. J. Murray, K. I. Beverley, “Spatial frequency discrimination in normal vision and in patients with multiple sclerosis,” Brain 105, 735–754 (1982).
[CrossRef] [PubMed]

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

1981 (1)

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

1980 (1)

Albrecht, D. G.

W. S. Geisler, D. G. Albrecht, “Bayesian analysis of identification performance in monkey visual cortex: nonlinear mechanisms and stimulus certainty,” Vision Res. 35, 2723–2730 (1995).
[CrossRef] [PubMed]

D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
[PubMed]

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

Bartol, S.

D. Regan, S. Bartol, T. J. Murray, K. I. Beverley, “Spatial frequency discrimination in normal vision and in patients with multiple sclerosis,” Brain 105, 735–754 (1982).
[CrossRef] [PubMed]

Beverley, K. I.

D. Regan, K. I. Beverley, “Postadaptation orientation discrimination,” J. Opt. Soc. Am. A 2, 147–155 (1985).
[CrossRef] [PubMed]

D. Regan, S. Bartol, T. J. Murray, K. I. Beverley, “Spatial frequency discrimination in normal vision and in patients with multiple sclerosis,” Brain 105, 735–754 (1982).
[CrossRef] [PubMed]

Bowne, S. F.

S. F. Bowne, “Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination,” Vision Res. 30, 449–461 (1990).
[CrossRef] [PubMed]

Cannon, M. W.

M. W. Cannon, S. C. Fullenkamp, “A model for lateral inhibitory interaction in perceived contrast,” Vision Res. 36, 1115–1125 (1996).
[CrossRef] [PubMed]

M. W. Cannon, S. C. Fullenkamp, “Spatial interactions in apparent contrast: individual differences in enhancement and suppression effects,” Vision Res. 33, 1685–1695 (1993).
[CrossRef] [PubMed]

Chubb, C.

J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2684 (1993).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, J. A. Solomon, “Texture interactions determine perceived contrast,” Proc. Natl. Acad. Sci. USA 86, 9631–9635 (1989).
[CrossRef] [PubMed]

C. Chubb, M. S. Landy, “Orthogonal distribution analysis: a new approach to the study of texture perception,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 291–301.

D’Zmura, M.

B. Singer, M. D’Zmura, “Color contrast induction,” Vision Res. 34, 3111–3126 (1994).
[CrossRef] [PubMed]

DeValois, K. K.

R. L. DeValois, K. K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).

DeValois, R. L.

R. L. DeValois, K. K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).

Foley, J. M.

Fullenkamp, S. C.

M. W. Cannon, S. C. Fullenkamp, “A model for lateral inhibitory interaction in perceived contrast,” Vision Res. 36, 1115–1125 (1996).
[CrossRef] [PubMed]

M. W. Cannon, S. C. Fullenkamp, “Spatial interactions in apparent contrast: individual differences in enhancement and suppression effects,” Vision Res. 33, 1685–1695 (1993).
[CrossRef] [PubMed]

Geisler, W. S.

W. S. Geisler, D. G. Albrecht, “Bayesian analysis of identification performance in monkey visual cortex: nonlinear mechanisms and stimulus certainty,” Vision Res. 35, 2723–2730 (1995).
[CrossRef] [PubMed]

D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
[PubMed]

Graham, N.

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

Greenlee, M. G.

M. G. Greenlee, “Spatial frequency discrimination of band-limited periodic targets: effects of stimulus contrast, bandwidth and retinal eccentricity,” Vision Res. 32, 275–283 (1992).
[CrossRef] [PubMed]

Greenlee, M. W.

Hamilton, D. B.

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

Heeger, D. J.

D. J. Heeger, “Modeling simple-cell direction selectivity with normalized, half-squared, linear operators,” J. Neurophysiol. 70, 1885–1898 (1993).
[PubMed]

Howard, E. L.

E. L. Howard, “Perception of sinusoidal gratings as a function of Gaussian truncation,” Ph.D. dissertation (University of California, Los Angeles, Los Angeles, Calif., 1989).

Landy, M. S.

C. Chubb, M. S. Landy, “Orthogonal distribution analysis: a new approach to the study of texture perception,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 291–301.

Legge, G. E.

Murray, T. J.

D. Regan, S. Bartol, T. J. Murray, K. I. Beverley, “Spatial frequency discrimination in normal vision and in patients with multiple sclerosis,” Brain 105, 735–754 (1982).
[CrossRef] [PubMed]

Olzak, L. A.

J. P. Thomas, L. A. Olzak, “Uncertainty experiments support the roles of second-order mechanisms in spatial frequency and orientation discriminations,” J. Opt. Soc. Am. A 13, 689–696 (1996).
[CrossRef]

L. A. Olzak, J. P. Thomas, “Configural effects constrain Fourier models of pattern discrimination,” Vision Res. 32, 1885–1898 (1992).
[CrossRef] [PubMed]

L. A. Olzak, J. P. Thomas, “When orthogonal orientations are not processed independently,” Vision Res. 31, 51–57 (1991).
[CrossRef] [PubMed]

J. P. Thomas, L. A. Olzak, “Cue summation in spatial discriminations,” Vision Res. 30, 1865–1875 (1990).
[CrossRef] [PubMed]

L. A. Olzak, J. P. Thomas, “Seeing spatial patterns,” in Handbook of Perception and Human Performance, Vol. 1: Sensory Processes and Perception, K. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), pp. 7-1– 7-56.

Regan, D.

D. Regan, K. I. Beverley, “Postadaptation orientation discrimination,” J. Opt. Soc. Am. A 2, 147–155 (1985).
[CrossRef] [PubMed]

D. Regan, S. Bartol, T. J. Murray, K. I. Beverley, “Spatial frequency discrimination in normal vision and in patients with multiple sclerosis,” Brain 105, 735–754 (1982).
[CrossRef] [PubMed]

Robson, J. G.

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

Singer, B.

B. Singer, M. D’Zmura, “Color contrast induction,” Vision Res. 34, 3111–3126 (1994).
[CrossRef] [PubMed]

Smith, B. G.

Solomon, J. A.

J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2684 (1993).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, J. A. Solomon, “Texture interactions determine perceived contrast,” Proc. Natl. Acad. Sci. USA 86, 9631–9635 (1989).
[CrossRef] [PubMed]

Sperling, G.

J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2684 (1993).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, J. A. Solomon, “Texture interactions determine perceived contrast,” Proc. Natl. Acad. Sci. USA 86, 9631–9635 (1989).
[CrossRef] [PubMed]

Thomas, J. P.

J. P. Thomas, L. A. Olzak, “Uncertainty experiments support the roles of second-order mechanisms in spatial frequency and orientation discriminations,” J. Opt. Soc. Am. A 13, 689–696 (1996).
[CrossRef]

M. W. Greenlee, J. P. Thomas, “Effect of pattern adaptation on spatial frequency discrimination,” J. Opt. Soc. Am. A 9, 857–862 (1992).
[CrossRef] [PubMed]

L. A. Olzak, J. P. Thomas, “Configural effects constrain Fourier models of pattern discrimination,” Vision Res. 32, 1885–1898 (1992).
[CrossRef] [PubMed]

L. A. Olzak, J. P. Thomas, “When orthogonal orientations are not processed independently,” Vision Res. 31, 51–57 (1991).
[CrossRef] [PubMed]

J. P. Thomas, L. A. Olzak, “Cue summation in spatial discriminations,” Vision Res. 30, 1865–1875 (1990).
[CrossRef] [PubMed]

B. G. Smith, J. P. Thomas, “Why are some spatial discriminations independent of contrast?” J. Opt. Soc. Am. A 6, 713–724 (1989).
[CrossRef] [PubMed]

J. P. Thomas, “Independent processing of suprathreshold spatial gratings as a function of their separation in spatial frequency,” J. Opt. Soc. Am. A 6, 1102–1111 (1989).
[CrossRef] [PubMed]

J. P. Thomas, “Underlying psychometric function for detecting gratings and identifying spatial frequency,” J. Opt. Soc. Am. 73, 751–758 (1983).
[CrossRef] [PubMed]

L. A. Olzak, J. P. Thomas, “Seeing spatial patterns,” in Handbook of Perception and Human Performance, Vol. 1: Sensory Processes and Perception, K. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), pp. 7-1– 7-56.

Brain (1)

D. Regan, S. Bartol, T. J. Murray, K. I. Beverley, “Spatial frequency discrimination in normal vision and in patients with multiple sclerosis,” Brain 105, 735–754 (1982).
[CrossRef] [PubMed]

J. Neurophysiol. (2)

D. J. Heeger, “Modeling simple-cell direction selectivity with normalized, half-squared, linear operators,” J. Neurophysiol. 70, 1885–1898 (1993).
[PubMed]

D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (6)

Proc. Natl. Acad. Sci. USA (1)

C. Chubb, G. Sperling, J. A. Solomon, “Texture interactions determine perceived contrast,” Proc. Natl. Acad. Sci. USA 86, 9631–9635 (1989).
[CrossRef] [PubMed]

Vision Res. (11)

B. Singer, M. D’Zmura, “Color contrast induction,” Vision Res. 34, 3111–3126 (1994).
[CrossRef] [PubMed]

J. A. Solomon, G. Sperling, C. Chubb, “The lateral inhibition of perceived contrast is indifferent to on-center/off-center segregation, but specific to orientation,” Vision Res. 33, 2671–2684 (1993).
[CrossRef] [PubMed]

W. S. Geisler, D. G. Albrecht, “Bayesian analysis of identification performance in monkey visual cortex: nonlinear mechanisms and stimulus certainty,” Vision Res. 35, 2723–2730 (1995).
[CrossRef] [PubMed]

M. W. Cannon, S. C. Fullenkamp, “Spatial interactions in apparent contrast: individual differences in enhancement and suppression effects,” Vision Res. 33, 1685–1695 (1993).
[CrossRef] [PubMed]

L. A. Olzak, J. P. Thomas, “When orthogonal orientations are not processed independently,” Vision Res. 31, 51–57 (1991).
[CrossRef] [PubMed]

L. A. Olzak, J. P. Thomas, “Configural effects constrain Fourier models of pattern discrimination,” Vision Res. 32, 1885–1898 (1992).
[CrossRef] [PubMed]

M. G. Greenlee, “Spatial frequency discrimination of band-limited periodic targets: effects of stimulus contrast, bandwidth and retinal eccentricity,” Vision Res. 32, 275–283 (1992).
[CrossRef] [PubMed]

J. P. Thomas, L. A. Olzak, “Cue summation in spatial discriminations,” Vision Res. 30, 1865–1875 (1990).
[CrossRef] [PubMed]

S. F. Bowne, “Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination,” Vision Res. 30, 449–461 (1990).
[CrossRef] [PubMed]

J. G. Robson, N. Graham, “Probability summation and regional variation in contrast sensitivity across the visual field,” Vision Res. 21, 409–418 (1981).
[CrossRef] [PubMed]

M. W. Cannon, S. C. Fullenkamp, “A model for lateral inhibitory interaction in perceived contrast,” Vision Res. 36, 1115–1125 (1996).
[CrossRef] [PubMed]

Visual Neurosci. (1)

D. G. Albrecht, W. S. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
[PubMed]

Other (5)

R. L. DeValois, K. K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).

L. A. Olzak, J. P. Thomas, “Seeing spatial patterns,” in Handbook of Perception and Human Performance, Vol. 1: Sensory Processes and Perception, K. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), pp. 7-1– 7-56.

C. Chubb, M. S. Landy, “Orthogonal distribution analysis: a new approach to the study of texture perception,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 291–301.

The derivation of Eq. (7) is sketched here for the energy-driven model. The derivation for the filter-driven model is exactly parallel. Given that test and mask components activate separate groups of pathways and that activity in the gain normalization pool is independent of which test stimulus is presented, and if we proceed from Eq. (6b), Eq. (4) can be factored and rewritten as follows: (8)Ri,j=1c22+∑testg(i)fi,t2+∑maskg(i)fi,m2×∑testwk(i)fi,t2+∑maskwk(i)fi,m2. Equation (5) then takes the following form: (9)d′=k1c22+∑testg(i)fi,t2+∑maskg(i)fi,m2-∑testwα(i)fi,A2+∑maskwα(i)fi,m2-∑testwβ(i)fi,A2+∑maskwβ(i)fi,m2∑testwα(i)fi,B2+∑maskwa(i)fi,m2-∑testwβ(i)fi,B2+∑maskwβ(i)fi,m2=k1c22+∑testg(i)fi,t2+∑maskg(i)fi,m2∑testwα(i)fi,A2-∑testwβ(i)fi,A2-∑testwα(i)fi,B2+∑testwβ(i)fi,B2.  The reciprocals of both sides of Eq. (9) are taken: (10)1d′=c22+∑testg(i)fi,t2+∑maskg(i)fi,m2k1∑testwα(i)fi,A2-∑testwβ(i)fi,A2-∑testwα(i)fi,B2+∑testwβ(i)fi,B2. Taking the difference between this expression when the mask is present and when it is absent yields (11)1dmask′-1dtest′=∑maskg(i)fi,m2k1∑testwα(i)fi,A2-∑testwβ(i)fi,A2-∑testwα(i)fi,B2+∑testwβ(i)fi,B2. Given that only the contrast of the mask component is varied, the variable fi,j can be replaced by the product si,mcmask, where si,m is the sensitivity of the filter in pathway i to the mask component and cmask is the contrast of the mask component. Equation (11) can then be factored and simplified to yield (12)1dmask′-1dtest′=cmask2∑maskg(i)Si,m2k1∑testwα(i)fi,A2-∑testwβ(i)fi,A2-∑testwα(i)fi,B2+∑testwβ(i)fi,B2=k3cmask2.  

E. L. Howard, “Perception of sinusoidal gratings as a function of Gaussian truncation,” Ph.D. dissertation (University of California, Los Angeles, Los Angeles, Calif., 1989).

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Figures (8)

Fig. 1
Fig. 1

Matrices used in the simulations. See text for explanation.

Fig. 2
Fig. 2

Predicted accuracy versus contrast functions for discrimination between simple gratings. The difference to be discriminated is twice as large for the upper curves as for the lower curves. (a) Prediction of the filter-driven model, (b) prediction of the energy model.

Fig. 3
Fig. 3

Effect of stimulus size. The dashed curves are for the larger stimulus; the solid curves, for the smaller one. (a) Prediction of the energy model, (b) observed results for subject SSS (2.94 versus 3.06 c/deg), (c) results for subject LDC (2.89 versus 3.11 c/deg).  

Fig. 4
Fig. 4

Effect of adding a second component as a cue. The dashed curves are for the two-component, two-cue condition; the solid curves are for the single-component, single-cue condition. (a) Prediction of the energy model, (b) results for subject LAO (2.93 versus 3.07 c/deg), (c) results for subject JPT (2.92 versus 3.08 c/deg).

Fig. 5
Fig. 5

Effect of adding a second component as a mask. The solid curves, with filled triangles, are for the unmasked control condition. The long-dashed curves, with filled squares, are for the parallel mask condition. The short-dashed curves, with open squares, are for the orthogonally oriented mask condition. (a) Prediction of the energy model, (b) results for subject LAO (2.93 versus 3.07), (c) results for subject JPT (2.92 versus 3.08).

Fig. 6
Fig. 6

Bandwidth of the gain control pool. Masking effect, as defined in the text, is shown as a function of the separation in spatial frequency of test and mask components. Filled triangles:contrast discrimination, parallel mask and test components (data from Thomas27). Filled squares: spatial-frequency discrimination, parallel mask and test components (data from Fig. 5 and Thomas27). Open squares: spatial-frequency discrimination, orthogonal mask, and test components (data from Fig. 5). Open circle: orientation discrimination, vertical mask, and test tilted approximately ±1 deg from vertical (data from Olzak and Thomas13).

Fig. 7
Fig. 7

Effect of mask contrast. Filled triangles: contrast of test component, 0.0375. Open circles: test contrast, 0.05. Filled squares: test contrast, 0.075. (a) Results for subject SST, (b) results for subject JPT, (c) results for subject JLG.

Fig. 8
Fig. 8

Derived contribution of mask component to the gain control pool as a function of mask contrast. Data for (a) subject SST and (b) subject JPT. Filled triangles: contrast of test component, 0.0375. Open circles: test contrast, 0.05. Filled squares: test contrast, 0.075.

Equations (14)

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fi,j=Si(x, y)lj(x, y)dxdy,
ri,j=fi,jc1+ig(i)fi,j fi,j2(ssc2+fi,j2),
ri,j=fi,j2c22+ig(i)fi,j2,
Rk,j=wk(i)ri,j,
dv=Rα-Rβ,
d=k1[(dv|A)-(dv|B)]=k1[(Rα,A-Rβ,A)-(Rα,B-Rβ,B)],
ri,j=fi,jc1+testg(i)fi,t+maskg(i)fi,m×fi,j2(ssc2+fi,j2)=1c1+testg(i)fi,t+maskg(i)fi,m×fi,j3(ssc2+fi,j2),
ri,j=fi,j2c22+testg(i)fi,t2+maskg(i)fi,m2=1c22+testg(i)fi,t2+maskg(i)fi,m2,
1dm-1dt=k3cmaskq,
Ri,j=1c22+testg(i)fi,t2+maskg(i)fi,m2×testwk(i)fi,t2+maskwk(i)fi,m2.
d=k1c22+testg(i)fi,t2+maskg(i)fi,m2-testwα(i)fi,A2+maskwα(i)fi,m2-testwβ(i)fi,A2+maskwβ(i)fi,m2testwα(i)fi,B2+maskwa(i)fi,m2-testwβ(i)fi,B2+maskwβ(i)fi,m2=k1c22+testg(i)fi,t2+maskg(i)fi,m2testwα(i)fi,A2-testwβ(i)fi,A2-testwα(i)fi,B2+testwβ(i)fi,B2.
1d=c22+testg(i)fi,t2+maskg(i)fi,m2k1testwα(i)fi,A2-testwβ(i)fi,A2-testwα(i)fi,B2+testwβ(i)fi,B2.
1dmask-1dtest=maskg(i)fi,m2k1testwα(i)fi,A2-testwβ(i)fi,A2-testwα(i)fi,B2+testwβ(i)fi,B2.
1dmask-1dtest=cmask2maskg(i)Si,m2k1testwα(i)fi,A2-testwβ(i)fi,A2-testwα(i)fi,B2+testwβ(i)fi,B2=k3cmask2.

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