Abstract

The accuracy of some spatial discriminations, including spatial frequency and orientation, is independent of the contrasts of the stimuli discriminated except when contrasts are near the detection threshold. This fact is surprising because higher contrasts should improve signal-to-noise ratios and performance. Two alternative explanations of this puzzle are examined, using a signal-detection-theory vector model: (1) noise increases with stimulus contrast in such a way that signal-to-noise ratios remain constant; (2) noise is constant, but the difference signal generated by each individual tuned mechanism is independent of contrast because the response function of the mechanism becomes compressive (approximately logarithmic) at a low contrast. The alternative explanations generate different predictions, which have been tested in several experiments. The results reject alternative (1) as a model of suprathreshold discrimination and give mixed support to alternative (2).

© 1989 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. A. Burgess, “Visual signal detection. III. On Bayesian use of prior knowledge and cross correlation,” J. Opt. Soc. Am. A 2, 1498–1507 (1985).
    [CrossRef] [PubMed]
  8. D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508–1532 (1985).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. H. R. Wilson, “A transducer function for threshold and supra-threshold human vision,” Biol. Cybernet. 38, 171–178 (1980).
    [CrossRef]
  13. W. P. Tanner, “Theory of recognition,”J. Acoust. Soc. Am. 28, 882–888 (1956).
    [CrossRef]
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  16. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Kreiger, New York, 1974).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  20. B. G. Smith, “The psychometric function for contrast discrimination,” dissertation (University of California, Los Angeles, Los Angeles, California, 1986).
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    [PubMed]
  27. E. Kaplan, R. M. Shapley, “The primate retina contains two types of ganglion cells, with high and low contrast sensitivity,” Proc. Natl. Acad. Sci. USA 83, 2755–2757 (1986).
    [CrossRef] [PubMed]
  28. W. H. Swanson, H. R. Wilson, S. C. Geise, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
    [CrossRef] [PubMed]
  29. D. J. Gelb, H. R. Wilson, “Shifts in perceived size as a function of contrast and temporal modulation,” Vision Res. 23, 71–82 (1983).
    [CrossRef] [PubMed]
  30. E. T. Davis, P. Kramer, D. Yager, “Shifts in perceived spatial frequency of low contrast stimuli: data and theory,” J. Opt. Soc. Am. A 3, 1189–1202 (1986).
    [CrossRef] [PubMed]
  31. M. W. Cannon, “Perceived contrast in the fovea and periphery,” J. Opt. Soc. Am. A 2, 1760–1768 (1985).
    [CrossRef] [PubMed]

1987 (1)

1986 (4)

H. R. Wilson, “Responses of spatial mechanisms can explain hyperacuity,” Vision Res. 26, 453–469 (1986).
[CrossRef] [PubMed]

T. E. Cohn, D. J. Lasley, “Visual Sensitivity,” Ann. Rev. Psychol. 37, 495–521 (1986).
[CrossRef]

E. Kaplan, R. M. Shapley, “The primate retina contains two types of ganglion cells, with high and low contrast sensitivity,” Proc. Natl. Acad. Sci. USA 83, 2755–2757 (1986).
[CrossRef] [PubMed]

E. T. Davis, P. Kramer, D. Yager, “Shifts in perceived spatial frequency of low contrast stimuli: data and theory,” J. Opt. Soc. Am. A 3, 1189–1202 (1986).
[CrossRef] [PubMed]

1985 (5)

1984 (5)

1983 (2)

D. J. Gelb, H. R. Wilson, “Shifts in perceived size as a function of contrast and temporal modulation,” Vision Res. 23, 71–82 (1983).
[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]

1982 (1)

1981 (1)

G. Westheimer, “Visual hyperacuity,” Prog. Sensory Physiol. 1, 1–30 (1981).
[CrossRef]

1980 (2)

G. E. Legge, J. M. Foley, “Contrast masking in human vision,”J. Opt. Soc. Am. 70, 1458–1471 (1980).
[CrossRef] [PubMed]

H. R. Wilson, “A transducer function for threshold and supra-threshold human vision,” Biol. Cybernet. 38, 171–178 (1980).
[CrossRef]

1979 (1)

1974 (2)

1970 (1)

1967 (1)

L. W. Nolte, D. Jaarsma, “More on the detection of one of M orthogonal signals,”J. Acoust. Soc. Am. 41, 497–505 (1967).
[CrossRef]

1961 (1)

J. A. Swets, W. P. Tanner, T. G. Birdsall, “Decision processes in perception,” Psychol. Rev. 68, 301–340 (1961).
[CrossRef] [PubMed]

1956 (1)

W. P. Tanner, “Theory of recognition,”J. Acoust. Soc. Am. 28, 882–888 (1956).
[CrossRef]

Barker, R. A.

Birdsall, T. G.

J. A. Swets, W. P. Tanner, T. G. Birdsall, “Decision processes in perception,” Psychol. Rev. 68, 301–340 (1961).
[CrossRef] [PubMed]

Burgess, A.

Burgess, A. E.

Cannon, M. W.

Cohn, T. E.

Davis, E. T.

Derrington, A. M.

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,”J. Physiol. 357, 219–240 (1984).
[PubMed]

Foley, J. M.

Geise, S. C.

W. H. Swanson, H. R. Wilson, S. C. Geise, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

Gelb, D. J.

H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984).
[CrossRef] [PubMed]

D. J. Gelb, H. R. Wilson, “Shifts in perceived size as a function of contrast and temporal modulation,” Vision Res. 23, 71–82 (1983).
[CrossRef] [PubMed]

Ghandeharian, H.

Gille, J.

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Kreiger, New York, 1974).

Jaarsma, D.

L. W. Nolte, D. Jaarsma, “More on the detection of one of M orthogonal signals,”J. Acoust. Soc. Am. 41, 497–505 (1967).
[CrossRef]

Kaplan, E.

E. Kaplan, R. M. Shapley, “The primate retina contains two types of ganglion cells, with high and low contrast sensitivity,” Proc. Natl. Acad. Sci. USA 83, 2755–2757 (1986).
[CrossRef] [PubMed]

Kersten, D.

Kleinstein, R. N.

Kocher, E. C.

Kramer, P.

Lasley, D. J.

Legge, G. E.

Lennie, P.

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,”J. Physiol. 357, 219–240 (1984).
[PubMed]

Nachmias, J.

J. Nachmias, E. C. Kocher, “Visual detection and discrimination of luminance increments,”J. Opt. Soc. Am. 60, 382–389 (1970).
[CrossRef] [PubMed]

J. Nachmias, “Signal detection theory and its application to problems in vision,” in Visual Psychophysics, D. Jameson, L. Hurvich, eds. (Springer-Verlag, Berlin, 1972), pp. 56–77.
[CrossRef]

Nolte, L. W.

L. W. Nolte, D. Jaarsma, “More on the detection of one of M orthogonal signals,”J. Acoust. Soc. Am. 41, 497–505 (1967).
[CrossRef]

Pelli, D. G.

Shapley, R. M.

E. Kaplan, R. M. Shapley, “The primate retina contains two types of ganglion cells, with high and low contrast sensitivity,” Proc. Natl. Acad. Sci. USA 83, 2755–2757 (1986).
[CrossRef] [PubMed]

Smith, B. G.

B. G. Smith, “The psychometric function for contrast discrimination,” dissertation (University of California, Los Angeles, Los Angeles, California, 1986).

Swanson, W. H.

W. H. Swanson, H. R. Wilson, S. C. Geise, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

Swets, J. A.

J. A. Swets, W. P. Tanner, T. G. Birdsall, “Decision processes in perception,” Psychol. Rev. 68, 301–340 (1961).
[CrossRef] [PubMed]

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Kreiger, New York, 1974).

Tanner, W. P.

J. A. Swets, W. P. Tanner, T. G. Birdsall, “Decision processes in perception,” Psychol. Rev. 68, 301–340 (1961).
[CrossRef] [PubMed]

W. P. Tanner, “Theory of recognition,”J. Acoust. Soc. Am. 28, 882–888 (1956).
[CrossRef]

Thibos, L. N.

Thomas, J. P.

Westheimer, G.

G. Westheimer, “Visual hyperacuity,” Prog. Sensory Physiol. 1, 1–30 (1981).
[CrossRef]

Wilson, H. R.

H. R. Wilson, “Responses of spatial mechanisms can explain hyperacuity,” Vision Res. 26, 453–469 (1986).
[CrossRef] [PubMed]

H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984).
[CrossRef] [PubMed]

W. H. Swanson, H. R. Wilson, S. C. Geise, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

D. J. Gelb, H. R. Wilson, “Shifts in perceived size as a function of contrast and temporal modulation,” Vision Res. 23, 71–82 (1983).
[CrossRef] [PubMed]

H. R. Wilson, “A transducer function for threshold and supra-threshold human vision,” Biol. Cybernet. 38, 171–178 (1980).
[CrossRef]

Yager, D.

Ann. Rev. Psychol. (1)

T. E. Cohn, D. J. Lasley, “Visual Sensitivity,” Ann. Rev. Psychol. 37, 495–521 (1986).
[CrossRef]

Biol. Cybernet. (1)

H. R. Wilson, “A transducer function for threshold and supra-threshold human vision,” Biol. Cybernet. 38, 171–178 (1980).
[CrossRef]

J. Acoust. Soc. Am. (2)

W. P. Tanner, “Theory of recognition,”J. Acoust. Soc. Am. 28, 882–888 (1956).
[CrossRef]

L. W. Nolte, D. Jaarsma, “More on the detection of one of M orthogonal signals,”J. Acoust. Soc. Am. 41, 497–505 (1967).
[CrossRef]

J. Opt. Soc. Am. (7)

J. Opt. Soc. Am. A (10)

A. Burgess, H. Ghandeharian, “Visual signal detection. I. Ability to use phase information,” J. Opt. Soc. Am. A 1, 900–905 (1984).
[CrossRef] [PubMed]

A. E. Burgess, H. Ghandeharian, “Visual signal detection. II. Signal-location identification,” J. Opt. Soc. Am. A 1, 906–910 (1984).
[CrossRef] [PubMed]

A. Burgess, “Visual signal detection. III. On Bayesian use of prior knowledge and cross correlation,” J. Opt. Soc. Am. A 2, 1498–1507 (1985).
[CrossRef] [PubMed]

D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508–1532 (1985).
[CrossRef] [PubMed]

J. P. Thomas, “Effect of static-noise and grating masks on detection and identification of grating targets,” J. Opt. Soc. Am. A 2, 1586–1592 (1985).
[CrossRef] [PubMed]

G. E. Legge, D. Kersten, A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. A 4, 391–404 (1987).
[CrossRef] [PubMed]

H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984).
[CrossRef] [PubMed]

J. P. Thomas, “Detection and identification: how are they related?” J. Opt. Soc. Am. A 2, 1457–1467 (1985).
[CrossRef] [PubMed]

E. T. Davis, P. Kramer, D. Yager, “Shifts in perceived spatial frequency of low contrast stimuli: data and theory,” J. Opt. Soc. Am. A 3, 1189–1202 (1986).
[CrossRef] [PubMed]

M. W. Cannon, “Perceived contrast in the fovea and periphery,” J. Opt. Soc. Am. A 2, 1760–1768 (1985).
[CrossRef] [PubMed]

J. Physiol. (1)

A. M. Derrington, P. Lennie, “Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus of macaque,”J. Physiol. 357, 219–240 (1984).
[PubMed]

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

E. Kaplan, R. M. Shapley, “The primate retina contains two types of ganglion cells, with high and low contrast sensitivity,” Proc. Natl. Acad. Sci. USA 83, 2755–2757 (1986).
[CrossRef] [PubMed]

Prog. Sensory Physiol. (1)

G. Westheimer, “Visual hyperacuity,” Prog. Sensory Physiol. 1, 1–30 (1981).
[CrossRef]

Psychol. Rev. (1)

J. A. Swets, W. P. Tanner, T. G. Birdsall, “Decision processes in perception,” Psychol. Rev. 68, 301–340 (1961).
[CrossRef] [PubMed]

Vision Res. (3)

W. H. Swanson, H. R. Wilson, S. C. Geise, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

D. J. Gelb, H. R. Wilson, “Shifts in perceived size as a function of contrast and temporal modulation,” Vision Res. 23, 71–82 (1983).
[CrossRef] [PubMed]

H. R. Wilson, “Responses of spatial mechanisms can explain hyperacuity,” Vision Res. 26, 453–469 (1986).
[CrossRef] [PubMed]

Other (3)

B. G. Smith, “The psychometric function for contrast discrimination,” dissertation (University of California, Los Angeles, Los Angeles, California, 1986).

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Kreiger, New York, 1974).

J. Nachmias, “Signal detection theory and its application to problems in vision,” in Visual Psychophysics, D. Jameson, L. Hurvich, eds. (Springer-Verlag, Berlin, 1972), pp. 56–77.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Illustration of the basic vector model. Visual responses to two stimuli, x0 and xj, are illustrated. Each response is the vector of the responses of individual spatially tuned mechanisms. External and internal noise perturb the responses so that, over many presentations, each stimulus is represented by a distribution of responses centered on the expected response. Point R0 represents the expected response to x0 and is defined by a vector of length V. Point Rj is the expected response to xj. The difference between the two stimuli is represented by the difference vector of length D.

Fig. 2
Fig. 2

Simulation results for the constant-noise model. The two functions shown as solid lines are PVC function for spatial-frequency and/or orientation discriminations of different difficulties. To a close approximation, they have the same shape and are simply translated vertically from each other. The PVC function for contrast discrimination is shown by the dashed lines. It differs in shape, approaching its asymptote at a lower contrast.

Fig. 3
Fig. 3

PVC functions for three different discriminations: ●, spatial-frequency discrimination; ○, orientation discrimination; □ contrast discrimination. Observer PJM.

Fig. 4
Fig. 4

Same as Fig. 3 but for observer JJL.

Fig. 5
Fig. 5

Same as Fig. 3 but for observer NXT.

Fig. 6
Fig. 6

Same as Fig. 3 but for observer ZOE.

Fig. 7
Fig. 7

PVC functions for contrast-discriminations of different difficulties. The top part of the figure shows PVC functions for G = 1.1, G = 1.3, and G = 1.4. The bottom part of the figure shows the ratio of performance when G = 1.4 to performance when G = 1.1. The solid lines and filled data points show observed ratios, the upper dashed line shows ratios predicted by the increasing-noise model, and the lower dashed line shows the prediction of the constant-noise model. Observer JPT.

Fig. 8
Fig. 8

Same as Fig. 7 but for observer BGS.

Tables (1)

Tables Icon

Table 1 Slopes of Receiver Operating Characteristicsa

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

R i j = ( S i j C j ) p ,
σ 0 = 1 + B V ,
D / σ 0 = D / ( 1 + B V ) .
R i j = ( S i j C j ) p when ( S i j C j ) a
R i j = a p + log ( S i j C j / a ) when ( S i j C j ) > a .
Δ m G 1 / Δ m G 2 = ( 1 - G 1 p ) / ( 1 - G 2 p ) .
Δ m G 1 / Δ m G 2 = log ( G 1 ) / log ( G 2 ) .
b = ( b h , f / b f , h ) 0.5 ,
Δ m = M FA - ( M H / b ) .
D 0 , j = [ i = 1 n ( R i 0 - R i j ) 2 ] 0.5 ,
D 0 , j = [ i = 1 n ( R i 0 - R i j ) 2 ] 0.5 = { i = 1 n [ ( S i 0 C 0 ) p - ( S i j C 0 ) p ] 2 } 0.5 = C 0 p [ i = 1 n ( S i 0 p - S i j p ) 2 ] 0.5 ,
V 0 = [ i = 1 n R i 0 2 ] 0.5 = [ i = 1 n ( S i 0 C 0 ) 2 p ] 0.5 = C 0 p [ i = 1 n S i 0 2 p ] 0.5 ,
Δ m 0 , 1 / m 0 , 2 = ( D 0 , 1 / σ 0 ) / ( D 0 , 2 / σ 0 ) = D 0 , 1 / D 0 , 2 = { i = 1 n [ ( S i 0 C ) p - ( S i 1 C ) p ] 2 } 0.5 / { i = 1 n [ ( S i 0 C ) p - ( S i 2 C ) p ] 2 } 0.5 = [ i = 1 n ( S i 0 p - S i 1 p ) 2 ] 0.5 / [ i = 1 n ( S i 0 p - S i 2 p ) 2 ] 0.5 ,
Δ m 0 , 1 / Δ m 0 , 3 = D 0 , 1 / D 0 , 3 ,
D 0 , 3 = { i = 1 n [ ( S i 0 C ) p - ( S i 0 G C ) p ] 2 } 0.5 = C p ( 1 - G p ) ( i = 1 n S i 0 2 p ) 0.5 .
D 0 , 1 = C p [ i = 1 n ( S i 0 p - S i 1 p ) 2 ] 0.5 .
Δ m 0 , 1 / Δ m 0 , 3 = C p [ i = 1 n ( S i 0 p - S i 1 p ) 2 ] 0.5 / C p ( 1 - G p ) [ i = 1 n S i 0 2 p ] 0.5 .
Δ m G 1 / Δ m G 2 = D G 1 / D G 2 = C p ( 1 - G 1 p ) ( i = 1 n S i 0 2 p ) 0.5 / C p ( 1 - G 2 p ) ( i = 1 n S i 0 2 p ) 0.5 = ( 1 - G 1 p ) / ( 1 - G 2 p ) .
ROC slope = σ 0 / σ j = ( 1 + B V 0 ) / ( 1 + B V j ) = [ 1 + B C p ( i = 1 n S i 0 2 p ) 0.5 ] / [ 1 + B G p C p ( i = 1 n S i 0 2 p ) 0.5 ] .
ROC slope = G - p .
D 0 , j = [ i = 1 n ( R i 0 - R i j ) 2 ] 0.5 = ( i = 1 n { [ a p + log ( S i 0 C / a ) ] - [ a p + log ( S i j C / a ) ] } 2 ) 0.5 = { i = 1 n [ log ( S i 0 ) - log ( S i j ) 2 } } 0.5 .
R i j = ( S i j C j ) 2 for ( S i j C j ) 1.0 , R i j = 1 + log ( S i j C j ) for ( S i j C j ) > 1.0.
S i j = f ( x i - x j ) ,
Δ m G 1 / Δ m G 2 = D G 1 / D G 2 .
D G 1 = ( i = 1 n { [ a p + log ( S i 0 C / a ) ] - [ a p + log ( S i 0 G C / a ) 2 } ) 0.5 ,
D G 1 = n 0.5 log ( G 1 ) ,
Δ m G 1 / Δ m G 2 = log ( G 1 ) / log ( G 2 ) .

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