Abstract

The influential uncertainty model [J. Opt. Soc. Am. A 2, 1508 (1985)] attributes nonlinear contrast sensitivity near threshold to the inability of the observer to discriminate between the signal from stimulated locations and the noise from nonstimulated locations. We introduce an alternative interpretation, the distraction model, to describe the behavior of an observer who knows exactly which location was stimulated but may miss the test stimulus because attention has been distracted by irrelevant (noise) signals. For any stimulus sample, the observer is assumed to be certain of whether this sample is relevant or irrelevant to the stimulus. The nonlinear effects predicted by the distraction model without uncertainty are similar to those predicted by the uncertainty model.

© 1999 Optical Society of America

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References

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  1. W. P. Tanner, “Physiological implications of psychophysical data,” Ann. (N.Y.) Acad. Sci. 89, 752–765 (1961).
    [Crossref]
  2. J. Nachmias, E. C. Kocher, “Visual detection and discrimination of luminous increments,” J. Opt. Soc. Am. 60, 382–389 (1970).
    [Crossref] [PubMed]
  3. D. G. Pelli, “Uncertainty explains many aspects of visual contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1508–1532 (1985).
    [Crossref] [PubMed]
  4. W. W. Peterson, T. G. Birdsall, W. C. Fox, “Theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
    [Crossref]
  5. J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
    [Crossref] [PubMed]
  6. G. E. Legge, D. Kersten, A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. A 4, 391–404 (1987).
    [Crossref] [PubMed]
  7. F. J. J. Blommaert, J. A. J. Roufs, “Prediction threshold and latency on the basis of experimentally determined impulse responses,” Biol. Cybern. 56, 329–344 (1987).
    [Crossref]
  8. M. J. Mayer, C. W. Tyler, “Invariance of the slope of the psychometric function with spatial summation,” J. Opt. Soc. Am. A 3, 1166–1172 (1986).
    [Crossref] [PubMed]
  9. J. Palmer, C. T. Ames, D. T. Lindsey, “Measuring the effect of attention on simple visual search,” J. Exp. Psychol. 19, 108–130 (1993).
  10. U. Neisser, Cognitive Psychology (Appleton-Century Crofts, New York, 1967).
  11. M. I. Posner, C. R. R. Snyder, B. J. Davidson, “Attention and the detection of signals,” J. Exp. Psychol. 109, 160–174 (1980).
    [Crossref] [PubMed]
  12. J. M. Wolfe, K. R. Cave, S. L. Franzel, “Guided search: an alternative to the feature integration model for visual search,” J. Exp. Psychol. 15, 419–433 (1989).
  13. A. M. Treisman, G. Gelade, “A feature-integration theory of attention,” Cogn. Psychol. 12, 97–136 (1980).
    [Crossref] [PubMed]
  14. G. Sperling, E. Weichselgartner, “Episodic theory of the dynamics of spatial attention,” Psychol. Rev. 102, 503–532 (1995).
    [Crossref]
  15. C. W. Eriksen, J. D. St. James, “Visual attention within and around the field of focal attention: a zoom lens model,” Percept. Psychophys. 40, 225–240 (1986).
    [Crossref] [PubMed]
  16. D. Kahneman, Attention and Effort (Prentice-Hall, Englewood Cliffs, N.J., 1973).
  17. K. Nakayama, M. Mackeben, “Sustained and transient components of focal visual attention,” Vision Res. 29, 1631–1647 (1989).
    [Crossref] [PubMed]
  18. M. I. Posner, Y. Cohen, “Components of visual orienting,” in Attention and Performance X, H. Bouma, D. G. Bouwhuis, eds. (Erlbaum, Hillsdale, N.J., 1984), pp. 531–556.

1995 (1)

G. Sperling, E. Weichselgartner, “Episodic theory of the dynamics of spatial attention,” Psychol. Rev. 102, 503–532 (1995).
[Crossref]

1993 (1)

J. Palmer, C. T. Ames, D. T. Lindsey, “Measuring the effect of attention on simple visual search,” J. Exp. Psychol. 19, 108–130 (1993).

1989 (2)

J. M. Wolfe, K. R. Cave, S. L. Franzel, “Guided search: an alternative to the feature integration model for visual search,” J. Exp. Psychol. 15, 419–433 (1989).

K. Nakayama, M. Mackeben, “Sustained and transient components of focal visual attention,” Vision Res. 29, 1631–1647 (1989).
[Crossref] [PubMed]

1987 (2)

F. J. J. Blommaert, J. A. J. Roufs, “Prediction threshold and latency on the basis of experimentally determined impulse responses,” Biol. Cybern. 56, 329–344 (1987).
[Crossref]

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

1986 (2)

M. J. Mayer, C. W. Tyler, “Invariance of the slope of the psychometric function with spatial summation,” J. Opt. Soc. Am. A 3, 1166–1172 (1986).
[Crossref] [PubMed]

C. W. Eriksen, J. D. St. James, “Visual attention within and around the field of focal attention: a zoom lens model,” Percept. Psychophys. 40, 225–240 (1986).
[Crossref] [PubMed]

1985 (1)

1981 (1)

J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[Crossref] [PubMed]

1980 (2)

A. M. Treisman, G. Gelade, “A feature-integration theory of attention,” Cogn. Psychol. 12, 97–136 (1980).
[Crossref] [PubMed]

M. I. Posner, C. R. R. Snyder, B. J. Davidson, “Attention and the detection of signals,” J. Exp. Psychol. 109, 160–174 (1980).
[Crossref] [PubMed]

1970 (1)

1961 (1)

W. P. Tanner, “Physiological implications of psychophysical data,” Ann. (N.Y.) Acad. Sci. 89, 752–765 (1961).
[Crossref]

1954 (1)

W. W. Peterson, T. G. Birdsall, W. C. Fox, “Theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
[Crossref]

Ames, C. T.

J. Palmer, C. T. Ames, D. T. Lindsey, “Measuring the effect of attention on simple visual search,” J. Exp. Psychol. 19, 108–130 (1993).

Birdsall, T. G.

W. W. Peterson, T. G. Birdsall, W. C. Fox, “Theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
[Crossref]

Blommaert, F. J. J.

F. J. J. Blommaert, J. A. J. Roufs, “Prediction threshold and latency on the basis of experimentally determined impulse responses,” Biol. Cybern. 56, 329–344 (1987).
[Crossref]

Burgess, A. E.

Cave, K. R.

J. M. Wolfe, K. R. Cave, S. L. Franzel, “Guided search: an alternative to the feature integration model for visual search,” J. Exp. Psychol. 15, 419–433 (1989).

Cohen, Y.

M. I. Posner, Y. Cohen, “Components of visual orienting,” in Attention and Performance X, H. Bouma, D. G. Bouwhuis, eds. (Erlbaum, Hillsdale, N.J., 1984), pp. 531–556.

Davidson, B. J.

M. I. Posner, C. R. R. Snyder, B. J. Davidson, “Attention and the detection of signals,” J. Exp. Psychol. 109, 160–174 (1980).
[Crossref] [PubMed]

Eriksen, C. W.

C. W. Eriksen, J. D. St. James, “Visual attention within and around the field of focal attention: a zoom lens model,” Percept. Psychophys. 40, 225–240 (1986).
[Crossref] [PubMed]

Foley, J. M.

J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[Crossref] [PubMed]

Fox, W. C.

W. W. Peterson, T. G. Birdsall, W. C. Fox, “Theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
[Crossref]

Franzel, S. L.

J. M. Wolfe, K. R. Cave, S. L. Franzel, “Guided search: an alternative to the feature integration model for visual search,” J. Exp. Psychol. 15, 419–433 (1989).

Gelade, G.

A. M. Treisman, G. Gelade, “A feature-integration theory of attention,” Cogn. Psychol. 12, 97–136 (1980).
[Crossref] [PubMed]

Kahneman, D.

D. Kahneman, Attention and Effort (Prentice-Hall, Englewood Cliffs, N.J., 1973).

Kersten, D.

Kocher, E. C.

Legge, G. E.

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

J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[Crossref] [PubMed]

Lindsey, D. T.

J. Palmer, C. T. Ames, D. T. Lindsey, “Measuring the effect of attention on simple visual search,” J. Exp. Psychol. 19, 108–130 (1993).

Mackeben, M.

K. Nakayama, M. Mackeben, “Sustained and transient components of focal visual attention,” Vision Res. 29, 1631–1647 (1989).
[Crossref] [PubMed]

Mayer, M. J.

Nachmias, J.

Nakayama, K.

K. Nakayama, M. Mackeben, “Sustained and transient components of focal visual attention,” Vision Res. 29, 1631–1647 (1989).
[Crossref] [PubMed]

Neisser, U.

U. Neisser, Cognitive Psychology (Appleton-Century Crofts, New York, 1967).

Palmer, J.

J. Palmer, C. T. Ames, D. T. Lindsey, “Measuring the effect of attention on simple visual search,” J. Exp. Psychol. 19, 108–130 (1993).

Pelli, D. G.

Peterson, W. W.

W. W. Peterson, T. G. Birdsall, W. C. Fox, “Theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
[Crossref]

Posner, M. I.

M. I. Posner, C. R. R. Snyder, B. J. Davidson, “Attention and the detection of signals,” J. Exp. Psychol. 109, 160–174 (1980).
[Crossref] [PubMed]

M. I. Posner, Y. Cohen, “Components of visual orienting,” in Attention and Performance X, H. Bouma, D. G. Bouwhuis, eds. (Erlbaum, Hillsdale, N.J., 1984), pp. 531–556.

Roufs, J. A. J.

F. J. J. Blommaert, J. A. J. Roufs, “Prediction threshold and latency on the basis of experimentally determined impulse responses,” Biol. Cybern. 56, 329–344 (1987).
[Crossref]

Snyder, C. R. R.

M. I. Posner, C. R. R. Snyder, B. J. Davidson, “Attention and the detection of signals,” J. Exp. Psychol. 109, 160–174 (1980).
[Crossref] [PubMed]

Sperling, G.

G. Sperling, E. Weichselgartner, “Episodic theory of the dynamics of spatial attention,” Psychol. Rev. 102, 503–532 (1995).
[Crossref]

St. James, J. D.

C. W. Eriksen, J. D. St. James, “Visual attention within and around the field of focal attention: a zoom lens model,” Percept. Psychophys. 40, 225–240 (1986).
[Crossref] [PubMed]

Tanner, W. P.

W. P. Tanner, “Physiological implications of psychophysical data,” Ann. (N.Y.) Acad. Sci. 89, 752–765 (1961).
[Crossref]

Treisman, A. M.

A. M. Treisman, G. Gelade, “A feature-integration theory of attention,” Cogn. Psychol. 12, 97–136 (1980).
[Crossref] [PubMed]

Tyler, C. W.

Weichselgartner, E.

G. Sperling, E. Weichselgartner, “Episodic theory of the dynamics of spatial attention,” Psychol. Rev. 102, 503–532 (1995).
[Crossref]

Wolfe, J. M.

J. M. Wolfe, K. R. Cave, S. L. Franzel, “Guided search: an alternative to the feature integration model for visual search,” J. Exp. Psychol. 15, 419–433 (1989).

Ann. (N.Y.) Acad. Sci. (1)

W. P. Tanner, “Physiological implications of psychophysical data,” Ann. (N.Y.) Acad. Sci. 89, 752–765 (1961).
[Crossref]

Biol. Cybern. (1)

F. J. J. Blommaert, J. A. J. Roufs, “Prediction threshold and latency on the basis of experimentally determined impulse responses,” Biol. Cybern. 56, 329–344 (1987).
[Crossref]

Cogn. Psychol. (1)

A. M. Treisman, G. Gelade, “A feature-integration theory of attention,” Cogn. Psychol. 12, 97–136 (1980).
[Crossref] [PubMed]

IRE Trans. Inf. Theory (1)

W. W. Peterson, T. G. Birdsall, W. C. Fox, “Theory of signal detectability,” IRE Trans. Inf. Theory PGIT-4, 171–212 (1954).
[Crossref]

J. Exp. Psychol. (3)

J. Palmer, C. T. Ames, D. T. Lindsey, “Measuring the effect of attention on simple visual search,” J. Exp. Psychol. 19, 108–130 (1993).

M. I. Posner, C. R. R. Snyder, B. J. Davidson, “Attention and the detection of signals,” J. Exp. Psychol. 109, 160–174 (1980).
[Crossref] [PubMed]

J. M. Wolfe, K. R. Cave, S. L. Franzel, “Guided search: an alternative to the feature integration model for visual search,” J. Exp. Psychol. 15, 419–433 (1989).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Percept. Psychophys. (1)

C. W. Eriksen, J. D. St. James, “Visual attention within and around the field of focal attention: a zoom lens model,” Percept. Psychophys. 40, 225–240 (1986).
[Crossref] [PubMed]

Psychol. Rev. (1)

G. Sperling, E. Weichselgartner, “Episodic theory of the dynamics of spatial attention,” Psychol. Rev. 102, 503–532 (1995).
[Crossref]

Vision Res. (2)

K. Nakayama, M. Mackeben, “Sustained and transient components of focal visual attention,” Vision Res. 29, 1631–1647 (1989).
[Crossref] [PubMed]

J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[Crossref] [PubMed]

Other (3)

U. Neisser, Cognitive Psychology (Appleton-Century Crofts, New York, 1967).

M. I. Posner, Y. Cohen, “Components of visual orienting,” in Attention and Performance X, H. Bouma, D. G. Bouwhuis, eds. (Erlbaum, Hillsdale, N.J., 1984), pp. 531–556.

D. Kahneman, Attention and Effort (Prentice-Hall, Englewood Cliffs, N.J., 1973).

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Figures (4)

Fig. 1
Fig. 1

Uncertainty and distraction models. The two models have similar initial stages: The signals from local analyzers get mixed with additive Gaussian noise, after which the largest signal gets chosen. The uncertainty model makes the decision based directly on this signal; the distraction model first checks the relevance of the maximum signal.

Fig. 2
Fig. 2

Effective signal produced by the distraction model in the 2AFC task for a range of ratios K/M. The number of monitored channels M was kept constant at a value of 105. The nonlinearity of the transducer increases for small K/M.

Fig. 3
Fig. 3

Top, detection thresholds and bottom, slopes predicted by the distraction and the uncertainty models. The predictions of the uncertainty model are shown for the single relevant channel (K=1) and a variable number of the monitored channels. The predictions of the distraction model are obtained for two conditions: for the single relevant channel (K=1) and for a fixed number of monitored channels (M=105). The predictions of the two models for K=1 are similar, indicating that the effects of uncertainty and distraction are comparable.

Fig. 4
Fig. 4

Each curve illustrates the probability Pt(s)(relevant) of the relevant analyzer to be attended in the test trial as a function of signal s (the normalized contrast c) for a particular ratio K/M.

Tables (1)

Tables Icon

Table 1 Possible Outcomes of 2AFC Experiment Depending on the Relevance of the Samples

Equations (16)

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Fmax(r, u)(x)=Fr(x)Fu(x).
f(r=x, ux)=fr(x)Fu(x),
f(r=x, u>x)=fr(x)[1-Fu(x)].
ft¯(x, relevant)=fmax0<iK ni(x)FmaxK<iM ni(x)=dFn(x)KdxFn(x)M-K.
ft(s)(x, relevant)=fmax0<iK s+ni(x)FmaxK<iM ni(x)=dFn(x-s)KdxFn(x)M-K.
Pt¯(relevant)=-+ft¯(x, relevant)dx,
Pt¯(irrelevant)=1-Pt¯(relevant),
Pt(s)(relevant)=-+ft(s)(x, relevant)dx,
Pt(s)(irrelevant)=1-Pt(s)(relevant).
f{[t(s), relevant]=x, (t¯, relevant)x}=ft(s)(x, relevant)Ft¯(x, relevant),
P{[t(s), relevant](t¯, relevant)}=-+f{[t(s), relevant]=x, (t¯, relevant)x}dx.
Pcorr(s)=0.5Pt(s)(irrelevant)Pt¯(irrelevant)+Pt¯(irrelevant)Pt(s)(relevant)+P{[t¯(s), relevant](t¯, relevant)}.
Ft¯(x)=Fmax0<iM ni(x)=Fn(x)M,
ft(s)(x)=fmax(max0<iKs+ni, maxK<iM ni)(x)=dFn(x)M-KFn(x-s)Kdx,
f[t(s)=x, t¯x]=ft(s)(x)Ft¯(x),
Pcorr(s)=-+f[t(s)=x, t¯x]dx.

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