Abstract

The spatial extent of lateral interaction was determined for nonoverlapping equal-energy stimuli in a metacontrast design with targets and masks of constant separation but varying width. The weighting functions derived from these data are wholly negative. Unlike previous estimates of spatial extent in metacontrast, based on experiments in which the separation between target and mask was varied, our weighting functions subtend only about 10′ of visual angle, for both monoptic and dichoptic observations. However, the weighting functions resemble those derived from a wide variety of other psychophysical procedures such as sensitization. The differences of estimates of weighting functions are interpreted in terms of two spatial-lateral-interaction systems. One of these systems may depend critically on the proximity of stimuli; the independence of the spatial extent of the system from target size suggests the involvement of an edge mechanism.

© 1972 Optical Society of America

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References

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  1. V. O’Brien, J. Opt. Soc. Am. 48, 112 (1958).
    [Crossref]
  2. T. N. Cornsweet and D. Y. Teller, J. Opt. Soc. Am. 55, 1303 (1965).
    [Crossref] [PubMed]
  3. M. Davidson and J. A. Whiteside, J. Opt. Soc. Am. 61, 530 (1971).
    [Crossref] [PubMed]
  4. J. P. Thomas, Vision Res. 8, 49 (1968).
    [Crossref]
  5. J. P. Thomas, Psychol. Rev. 77, 121 (1970). We have modified the equation slightly.
    [Crossref] [PubMed]
  6. G. Westheimer, J. Physiol. (London) 190, 139 (1967).
  7. G. von Bekesy, J. Opt. Soc. Am. 50, 1060 (1960).
    [Crossref]
  8. O. Bryngdahl, Vision Res. 6, 553 (1966).
    [Crossref] [PubMed]
  9. D. Y. Teller and B. Lindsey, Vision Res. 10, 1045 (1970).
    [Crossref] [PubMed]
  10. A. S. Patel, J. Opt. Soc. Am. 56, 689 (1966).
    [Crossref] [PubMed]
  11. J. I. Markoff and J. F. Sturr, J. Opt. Soc. Am. 61, 1530 (1971).
    [Crossref] [PubMed]
  12. G. A. Fry, Am. J. Optom. Arch. Am. Acad. Optom. 25, 162 (1948).
    [Crossref] [PubMed]
  13. M. Alpern, J. Opt. Soc. Am. 43, 648 (1953).
    [Crossref] [PubMed]
  14. N. Weisstein and R. Growney, Percept. Psychophys. 5, 321 (1969).
    [Crossref]
  15. N. Weisstein, in Visual Psychophysics, edited by D. Jameson and L. M. Hurvich (Springer, Heidelberg, 1972). The hypothesis that metacontrast is a cortical interaction is supported by the dichoptic transfer of the effect, the time delay for which the mask is most effective, and the dependence of metacontrast on both target and mask as patterns.
  16. S. I. Cox, W. N. Dember, and M. F. Sherrick, Psychon. Sci. 17, 205 (1969).
  17. W. R. Uttal, Percept. Psychophys. 7, 321 (1970).
    [Crossref]
  18. M. S. Mayzner and M. E. Tresselt, Psychon. Sci. 17, 77 (1969).
  19. S. S. Stevens, Percept. Psychophys. 1, 96 (1966).
    [Crossref]
  20. P. H. Schiller and M. C. Smith, Percept. Psychophys. 3, 237 (1968).
    [Crossref]
  21. What is strictly appropriate for measuring the variability of a geometric mean is a standard deviation computed with the log data, analogous to the computation of the geometric mean. The standard deviations computed in this manner are quite small, however, and can be misleading in describing the actual variability of the data; the range of standard deviation is considerably compressed.
  22. This approximation can be obtained by taking the derivative of the convolution integral (see introduction) at a particular point, p, at the edge of the target [we assumed θ(−x) = θ(x)]. We solved for the weighting function so thatθ(x)=1F(x)dRdx,where dR is approximated by the difference between the magnitude estimations (ME 2 − ME1) corresponding to the change of distance along one dimension, x, and where dx is approximated by the difference between two successive mask sizes (M 2 − M 1). See Thomas (Ref. 4) for a similar procedure.
  23. T. N. Cornsweet, Visual Perception (Academic, New York, 1970).
  24. On the other hand, the edge mechanism involved in brightness might require a smaller target as an impulse function, or generally, metacontrast might not be an edge effect at all but a function of some larger detector cell for brightness. In either case, under the assumption of linearity, as targets get narrower and approach the width of an impulse, the computed functions should approach the actual weighting function.
  25. A. G. Goldstein, Percept. Psychophys. 7, 28 (1970).
    [Crossref]
  26. H. H. Matteson, J. Opt. Soc. Am. 59, 1461 (1969).
    [Crossref] [PubMed]
  27. F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden–Day, San Francisco, 1965).
  28. G. Sperling, Percept. Psychophys. 8, 143 (1970).
    [Crossref]
  29. M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).
  30. D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 195, 215 (1968).

1971 (2)

1970 (5)

W. R. Uttal, Percept. Psychophys. 7, 321 (1970).
[Crossref]

J. P. Thomas, Psychol. Rev. 77, 121 (1970). We have modified the equation slightly.
[Crossref] [PubMed]

D. Y. Teller and B. Lindsey, Vision Res. 10, 1045 (1970).
[Crossref] [PubMed]

A. G. Goldstein, Percept. Psychophys. 7, 28 (1970).
[Crossref]

G. Sperling, Percept. Psychophys. 8, 143 (1970).
[Crossref]

1969 (4)

H. H. Matteson, J. Opt. Soc. Am. 59, 1461 (1969).
[Crossref] [PubMed]

M. S. Mayzner and M. E. Tresselt, Psychon. Sci. 17, 77 (1969).

N. Weisstein and R. Growney, Percept. Psychophys. 5, 321 (1969).
[Crossref]

S. I. Cox, W. N. Dember, and M. F. Sherrick, Psychon. Sci. 17, 205 (1969).

1968 (3)

J. P. Thomas, Vision Res. 8, 49 (1968).
[Crossref]

P. H. Schiller and M. C. Smith, Percept. Psychophys. 3, 237 (1968).
[Crossref]

D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 195, 215 (1968).

1967 (1)

G. Westheimer, J. Physiol. (London) 190, 139 (1967).

1966 (3)

A. S. Patel, J. Opt. Soc. Am. 56, 689 (1966).
[Crossref] [PubMed]

S. S. Stevens, Percept. Psychophys. 1, 96 (1966).
[Crossref]

O. Bryngdahl, Vision Res. 6, 553 (1966).
[Crossref] [PubMed]

1965 (2)

T. N. Cornsweet and D. Y. Teller, J. Opt. Soc. Am. 55, 1303 (1965).
[Crossref] [PubMed]

M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).

1960 (1)

1958 (1)

1953 (1)

1948 (1)

G. A. Fry, Am. J. Optom. Arch. Am. Acad. Optom. 25, 162 (1948).
[Crossref] [PubMed]

Alpern, M.

Blatt, M. H.

M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).

Bryngdahl, O.

O. Bryngdahl, Vision Res. 6, 553 (1966).
[Crossref] [PubMed]

Bushsbaum, W. H.

M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).

Cornsweet, T. N.

T. N. Cornsweet and D. Y. Teller, J. Opt. Soc. Am. 55, 1303 (1965).
[Crossref] [PubMed]

T. N. Cornsweet, Visual Perception (Academic, New York, 1970).

Cox, S. I.

S. I. Cox, W. N. Dember, and M. F. Sherrick, Psychon. Sci. 17, 205 (1969).

Davidson, M.

Dember, W. N.

S. I. Cox, W. N. Dember, and M. F. Sherrick, Psychon. Sci. 17, 205 (1969).

Friedel, R. T.

M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).

Fry, G. A.

G. A. Fry, Am. J. Optom. Arch. Am. Acad. Optom. 25, 162 (1948).
[Crossref] [PubMed]

Goldstein, A. G.

A. G. Goldstein, Percept. Psychophys. 7, 28 (1970).
[Crossref]

Goodwin, P. E.

M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).

Growney, R.

N. Weisstein and R. Growney, Percept. Psychophys. 5, 321 (1969).
[Crossref]

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 195, 215 (1968).

Kanon, D.

M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).

Kelman, A.

M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).

Lindsey, B.

D. Y. Teller and B. Lindsey, Vision Res. 10, 1045 (1970).
[Crossref] [PubMed]

Markoff, J. I.

Matteson, H. H.

Mayzner, M. S.

M. S. Mayzner and M. E. Tresselt, Psychon. Sci. 17, 77 (1969).

M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).

Nilsson, W. D.

M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).

O’Brien, V.

Patel, A. S.

Ratliff, F.

F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden–Day, San Francisco, 1965).

Schiller, P. H.

P. H. Schiller and M. C. Smith, Percept. Psychophys. 3, 237 (1968).
[Crossref]

Sherrick, M. F.

S. I. Cox, W. N. Dember, and M. F. Sherrick, Psychon. Sci. 17, 205 (1969).

Smith, M. C.

P. H. Schiller and M. C. Smith, Percept. Psychophys. 3, 237 (1968).
[Crossref]

Sperling, G.

G. Sperling, Percept. Psychophys. 8, 143 (1970).
[Crossref]

Stevens, S. S.

S. S. Stevens, Percept. Psychophys. 1, 96 (1966).
[Crossref]

Sturr, J. F.

Teller, D. Y.

Thomas, J. P.

J. P. Thomas, Psychol. Rev. 77, 121 (1970). We have modified the equation slightly.
[Crossref] [PubMed]

J. P. Thomas, Vision Res. 8, 49 (1968).
[Crossref]

Tresselt, M. E.

M. S. Mayzner and M. E. Tresselt, Psychon. Sci. 17, 77 (1969).

Uttal, W. R.

W. R. Uttal, Percept. Psychophys. 7, 321 (1970).
[Crossref]

von Bekesy, G.

Weisstein, N.

N. Weisstein and R. Growney, Percept. Psychophys. 5, 321 (1969).
[Crossref]

N. Weisstein, in Visual Psychophysics, edited by D. Jameson and L. M. Hurvich (Springer, Heidelberg, 1972). The hypothesis that metacontrast is a cortical interaction is supported by the dichoptic transfer of the effect, the time delay for which the mask is most effective, and the dependence of metacontrast on both target and mask as patterns.

Westheimer, G.

G. Westheimer, J. Physiol. (London) 190, 139 (1967).

Whiteside, J. A.

Wiesel, T. N.

D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 195, 215 (1968).

Am. J. Optom. Arch. Am. Acad. Optom. (1)

G. A. Fry, Am. J. Optom. Arch. Am. Acad. Optom. 25, 162 (1948).
[Crossref] [PubMed]

J. Opt. Soc. Am. (8)

J. Physiol. (London) (2)

D. H. Hubel and T. N. Wiesel, J. Physiol. (London) 195, 215 (1968).

G. Westheimer, J. Physiol. (London) 190, 139 (1967).

Percept. Psychophys. (6)

W. R. Uttal, Percept. Psychophys. 7, 321 (1970).
[Crossref]

N. Weisstein and R. Growney, Percept. Psychophys. 5, 321 (1969).
[Crossref]

G. Sperling, Percept. Psychophys. 8, 143 (1970).
[Crossref]

A. G. Goldstein, Percept. Psychophys. 7, 28 (1970).
[Crossref]

S. S. Stevens, Percept. Psychophys. 1, 96 (1966).
[Crossref]

P. H. Schiller and M. C. Smith, Percept. Psychophys. 3, 237 (1968).
[Crossref]

Psychol. Rev. (1)

J. P. Thomas, Psychol. Rev. 77, 121 (1970). We have modified the equation slightly.
[Crossref] [PubMed]

Psychon. Sci. (3)

M. S. Mayzner and M. E. Tresselt, Psychon. Sci. 17, 77 (1969).

S. I. Cox, W. N. Dember, and M. F. Sherrick, Psychon. Sci. 17, 205 (1969).

M. S. Mayzner, M. H. Blatt, W. H. Bushsbaum, R. T. Friedel, P. E. Goodwin, D. Kanon, A. Kelman, and W. D. Nilsson, Psychon. Sci. 3, 79 (1965).

Vision Res. (3)

O. Bryngdahl, Vision Res. 6, 553 (1966).
[Crossref] [PubMed]

D. Y. Teller and B. Lindsey, Vision Res. 10, 1045 (1970).
[Crossref] [PubMed]

J. P. Thomas, Vision Res. 8, 49 (1968).
[Crossref]

Other (6)

N. Weisstein, in Visual Psychophysics, edited by D. Jameson and L. M. Hurvich (Springer, Heidelberg, 1972). The hypothesis that metacontrast is a cortical interaction is supported by the dichoptic transfer of the effect, the time delay for which the mask is most effective, and the dependence of metacontrast on both target and mask as patterns.

F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden–Day, San Francisco, 1965).

What is strictly appropriate for measuring the variability of a geometric mean is a standard deviation computed with the log data, analogous to the computation of the geometric mean. The standard deviations computed in this manner are quite small, however, and can be misleading in describing the actual variability of the data; the range of standard deviation is considerably compressed.

This approximation can be obtained by taking the derivative of the convolution integral (see introduction) at a particular point, p, at the edge of the target [we assumed θ(−x) = θ(x)]. We solved for the weighting function so thatθ(x)=1F(x)dRdx,where dR is approximated by the difference between the magnitude estimations (ME 2 − ME1) corresponding to the change of distance along one dimension, x, and where dx is approximated by the difference between two successive mask sizes (M 2 − M 1). See Thomas (Ref. 4) for a similar procedure.

T. N. Cornsweet, Visual Perception (Academic, New York, 1970).

On the other hand, the edge mechanism involved in brightness might require a smaller target as an impulse function, or generally, metacontrast might not be an edge effect at all but a function of some larger detector cell for brightness. In either case, under the assumption of linearity, as targets get narrower and approach the width of an impulse, the computed functions should approach the actual weighting function.

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Figures (6)

Fig. 1
Fig. 1

Masking amplitude as a function of interstimulus interval (ISI) for monoptic presentation of the 25′ target. Results are shown for representative masks of width 1′ ●—● 3′ ×—×, 4′ □—□, 8′ △—△, 12′ ○- -○, and 74′ ▲- -▲ for the three observers (a) observer 1, (b) observer 2, and (c) observer 3. SP is simultaneous presentation of target and mask (Δt = 0). Minus ISI indicates forward masking.

Fig. 2
Fig. 2

Same as Fig. 1, for dichoptic presentation of the 25′ target.

Fig. 3
Fig. 3

Peak masking amplitude as a function of mask width for monoptic presentation of targets of width 8′ ○—○, 25′ ▲- -▲, and 49′ □- -□ for the three observers (a) observer 1, (b) observer 2, and (c) observer 3.

Fig. 4
Fig. 4

Same as Fig. 2, for dichoptic presentation of two targets of width 25′ ○—○ and 49′ ▲- -▲.

Fig. 5
Fig. 5

Weighting functions computed from the monoptic data of each observer: observer 1 ○—○, observer 2 ▲—▲, and observer 3 □—□ for the three targets, from left to right, 8′, 25′, and 49′ width.

Fig. 6
Fig. 6

Same as Fig. 3. The functions are computed from the dichoptic data for two targets, from left to right, 25′ and 49′ width.

Tables (4)

Tables Icon

Table I Significant effects for the four-way (observer × target × mask width × ISI) analysis of variance (p < 0.01).

Tables Icon

Table II Significant effects for the five-way (observer × target × mask width × ISI × state: monoptic vs dichoptic) analysis of variance (p < 0.01).

Tables Icon

Table III Arithmetic standard deviations of the magnitude estimations for the peak masking ISI, averaged across masks for each observer and target.

Tables Icon

Table IV ISIs at which peak masking occurred for each observer and mask for monoptic and dichoptic presentations. The values are averaged across targets. Mask width is in minutes of visual angle.

Equations (2)

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R ( p ) = g - + F ( x ) θ ( p - x ) d x .
θ(x)=1F(x)dRdx,