Abstract

The concept of local scale asserts that for a given class of psychophysical measurements, performance at any two visual field locations is equated by magnifying the targets by the local scale associated with each location. Local scale has been hypothesized to be equal to cortical magnification or alternatively to the linear density of receptors or ganglion cells. Here, we show that it is possible to estimate local scale without prior knowledge about the scale or its physiological basis.

© 1987 Optical Society of America

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  1. F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).
    [PubMed]
  2. M. Millodot, "Foveal and extra-foveal acuity with and without stabilized retinal images," Br. J. Physiol. Opt. 23,75–106 (1966).
    [PubMed]
  3. R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).
    [Crossref] [PubMed]
  4. J. J. Koenderink, M. A. Bouman, A. E. Bueno de Mesquita, and S. Slappendel, "Perimetry of contrast detection thresholds of moving spatial sine wave patterns. III. The target extent as a sensitivity controlling parameter," J. Opt. Soc. Am. 68,854–860 (1978).
    [Crossref] [PubMed]
  5. J. Rovamo, V. Virsu, and R. Nasanen, "Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision," Nature 271, 54–56 (1978).
    [Crossref] [PubMed]
  6. Dennis M. Levi, Stanley A. Klein, and A. P. Aitsebaomo, "Vernier acuity, crowding and cortical magnification," Vision Res. 25, 963–977 (1985).
    [Crossref] [PubMed]
  7. J. Rovamo and V. Virsu, "An estimation and application of the human cortical magnification factor," Exp. Brain Res. 37, 495–510 (1979).
    [Crossref] [PubMed]
  8. V. Virsu, J. Rovamo, P. Laurinen, and R. Nasanen, "Temporal contrast sensitivity and cortical magnification," Vision Res. 22, 1211–1217 (1982).
    [Crossref] [PubMed]
  9. J. Rovamo, "Cortical magnification factor and contrast sensitivity to luminance-modulated chromatic gratings," Acta Physiol. Scand. 119, 365–371 (1983).
    [Crossref] [PubMed]
  10. Swanson and Wilson used a shift rule but applied it to targets that were size scaled only in one dimension. In the other dimension, size was fixed according to a prior estimate of cortical magnification. [W. H. Swanson and H. R. Wilson, "Eccentricity dependence of contrast masking and oblique masking," Vision Res. 25, 1285–1295 (1985).]
    [Crossref]
  11. A. B. Watson and D. G. Pelli, "QUEST: a Bayesian adaptive psychometric method," Percept. Psychophys. 33, 113–120 (1983).
    [Crossref] [PubMed]
  12. A. B. Watson, "Probability summation over time," Vision Res. 19, 515–522 (1979).
    [Crossref] [PubMed]
  13. A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, and A. J. Ahumada, Jr., "Use of a raster framebuffer in vision research," Behav. Res. Methods Instrum. 18, 587–594 (1986).
    [Crossref]
  14. A. B. Watson, "Detection and recognition of simple spatial forms," in Physical and Biological Processing of Images, 0. J. Braddick and A. C. Sleigh, eds. (Springer-Verlag, New York, 1983), pp. 100–114.
    [Crossref]
  15. D. G. Pelli, "Uncertainty explains many aspects of visual contrast detection and discrimination," J. Opt. Soc. Am. A 2, 1508–1532 (1986).
    [Crossref]
  16. G. Westheimer, "The spatial grain of the perifoveal visual field," Vision Res. 22, 157–162 (1982).
    [Crossref] [PubMed]
  17. Levi et al.6 measured foveal and peripheral hyperacuity using scaled targets. However, they did not use the scheme suggested here but instead used targets at each eccentricity scaled in advance by an estimate of cortical magnification.

1986 (2)

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, and A. J. Ahumada, Jr., "Use of a raster framebuffer in vision research," Behav. Res. Methods Instrum. 18, 587–594 (1986).
[Crossref]

D. G. Pelli, "Uncertainty explains many aspects of visual contrast detection and discrimination," J. Opt. Soc. Am. A 2, 1508–1532 (1986).
[Crossref]

1985 (1)

Dennis M. Levi, Stanley A. Klein, and A. P. Aitsebaomo, "Vernier acuity, crowding and cortical magnification," Vision Res. 25, 963–977 (1985).
[Crossref] [PubMed]

1983 (2)

J. Rovamo, "Cortical magnification factor and contrast sensitivity to luminance-modulated chromatic gratings," Acta Physiol. Scand. 119, 365–371 (1983).
[Crossref] [PubMed]

A. B. Watson and D. G. Pelli, "QUEST: a Bayesian adaptive psychometric method," Percept. Psychophys. 33, 113–120 (1983).
[Crossref] [PubMed]

1982 (2)

V. Virsu, J. Rovamo, P. Laurinen, and R. Nasanen, "Temporal contrast sensitivity and cortical magnification," Vision Res. 22, 1211–1217 (1982).
[Crossref] [PubMed]

G. Westheimer, "The spatial grain of the perifoveal visual field," Vision Res. 22, 157–162 (1982).
[Crossref] [PubMed]

1979 (2)

J. Rovamo and V. Virsu, "An estimation and application of the human cortical magnification factor," Exp. Brain Res. 37, 495–510 (1979).
[Crossref] [PubMed]

A. B. Watson, "Probability summation over time," Vision Res. 19, 515–522 (1979).
[Crossref] [PubMed]

1978 (2)

1974 (1)

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).
[Crossref] [PubMed]

1966 (1)

M. Millodot, "Foveal and extra-foveal acuity with and without stabilized retinal images," Br. J. Physiol. Opt. 23,75–106 (1966).
[PubMed]

1958 (1)

F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).
[PubMed]

de Mesquita, A. E. Bueno

Ahumada, Jr., A. J.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, and A. J. Ahumada, Jr., "Use of a raster framebuffer in vision research," Behav. Res. Methods Instrum. 18, 587–594 (1986).
[Crossref]

Aitsebaomo, A. P.

Dennis M. Levi, Stanley A. Klein, and A. P. Aitsebaomo, "Vernier acuity, crowding and cortical magnification," Vision Res. 25, 963–977 (1985).
[Crossref] [PubMed]

Bilson, A.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, and A. J. Ahumada, Jr., "Use of a raster framebuffer in vision research," Behav. Res. Methods Instrum. 18, 587–594 (1986).
[Crossref]

Bouman, M. A.

Cavonius, C. R.

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).
[Crossref] [PubMed]

Fitzhugh, A.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, and A. J. Ahumada, Jr., "Use of a raster framebuffer in vision research," Behav. Res. Methods Instrum. 18, 587–594 (1986).
[Crossref]

Hilz, R.

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).
[Crossref] [PubMed]

Klein, Stanley A.

Dennis M. Levi, Stanley A. Klein, and A. P. Aitsebaomo, "Vernier acuity, crowding and cortical magnification," Vision Res. 25, 963–977 (1985).
[Crossref] [PubMed]

Koenderink, J. J.

Laurinen, P.

V. Virsu, J. Rovamo, P. Laurinen, and R. Nasanen, "Temporal contrast sensitivity and cortical magnification," Vision Res. 22, 1211–1217 (1982).
[Crossref] [PubMed]

Levi, Dennis M.

Dennis M. Levi, Stanley A. Klein, and A. P. Aitsebaomo, "Vernier acuity, crowding and cortical magnification," Vision Res. 25, 963–977 (1985).
[Crossref] [PubMed]

Millodot, M.

M. Millodot, "Foveal and extra-foveal acuity with and without stabilized retinal images," Br. J. Physiol. Opt. 23,75–106 (1966).
[PubMed]

Nasanen, R.

V. Virsu, J. Rovamo, P. Laurinen, and R. Nasanen, "Temporal contrast sensitivity and cortical magnification," Vision Res. 22, 1211–1217 (1982).
[Crossref] [PubMed]

J. Rovamo, V. Virsu, and R. Nasanen, "Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision," Nature 271, 54–56 (1978).
[Crossref] [PubMed]

Nguyen, K.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, and A. J. Ahumada, Jr., "Use of a raster framebuffer in vision research," Behav. Res. Methods Instrum. 18, 587–594 (1986).
[Crossref]

Nielsen, K. R. K.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, and A. J. Ahumada, Jr., "Use of a raster framebuffer in vision research," Behav. Res. Methods Instrum. 18, 587–594 (1986).
[Crossref]

Pelli, D. G.

D. G. Pelli, "Uncertainty explains many aspects of visual contrast detection and discrimination," J. Opt. Soc. Am. A 2, 1508–1532 (1986).
[Crossref]

A. B. Watson and D. G. Pelli, "QUEST: a Bayesian adaptive psychometric method," Percept. Psychophys. 33, 113–120 (1983).
[Crossref] [PubMed]

Poirson, A.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, and A. J. Ahumada, Jr., "Use of a raster framebuffer in vision research," Behav. Res. Methods Instrum. 18, 587–594 (1986).
[Crossref]

Rovamo, J.

J. Rovamo, "Cortical magnification factor and contrast sensitivity to luminance-modulated chromatic gratings," Acta Physiol. Scand. 119, 365–371 (1983).
[Crossref] [PubMed]

V. Virsu, J. Rovamo, P. Laurinen, and R. Nasanen, "Temporal contrast sensitivity and cortical magnification," Vision Res. 22, 1211–1217 (1982).
[Crossref] [PubMed]

J. Rovamo and V. Virsu, "An estimation and application of the human cortical magnification factor," Exp. Brain Res. 37, 495–510 (1979).
[Crossref] [PubMed]

J. Rovamo, V. Virsu, and R. Nasanen, "Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision," Nature 271, 54–56 (1978).
[Crossref] [PubMed]

Slappendel, S.

Virsu, V.

V. Virsu, J. Rovamo, P. Laurinen, and R. Nasanen, "Temporal contrast sensitivity and cortical magnification," Vision Res. 22, 1211–1217 (1982).
[Crossref] [PubMed]

J. Rovamo and V. Virsu, "An estimation and application of the human cortical magnification factor," Exp. Brain Res. 37, 495–510 (1979).
[Crossref] [PubMed]

J. Rovamo, V. Virsu, and R. Nasanen, "Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision," Nature 271, 54–56 (1978).
[Crossref] [PubMed]

Watson, A. B.

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, and A. J. Ahumada, Jr., "Use of a raster framebuffer in vision research," Behav. Res. Methods Instrum. 18, 587–594 (1986).
[Crossref]

A. B. Watson and D. G. Pelli, "QUEST: a Bayesian adaptive psychometric method," Percept. Psychophys. 33, 113–120 (1983).
[Crossref] [PubMed]

A. B. Watson, "Probability summation over time," Vision Res. 19, 515–522 (1979).
[Crossref] [PubMed]

A. B. Watson, "Detection and recognition of simple spatial forms," in Physical and Biological Processing of Images, 0. J. Braddick and A. C. Sleigh, eds. (Springer-Verlag, New York, 1983), pp. 100–114.
[Crossref]

Westheimer, G.

G. Westheimer, "The spatial grain of the perifoveal visual field," Vision Res. 22, 157–162 (1982).
[Crossref] [PubMed]

Weymouth, F. W.

F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).
[PubMed]

Acta Physiol. Scand. (1)

J. Rovamo, "Cortical magnification factor and contrast sensitivity to luminance-modulated chromatic gratings," Acta Physiol. Scand. 119, 365–371 (1983).
[Crossref] [PubMed]

Am. J. Ophthalmol. (1)

F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).
[PubMed]

Behav. Res. Methods Instrum. (1)

A. B. Watson, K. R. K. Nielsen, A. Poirson, A. Fitzhugh, A. Bilson, K. Nguyen, and A. J. Ahumada, Jr., "Use of a raster framebuffer in vision research," Behav. Res. Methods Instrum. 18, 587–594 (1986).
[Crossref]

Br. J. Physiol. Opt. (1)

M. Millodot, "Foveal and extra-foveal acuity with and without stabilized retinal images," Br. J. Physiol. Opt. 23,75–106 (1966).
[PubMed]

Exp. Brain Res. (1)

J. Rovamo and V. Virsu, "An estimation and application of the human cortical magnification factor," Exp. Brain Res. 37, 495–510 (1979).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nature (1)

J. Rovamo, V. Virsu, and R. Nasanen, "Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision," Nature 271, 54–56 (1978).
[Crossref] [PubMed]

Percept. Psychophys. (1)

A. B. Watson and D. G. Pelli, "QUEST: a Bayesian adaptive psychometric method," Percept. Psychophys. 33, 113–120 (1983).
[Crossref] [PubMed]

Vision Res. (5)

A. B. Watson, "Probability summation over time," Vision Res. 19, 515–522 (1979).
[Crossref] [PubMed]

G. Westheimer, "The spatial grain of the perifoveal visual field," Vision Res. 22, 157–162 (1982).
[Crossref] [PubMed]

Dennis M. Levi, Stanley A. Klein, and A. P. Aitsebaomo, "Vernier acuity, crowding and cortical magnification," Vision Res. 25, 963–977 (1985).
[Crossref] [PubMed]

R. Hilz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1337 (1974).
[Crossref] [PubMed]

V. Virsu, J. Rovamo, P. Laurinen, and R. Nasanen, "Temporal contrast sensitivity and cortical magnification," Vision Res. 22, 1211–1217 (1982).
[Crossref] [PubMed]

Other (3)

Swanson and Wilson used a shift rule but applied it to targets that were size scaled only in one dimension. In the other dimension, size was fixed according to a prior estimate of cortical magnification. [W. H. Swanson and H. R. Wilson, "Eccentricity dependence of contrast masking and oblique masking," Vision Res. 25, 1285–1295 (1985).]
[Crossref]

Levi et al.6 measured foveal and peripheral hyperacuity using scaled targets. However, they did not use the scheme suggested here but instead used targets at each eccentricity scaled in advance by an estimate of cortical magnification.

A. B. Watson, "Detection and recognition of simple spatial forms," in Physical and Biological Processing of Images, 0. J. Braddick and A. C. Sleigh, eds. (Springer-Verlag, New York, 1983), pp. 100–114.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

A set of size-scaled Gabor stimuli that increase in size by factors of 2.

Fig. 2
Fig. 2

A method of estimating local scale. A, A contrast-sensitivity function measured with size-scaled stimuli centered at the fovea. B, Comparison of the same measurements made at the fovea and a peripheral location (filled symbols). C, The peripheral curve has been slid to superimpose the foveal curve. The horizontal shift required is an estimate of local scale at the peripheral location.

Fig. 3
Fig. 3

Contrast-detection thresholds for size-scaled Gabor stimuli at eccentricities of 0 deg (⊡) and 3 deg (◆).

Fig. 4
Fig. 4

Data from Fig. 3, with peripheral data shifted to the right to superimpose the foveal data at high spatial frequencies.

Fig. 5
Fig. 5

Data from Fig. 3 fitted by a model of contrast detection embodying local scale proportional to eccentricity. Symbols: ⊡, data for 0 deg; ×, fit for 0 deg; ◘, data for 3 deg; ⟐, fit for 3 deg.

Equations (2)

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s = 1 + κ e ,
c = ( i = 0 N v i β ) - 1 / β ,

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