Abstract

Recent data from several laboratories have shown that spatial-frequency discrimination is not a smooth function of frequency but rather exhibits alternate peaks and troughs. A model for spatial-frequency discrimination analogous to line-element models for color discrimination is presented here and shown to provide a reasonable fit to the available data. This model is based on the predicted responses of six spatial-frequency-tuned mechanisms, whose sensitivity curves have been estimated in previously published masking experiments. In order to fit the data it is necessary to pool responses from units centered under the stimulus as well as from spatially neighboring units. Thus it appears that the visual system utilizes both spatial and spatial-frequency information in discrimination tasks.

© 1984 Optical Society of America

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References

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  1. A. Koenig, C. Dieterici, “Ueber die Empfindlichkeit des normalen Auges fuer Wellenlaengenunterschiede des Lichtes,” Ann. Phys. Chem. 22, 579–589 (1884).
  2. C. H. Graham, “Color: data and theories,” in Vision and Visual Perception, C. H. Graham, ed. (Wiley, New York, 1965), pp. 414–451.
  3. M. A. Bouman, P. L. Walraven, “Color discrimination data,” in Handbook of Sensory Physiology: VII/4: Visual Psychophysics, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, New York, 1972, pp. 484–516.
    [Crossref]
  4. J. Hirsch, R. Hylton, “Limits of spatial-frequency discrimination as evidence of neural interpolation,” J. Opt. Soc. Am. 72, 1367–1374 (1982).
    [Crossref] [PubMed]
  5. D. Yager, E. Richter, “Spatial frequency difference thresholds are not monotonic with frequency,” Inv. Ophthalmol. Visual Science Suppl. 22, 251 (1982).
  6. H. R. Wilson, D. J. Gelb, “Spatial and temporal influences on size discrimination,” Invest. Ophthalmol. Visual Science Suppl. 18, 61 (1979).
  7. H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
    [Crossref] [PubMed]
  8. H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
    [Crossref]
  9. D. W. Williams, H. R. Wilson, J. D. Cowan, “Localized effects of spatial-frequency adaptation,” J. Opt. Soc. Am. 72, 878–887 (1982).
    [Crossref] [PubMed]
  10. R. W. Sekuler, H. R. Wilson, C. J. Owsley, “Structural modeling of spatial vision,” Vision Res. (to be published).
  11. A. B. Watson, J. G. Robson, “Discrimination at threshold: labelled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
    [Crossref] [PubMed]
  12. R. L. DeValois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
    [Crossref]
  13. H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybernetics 38, 171–178 (1980).
    [Crossref]
  14. J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
    [Crossref] [PubMed]
  15. G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–469 (1981).
    [Crossref] [PubMed]
  16. G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1470 (1980).
    [Crossref] [PubMed]
  17. C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
    [Crossref] [PubMed]
  18. C. R. Carlson, “Thresholds for perceived image sharpness,” Photogr. Sci. Eng. 22, 69–71 (1978).
  19. C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Disp. 21, 229–246 (1980).
  20. R. F. Quick, “A vector-magnitude model for contrast detection,” Kybernetik 16, 65–67 (1974).
    [Crossref]
  21. Y. LeGrand, Light, Color, and Vision (Wiley, New York, 1957).
  22. D. J. Gelb, H. R. Wilson, “Shifts in perceived size due to masking,” Vision Res. 23, 589–597 (1983).
    [Crossref] [PubMed]
  23. B. Sakitt, H. B. Barlow, “A model for the economical encoding of the visual image in cerebral cortex,” Biol. Cybernetics 43, 97–108 (1982).
    [Crossref]
  24. J. G. Robson, “Receptive fields: neural representation of the spatial and intensive attributes of the visual image,” in Handbook of Perception, V: Seeing, E. C. Carterette, M. P. Friedman, eds. (Academic, New York, 1975), pp. 81–116.
  25. B. G. Cleland, T. H. Harding, U. Tulunay-Keesey, “Visual resolution and receptive field size: examination of two kinds of cat retinal ganglion cell,” Science 205, 1015–1017 (1979).
    [Crossref] [PubMed]
  26. J. I. Yellott, “Spectral analysis of spatial sampling by photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
    [Crossref] [PubMed]
  27. G. Westheimer, “Spatial sense of the eye,” Invest. Ophthalmol. Visual Sci. 18, 893–912 (1979).
  28. Data are summarized in Y. LeGrand, Form and Space Vision (Indiana U. Press, Bloomington, Ind., 1967), p. 141.
  29. W. S. Stiles, “A modified Helmholtz line-element in brightness-color space,” Proc. Phys. Soc. 58, 41–65 (1946).
    [Crossref]
  30. F. W. Campbell, J. Nachmias, J. Jukes, “Spatial-frequency discrimination in human vision,” J. Opt. Soc. Am. 60, 555–559 (1970).
    [Crossref] [PubMed]
  31. A. B. Watson, “Detection and recognition of simple spatial forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Sleigh, eds. (Springer-Verlag, New York, 1983), pp. 100–114.
    [Crossref]
  32. F. W. Campbell, J. G. Robson, “Application of fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
    [PubMed]
  33. D. Regan, K. I. Beverley, “Spatial-frequency discrimination and detection: comparison of postadaptation thresholds,” J. Opt. Soc. Am. 73, 1685–1691 (1983).
    [Crossref]
  34. D. H. Foster, “A spatial perturbation technique for the investigation of discrete internal representations of visual patterns,” Biol. Cybernetics 38, 159–169 (1980).
    [Crossref]

1983 (3)

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[Crossref]

D. J. Gelb, H. R. Wilson, “Shifts in perceived size due to masking,” Vision Res. 23, 589–597 (1983).
[Crossref] [PubMed]

D. Regan, K. I. Beverley, “Spatial-frequency discrimination and detection: comparison of postadaptation thresholds,” J. Opt. Soc. Am. 73, 1685–1691 (1983).
[Crossref]

1982 (6)

J. I. Yellott, “Spectral analysis of spatial sampling by photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
[Crossref] [PubMed]

B. Sakitt, H. B. Barlow, “A model for the economical encoding of the visual image in cerebral cortex,” Biol. Cybernetics 43, 97–108 (1982).
[Crossref]

D. W. Williams, H. R. Wilson, J. D. Cowan, “Localized effects of spatial-frequency adaptation,” J. Opt. Soc. Am. 72, 878–887 (1982).
[Crossref] [PubMed]

R. L. DeValois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[Crossref]

J. Hirsch, R. Hylton, “Limits of spatial-frequency discrimination as evidence of neural interpolation,” J. Opt. Soc. Am. 72, 1367–1374 (1982).
[Crossref] [PubMed]

D. Yager, E. Richter, “Spatial frequency difference thresholds are not monotonic with frequency,” Inv. Ophthalmol. Visual Science Suppl. 22, 251 (1982).

1981 (2)

A. B. Watson, J. G. Robson, “Discrimination at threshold: labelled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
[Crossref] [PubMed]

G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–469 (1981).
[Crossref] [PubMed]

1980 (4)

G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1470 (1980).
[Crossref] [PubMed]

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Disp. 21, 229–246 (1980).

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybernetics 38, 171–178 (1980).
[Crossref]

D. H. Foster, “A spatial perturbation technique for the investigation of discrete internal representations of visual patterns,” Biol. Cybernetics 38, 159–169 (1980).
[Crossref]

1979 (4)

G. Westheimer, “Spatial sense of the eye,” Invest. Ophthalmol. Visual Sci. 18, 893–912 (1979).

H. R. Wilson, D. J. Gelb, “Spatial and temporal influences on size discrimination,” Invest. Ophthalmol. Visual Science Suppl. 18, 61 (1979).

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[Crossref] [PubMed]

B. G. Cleland, T. H. Harding, U. Tulunay-Keesey, “Visual resolution and receptive field size: examination of two kinds of cat retinal ganglion cell,” Science 205, 1015–1017 (1979).
[Crossref] [PubMed]

1978 (1)

C. R. Carlson, “Thresholds for perceived image sharpness,” Photogr. Sci. Eng. 22, 69–71 (1978).

1974 (3)

C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[Crossref] [PubMed]

R. F. Quick, “A vector-magnitude model for contrast detection,” Kybernetik 16, 65–67 (1974).
[Crossref]

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

1970 (1)

1968 (1)

F. W. Campbell, J. G. Robson, “Application of fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

1946 (1)

W. S. Stiles, “A modified Helmholtz line-element in brightness-color space,” Proc. Phys. Soc. 58, 41–65 (1946).
[Crossref]

1884 (1)

A. Koenig, C. Dieterici, “Ueber die Empfindlichkeit des normalen Auges fuer Wellenlaengenunterschiede des Lichtes,” Ann. Phys. Chem. 22, 579–589 (1884).

Albrecht, D. G.

R. L. DeValois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[Crossref]

Barlow, H. B.

B. Sakitt, H. B. Barlow, “A model for the economical encoding of the visual image in cerebral cortex,” Biol. Cybernetics 43, 97–108 (1982).
[Crossref]

Bergen, J. R.

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[Crossref] [PubMed]

Beverley, K. I.

D. Regan, K. I. Beverley, “Spatial-frequency discrimination and detection: comparison of postadaptation thresholds,” J. Opt. Soc. Am. 73, 1685–1691 (1983).
[Crossref]

Bouman, M. A.

M. A. Bouman, P. L. Walraven, “Color discrimination data,” in Handbook of Sensory Physiology: VII/4: Visual Psychophysics, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, New York, 1972, pp. 484–516.
[Crossref]

Campbell, F. W.

F. W. Campbell, J. Nachmias, J. Jukes, “Spatial-frequency discrimination in human vision,” J. Opt. Soc. Am. 60, 555–559 (1970).
[Crossref] [PubMed]

F. W. Campbell, J. G. Robson, “Application of fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

Carlson, C. R.

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Disp. 21, 229–246 (1980).

C. R. Carlson, “Thresholds for perceived image sharpness,” Photogr. Sci. Eng. 22, 69–71 (1978).

Cleland, B. G.

B. G. Cleland, T. H. Harding, U. Tulunay-Keesey, “Visual resolution and receptive field size: examination of two kinds of cat retinal ganglion cell,” Science 205, 1015–1017 (1979).
[Crossref] [PubMed]

Cohen, R. W.

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Disp. 21, 229–246 (1980).

Cowan, J. D.

DeValois, R. L.

R. L. DeValois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[Crossref]

Dieterici, C.

A. Koenig, C. Dieterici, “Ueber die Empfindlichkeit des normalen Auges fuer Wellenlaengenunterschiede des Lichtes,” Ann. Phys. Chem. 22, 579–589 (1884).

Foley, J. M.

Foster, D. H.

D. H. Foster, “A spatial perturbation technique for the investigation of discrete internal representations of visual patterns,” Biol. Cybernetics 38, 159–169 (1980).
[Crossref]

Gelb, D. J.

D. J. Gelb, H. R. Wilson, “Shifts in perceived size due to masking,” Vision Res. 23, 589–597 (1983).
[Crossref] [PubMed]

H. R. Wilson, D. J. Gelb, “Spatial and temporal influences on size discrimination,” Invest. Ophthalmol. Visual Science Suppl. 18, 61 (1979).

Graham, C. H.

C. H. Graham, “Color: data and theories,” in Vision and Visual Perception, C. H. Graham, ed. (Wiley, New York, 1965), pp. 414–451.

Harding, T. H.

B. G. Cleland, T. H. Harding, U. Tulunay-Keesey, “Visual resolution and receptive field size: examination of two kinds of cat retinal ganglion cell,” Science 205, 1015–1017 (1979).
[Crossref] [PubMed]

Hirsch, J.

Hylton, R.

Jukes, J.

Klein, S.

C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[Crossref] [PubMed]

Koenig, A.

A. Koenig, C. Dieterici, “Ueber die Empfindlichkeit des normalen Auges fuer Wellenlaengenunterschiede des Lichtes,” Ann. Phys. Chem. 22, 579–589 (1884).

Legge, G. E.

LeGrand, Y.

Data are summarized in Y. LeGrand, Form and Space Vision (Indiana U. Press, Bloomington, Ind., 1967), p. 141.

Y. LeGrand, Light, Color, and Vision (Wiley, New York, 1957).

McFarlane, D. K.

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[Crossref]

Nachmias, J.

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

F. W. Campbell, J. Nachmias, J. Jukes, “Spatial-frequency discrimination in human vision,” J. Opt. Soc. Am. 60, 555–559 (1970).
[Crossref] [PubMed]

Owsley, C. J.

R. W. Sekuler, H. R. Wilson, C. J. Owsley, “Structural modeling of spatial vision,” Vision Res. (to be published).

Phillips, G. C.

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[Crossref]

Quick, R. F.

R. F. Quick, “A vector-magnitude model for contrast detection,” Kybernetik 16, 65–67 (1974).
[Crossref]

Regan, D.

D. Regan, K. I. Beverley, “Spatial-frequency discrimination and detection: comparison of postadaptation thresholds,” J. Opt. Soc. Am. 73, 1685–1691 (1983).
[Crossref]

Richter, E.

D. Yager, E. Richter, “Spatial frequency difference thresholds are not monotonic with frequency,” Inv. Ophthalmol. Visual Science Suppl. 22, 251 (1982).

Robson, J. G.

A. B. Watson, J. G. Robson, “Discrimination at threshold: labelled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
[Crossref] [PubMed]

F. W. Campbell, J. G. Robson, “Application of fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

J. G. Robson, “Receptive fields: neural representation of the spatial and intensive attributes of the visual image,” in Handbook of Perception, V: Seeing, E. C. Carterette, M. P. Friedman, eds. (Academic, New York, 1975), pp. 81–116.

Sakitt, B.

B. Sakitt, H. B. Barlow, “A model for the economical encoding of the visual image in cerebral cortex,” Biol. Cybernetics 43, 97–108 (1982).
[Crossref]

Sansbury, R. V.

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

Sekuler, R. W.

R. W. Sekuler, H. R. Wilson, C. J. Owsley, “Structural modeling of spatial vision,” Vision Res. (to be published).

Stiles, W. S.

W. S. Stiles, “A modified Helmholtz line-element in brightness-color space,” Proc. Phys. Soc. 58, 41–65 (1946).
[Crossref]

Stromeyer, C. F.

C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[Crossref] [PubMed]

Thorell, L. G.

R. L. DeValois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[Crossref]

Tulunay-Keesey, U.

B. G. Cleland, T. H. Harding, U. Tulunay-Keesey, “Visual resolution and receptive field size: examination of two kinds of cat retinal ganglion cell,” Science 205, 1015–1017 (1979).
[Crossref] [PubMed]

Walraven, P. L.

M. A. Bouman, P. L. Walraven, “Color discrimination data,” in Handbook of Sensory Physiology: VII/4: Visual Psychophysics, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, New York, 1972, pp. 484–516.
[Crossref]

Watson, A. B.

A. B. Watson, J. G. Robson, “Discrimination at threshold: labelled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
[Crossref] [PubMed]

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

Westheimer, G.

G. Westheimer, “Spatial sense of the eye,” Invest. Ophthalmol. Visual Sci. 18, 893–912 (1979).

Williams, D. W.

Wilson, H. R.

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[Crossref]

D. J. Gelb, H. R. Wilson, “Shifts in perceived size due to masking,” Vision Res. 23, 589–597 (1983).
[Crossref] [PubMed]

D. W. Williams, H. R. Wilson, J. D. Cowan, “Localized effects of spatial-frequency adaptation,” J. Opt. Soc. Am. 72, 878–887 (1982).
[Crossref] [PubMed]

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybernetics 38, 171–178 (1980).
[Crossref]

H. R. Wilson, D. J. Gelb, “Spatial and temporal influences on size discrimination,” Invest. Ophthalmol. Visual Science Suppl. 18, 61 (1979).

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[Crossref] [PubMed]

R. W. Sekuler, H. R. Wilson, C. J. Owsley, “Structural modeling of spatial vision,” Vision Res. (to be published).

Yager, D.

D. Yager, E. Richter, “Spatial frequency difference thresholds are not monotonic with frequency,” Inv. Ophthalmol. Visual Science Suppl. 22, 251 (1982).

Yellott, J. I.

J. I. Yellott, “Spectral analysis of spatial sampling by photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
[Crossref] [PubMed]

Ann. Phys. Chem. (1)

A. Koenig, C. Dieterici, “Ueber die Empfindlichkeit des normalen Auges fuer Wellenlaengenunterschiede des Lichtes,” Ann. Phys. Chem. 22, 579–589 (1884).

Biol. Cybernetics (3)

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybernetics 38, 171–178 (1980).
[Crossref]

B. Sakitt, H. B. Barlow, “A model for the economical encoding of the visual image in cerebral cortex,” Biol. Cybernetics 43, 97–108 (1982).
[Crossref]

D. H. Foster, “A spatial perturbation technique for the investigation of discrete internal representations of visual patterns,” Biol. Cybernetics 38, 159–169 (1980).
[Crossref]

Inv. Ophthalmol. Visual Science Suppl. (1)

D. Yager, E. Richter, “Spatial frequency difference thresholds are not monotonic with frequency,” Inv. Ophthalmol. Visual Science Suppl. 22, 251 (1982).

Invest. Ophthalmol. Visual Sci. (1)

G. Westheimer, “Spatial sense of the eye,” Invest. Ophthalmol. Visual Sci. 18, 893–912 (1979).

Invest. Ophthalmol. Visual Science Suppl. (1)

H. R. Wilson, D. J. Gelb, “Spatial and temporal influences on size discrimination,” Invest. Ophthalmol. Visual Science Suppl. 18, 61 (1979).

J. Opt. Soc. Am. (5)

J. Physiol. (1)

F. W. Campbell, J. G. Robson, “Application of fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

Kybernetik (1)

R. F. Quick, “A vector-magnitude model for contrast detection,” Kybernetik 16, 65–67 (1974).
[Crossref]

Photogr. Sci. Eng. (1)

C. R. Carlson, “Thresholds for perceived image sharpness,” Photogr. Sci. Eng. 22, 69–71 (1978).

Proc. Phys. Soc. (1)

W. S. Stiles, “A modified Helmholtz line-element in brightness-color space,” Proc. Phys. Soc. 58, 41–65 (1946).
[Crossref]

Proc. Soc. Inf. Disp. (1)

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Disp. 21, 229–246 (1980).

Science (1)

B. G. Cleland, T. H. Harding, U. Tulunay-Keesey, “Visual resolution and receptive field size: examination of two kinds of cat retinal ganglion cell,” Science 205, 1015–1017 (1979).
[Crossref] [PubMed]

Vision Res. (9)

J. I. Yellott, “Spectral analysis of spatial sampling by photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
[Crossref] [PubMed]

D. J. Gelb, H. R. Wilson, “Shifts in perceived size due to masking,” Vision Res. 23, 589–597 (1983).
[Crossref] [PubMed]

C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[Crossref] [PubMed]

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[Crossref] [PubMed]

G. E. Legge, “A power law for contrast discrimination,” Vision Res. 21, 457–469 (1981).
[Crossref] [PubMed]

A. B. Watson, J. G. Robson, “Discrimination at threshold: labelled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
[Crossref] [PubMed]

R. L. DeValois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
[Crossref]

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[Crossref] [PubMed]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
[Crossref]

Other (7)

R. W. Sekuler, H. R. Wilson, C. J. Owsley, “Structural modeling of spatial vision,” Vision Res. (to be published).

C. H. Graham, “Color: data and theories,” in Vision and Visual Perception, C. H. Graham, ed. (Wiley, New York, 1965), pp. 414–451.

M. A. Bouman, P. L. Walraven, “Color discrimination data,” in Handbook of Sensory Physiology: VII/4: Visual Psychophysics, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, New York, 1972, pp. 484–516.
[Crossref]

Y. LeGrand, Light, Color, and Vision (Wiley, New York, 1957).

J. G. Robson, “Receptive fields: neural representation of the spatial and intensive attributes of the visual image,” in Handbook of Perception, V: Seeing, E. C. Carterette, M. P. Friedman, eds. (Academic, New York, 1975), pp. 81–116.

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

Data are summarized in Y. LeGrand, Form and Space Vision (Indiana U. Press, Bloomington, Ind., 1967), p. 141.

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Figures (7)

Fig. 1
Fig. 1

Mean data from three subjects on the spatial-frequency tuning of six mechanisms as determined from masking data.8 Mechanisms A–F are arranged in order of increasing peak spatial frequency. The average standard deviation among subjects is plotted in C. Solid curves are fits obtained using Eq. (2) and the constants in Table 1. Note that the spatial-frequency scale is different for the left- and right-hand halves of the diagram.

Fig. 2
Fig. 2

Spatial-frequency discrimination Δω/ω as a function of test spatial frequency. Data for two subjects are replotted from the Hirsch–Hylton study4 and have been connected by dotted lines for clarity. The solid lines, which provide a reasonable fit to the data, are predictions obtained with a model that pools both spatial and spatial-frequency information. The dashed lines show the model results when only spatial-frequency information is pooled.

Fig. 3
Fig. 3

Spatial-frequency discrimination data from the third subject in the Hirsch–Hylton study.4 The solid line is the model prediction obtained by pooling both spatial and spatial-frequency information. As the peaks and troughs in this subject’s data were shifted toward higher spatial frequencies relative to the two subjects in Fig. 2, it was necessary to scale the model predictions towards higher spatial frequencies by a factor of 1.25.

Fig. 4
Fig. 4

Dependence of spatial-frequency discrimination on the number of cycles presented for an 8.0-cpd grating. The data are from Hirsch and Hylton,4 and the model prediction includes both spatial and spatial-frequency information. The model prediction (solid line) is flat beyond 2.5 cycles, as the mechanisms mediating discrimination require just 2.5 cycles for maximum stimulation (see text).

Fig. 5
Fig. 5

Percent-correct discrimination between pairs of DOG’s differing in width by 0.25 octave plotted as a function of the mean space constant for each pair. All DOG’s were presented at a contrast 2.5 times their threshold contrast. For reference, the peak spatial frequencies of the stimuli are indicated across the top. The filled circles and solid line are data and model predictions for a sustained temporal presentation, and the open circles and dashed line are for a transient presentation.

Fig. 6
Fig. 6

Percent-correct discrimination between pairs of DOG’s differing in width by 0.25 octave. Data were collected on two subjects under transient conditions, with contrast fixed at 0.10. The model predicts the average position of peaks and troughs for the two subjects.

Fig. 7
Fig. 7

Spatial-frequency discrimination at threshold under sustained (filled circles) and transient (open circles) temporal conditions. Data are replotted from Ref. 11. Sustained and transient model predictions are shown by solid and dashed curves, respectively. Given the spread of the data, the model predictions are accurate except under transient conditions at 2.0 cpd.

Tables (2)

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Table 1 Values of Constants Defining the Spatial and Spatial-Frequency Sensitivity for Each Mechanism as Determined from Masking dataa

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Table 2 Values of Constants Associated with the Contrast Nonlinearity for Each Mechanism as Determined from Masking Dataa

Equations (9)

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L S F ( x ) = A [ exp ( - x 2 / σ 1 2 ) - B exp ( - x 2 / σ 2 2 ) + C exp ( - x 2 / σ 3 2 ) ] ,
T { L S F } = A π 0.5 { σ 1 exp [ - ( π σ 1 ω ) 2 ] - B σ 2 exp [ - ( π σ 2 ω ) 2 ] + C σ 3 exp [ - ( π σ 3 ω ) 2 ] } .
S i ( x ) = - + L S F i ( x - x ) P ( x ) d x .
threshold elevation = H ( S M C M ) ,
F ( S C ) = ( S C ) 2 + K ( S C ) 3 - K + ( S C ) 2 ,
K = 1 / H ( 1 - ) .
Δ F i ( x ) = F i ( P 1 ) - F i ( P 2 ) ,
Δ F = [ i x Δ F i ( x ) Q ] 1 / Q ,
ψ ( Δ F ) = 1 - 2 ( 1 + k Δ f ) 3 .

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