Abstract

Previous studies of spatial-frequency masking and adaptation have shown that the contrast-detection threshold elevates maximally when the test spatial frequency is the same as the masking (or adapting) frequency but changes only slightly when they are separated by two or more octaves. At low spatial frequencies, however, the peak of the threshold-elevation function does not obey this rule: there is a well-established peak shift in the threshold-elevation functions toward higher spatial frequencies. We investigated whether this shift might be due to the masking effects caused by the background field, which contributes energy at the very low end of the spectrum. We first measured the effect of a 3-cycles/deg (c/deg) mask on detection of a range of test frequencies, compared with unmasked detection thresholds. We then measured the combined effect of a 2-c/deg and a 3-c/deg mask on detection, compared with detection with just the 2-c/deg mask. The comparison in the second case still tests the effect of the 3-c/deg mask, but the presence of the hidden 2-c/deg mask causes the peak masking effect to shift toward higher frequencies. This result provides a proof of concept for the hypothesis that the peak shift at low spatial frequencies is caused by the low-frequency energy in the background field, which is present in both masked and unmasked conditions. A five-parameter quantitative model of frequency masking is presented that describes the pure contrast-detection function, the frequency-masking functions at mask frequencies of 0.25, 0.5, 2, and 3 c/deg, and the peak-shift phenomenon.

© 1998 Optical Society of America

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    [CrossRef] [PubMed]
  36. N. Brady, D. J. Field, “What’s constant in contrast constancy? The effects of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
    [CrossRef] [PubMed]
  37. A. B. Watson, “Efficiency of a model human image code,” J. Opt. Soc. Am. A 4, 2401–2417 (1987).
    [CrossRef] [PubMed]
  38. J. Yang, W. Makous, “Implicit masking constrained by spatial inhomogeneities,” Vision Res. 37, 1917–1927 (1997).
    [CrossRef] [PubMed]
  39. J. Yang, W. Makous, “Three theories of the low frequency cut,” Invest. Ophthalmol. Visual Sci. (Suppl.), 37, S733 (1996).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

1997 (3)

M. Carandini, D. Ferster, “A tonic hyperpolarization underlying contrast adaptation in cat visual cortex,” Science 276, 949–952 (1997).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Implicit masking constrained by spatial inhomogeneities,” Vision Res. 37, 1917–1927 (1997).
[CrossRef] [PubMed]

W. L. Makous, “Fourier models and loci of adaptation,” J. Opt. Soc. Am. A 14, 2323–2345 (1997).
[CrossRef]

1996 (2)

J. Yang, W. Makous, “Three theories of the low frequency cut,” Invest. Ophthalmol. Visual Sci. (Suppl.), 37, S733 (1996).

D. H. Peterzell, D. Y. Teller, “Individual differences in contrast sensitivity functions: the lowest spatial frequency channels,” Vision Res. 36, 3077–3085 (1996).
[CrossRef] [PubMed]

1995 (4)

H. Akutsu, G. E. Legge, “Discrimination of compound gratings: spatial-frequency channels or local features?” Vision Res. 35, 2685–2695 (1995).
[CrossRef] [PubMed]

J. Yang, X. Qi, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Modeling pedestal experiments with amplitude instead of contrast,” Vision Res. 35, 1979–1989 (1995).
[CrossRef] [PubMed]

N. Brady, D. J. Field, “What’s constant in contrast constancy? The effects of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
[CrossRef] [PubMed]

1994 (2)

R. J. Snowden, “Adaptability of the visual system is inversely related to its sensitivity,” J. Opt. Soc. Am. A 11, 25–32 (1994).
[CrossRef]

J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
[CrossRef] [PubMed]

1993 (3)

J. M. Foley, G. M. Boynton, “Forward pattern masking and adaptation: effects of duration, interstimulus interval, contrast, and spatial and temporal frequency,” Vision Res. 33, 959–980 (1993).
[CrossRef] [PubMed]

J. Ross, H. D. Speed, M. J. Morgan, “The effects of adaptation and masking on incremental thresholds for contrast,” Vision Res. 33, 2051–2056 (1993).
[CrossRef] [PubMed]

J. Nachmias, “Masked detection of gratings: the standard model revised,” Vision Res. 33, 1359–1365 (1993).
[CrossRef] [PubMed]

1992 (1)

R. F. Hess, R. J. Snowden, “Temporal properties of human visual filters: number, shapes and spatial covariation,” Vision Res. 32, 47–59 (1992).
[CrossRef] [PubMed]

1991 (2)

J. Ross, H. D. Speed, “Contrast adaptation and contrast masking in human vision,” Proc. R. Soc. London, Ser. B 246, 61–69 (1991).
[CrossRef]

J. M. Foley, Y. Yang, “Forward pattern masking: effects of spatial frequency and contrast,” J. Opt. Soc. Am. A 8, 2026–2037 (1991).
[CrossRef] [PubMed]

1989 (1)

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989).
[CrossRef] [PubMed]

1988 (1)

M. W. Greenlee, S. Magnussen, K. Nordby, “Spatial vision of the achromat: spatial frequency and orientation-specific adaptation,” J. Physiol. (London) 395, 661–678 (1988).

1987 (2)

M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time-course and contrast dependence,” Vision Res. 27, 369–379 (1987).
[CrossRef] [PubMed]

A. B. Watson, “Efficiency of a model human image code,” J. Opt. Soc. Am. A 4, 2401–2417 (1987).
[CrossRef] [PubMed]

1985 (1)

R. Shapley, P. Lennie, “Spatial frequency analysis in the visual system,” Ann. Rev. Neurosci. 8, 547–583 (1985).
[CrossRef] [PubMed]

1983 (2)

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

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

1982 (2)

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

C. F. Stromeyer, S. Klein, B. M. Dawson, L. Spillmann, “Low spatial-frequency channels in human vision: adaptation and masking,” Vision Res. 22, 225–233 (1982).
[CrossRef] [PubMed]

1981 (1)

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

1979 (1)

1978 (2)

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

G. E. Legge, “Sustained and transient mechanisms in human vision: temporal and spatial properties,” Vision Res. 18, 69–81 (1978).
[CrossRef] [PubMed]

1975 (1)

C. F. Stromeyer, S. Klein, “Evidence against narrow-band spatial frequency channels in human vision: the detectability of frequency modulated gratings,” Vision Res. 15, 899–910 (1975).
[CrossRef] [PubMed]

1973 (2)

L. Maffei, A. Fiorentini, “The visual cortex as a spatial frequency analyser,” Vision Res. 13, 1255–1267 (1973).
[CrossRef] [PubMed]

D. J. Tolhurst, “Separate channels for the analysis of shape and movement of a moving visual stimulus,” J. Physiol. (London) 231, 385–402 (1973).

1972 (2)

1971 (1)

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

1970 (1)

J. P. Thomas, “Model of the function of receptive fields in human vision,” Psychol. Rev. 77, 121–134 (1970).
[CrossRef] [PubMed]

1969 (1)

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

1968 (2)

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

A. Pantle, R. Sekuler, “Size-detecting mechanisms in human vision,” Science 162, 1146–1148 (1968).
[CrossRef] [PubMed]

Akutsu, H.

H. Akutsu, G. E. Legge, “Discrimination of compound gratings: spatial-frequency channels or local features?” Vision Res. 35, 2685–2695 (1995).
[CrossRef] [PubMed]

Albrecht, D. G.

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

Blakemore, C.

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

Boynton, G. M.

J. M. Foley, G. M. Boynton, “Forward pattern masking and adaptation: effects of duration, interstimulus interval, contrast, and spatial and temporal frequency,” Vision Res. 33, 959–980 (1993).
[CrossRef] [PubMed]

Brady, N.

N. Brady, D. J. Field, “What’s constant in contrast constancy? The effects of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
[CrossRef] [PubMed]

Campbell, F. W.

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

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

Carandini, M.

M. Carandini, D. Ferster, “A tonic hyperpolarization underlying contrast adaptation in cat visual cortex,” Science 276, 949–952 (1997).
[CrossRef] [PubMed]

Dawson, B. M.

C. F. Stromeyer, S. Klein, B. M. Dawson, L. Spillmann, “Low spatial-frequency channels in human vision: adaptation and masking,” Vision Res. 22, 225–233 (1982).
[CrossRef] [PubMed]

De Valois, K. K.

R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, Oxford, 1988).

De Valois, R. L.

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989).
[CrossRef] [PubMed]

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

R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, Oxford, 1988).

Elfar, S. D.

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989).
[CrossRef] [PubMed]

Ferster, D.

M. Carandini, D. Ferster, “A tonic hyperpolarization underlying contrast adaptation in cat visual cortex,” Science 276, 949–952 (1997).
[CrossRef] [PubMed]

Field, D. J.

N. Brady, D. J. Field, “What’s constant in contrast constancy? The effects of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
[CrossRef] [PubMed]

Fiorentini, A.

L. Maffei, A. Fiorentini, “The visual cortex as a spatial frequency analyser,” Vision Res. 13, 1255–1267 (1973).
[CrossRef] [PubMed]

Foley, J. M.

J. M. Foley, G. M. Boynton, “Forward pattern masking and adaptation: effects of duration, interstimulus interval, contrast, and spatial and temporal frequency,” Vision Res. 33, 959–980 (1993).
[CrossRef] [PubMed]

J. M. Foley, Y. Yang, “Forward pattern masking: effects of spatial frequency and contrast,” J. Opt. Soc. Am. A 8, 2026–2037 (1991).
[CrossRef] [PubMed]

Georgeson, J. M.

M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time-course and contrast dependence,” Vision Res. 27, 369–379 (1987).
[CrossRef] [PubMed]

Georgeson, M. A.

M. A. Georgeson, J. M. Georgeson, “Facilitation and masking of briefly presented gratings: time-course and contrast dependence,” Vision Res. 27, 369–379 (1987).
[CrossRef] [PubMed]

Graham, N.

N. Graham, “Spatial frequency channels in the human visual system: effects of luminance and pattern drift rate,” Vision Res. 12, 53–68 (1972).
[CrossRef] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

Graham, N. V. S.

N. V. S. Graham, Visual Pattern Analyzers (Oxford U. Press, Oxford, 1989).

Greenlee, M. W.

M. W. Greenlee, S. Magnussen, K. Nordby, “Spatial vision of the achromat: spatial frequency and orientation-specific adaptation,” J. Physiol. (London) 395, 661–678 (1988).

Grosof, D. H.

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989).
[CrossRef] [PubMed]

Hess, R. F.

R. F. Hess, R. J. Snowden, “Temporal properties of human visual filters: number, shapes and spatial covariation,” Vision Res. 32, 47–59 (1992).
[CrossRef] [PubMed]

Julesz, B.

Klein, S.

C. F. Stromeyer, S. Klein, B. M. Dawson, L. Spillmann, “Low spatial-frequency channels in human vision: adaptation and masking,” Vision Res. 22, 225–233 (1982).
[CrossRef] [PubMed]

C. F. Stromeyer, S. Klein, “Evidence against narrow-band spatial frequency channels in human vision: the detectability of frequency modulated gratings,” Vision Res. 15, 899–910 (1975).
[CrossRef] [PubMed]

Legge, G. E.

H. Akutsu, G. E. Legge, “Discrimination of compound gratings: spatial-frequency channels or local features?” Vision Res. 35, 2685–2695 (1995).
[CrossRef] [PubMed]

G. E. Legge, “Spatial frequency masking in human vision: binocular interactions,” J. Opt. Soc. Am. 69, 838–847 (1979).
[CrossRef] [PubMed]

G. E. Legge, “Sustained and transient mechanisms in human vision: temporal and spatial properties,” Vision Res. 18, 69–81 (1978).
[CrossRef] [PubMed]

Lennie, P.

R. Shapley, P. Lennie, “Spatial frequency analysis in the visual system,” Ann. Rev. Neurosci. 8, 547–583 (1985).
[CrossRef] [PubMed]

Maffei, L.

L. Maffei, A. Fiorentini, “The visual cortex as a spatial frequency analyser,” Vision Res. 13, 1255–1267 (1973).
[CrossRef] [PubMed]

Magnussen, S.

M. W. Greenlee, S. Magnussen, K. Nordby, “Spatial vision of the achromat: spatial frequency and orientation-specific adaptation,” J. Physiol. (London) 395, 661–678 (1988).

Makous, W.

J. Yang, W. Makous, “Implicit masking constrained by spatial inhomogeneities,” Vision Res. 37, 1917–1927 (1997).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Three theories of the low frequency cut,” Invest. Ophthalmol. Visual Sci. (Suppl.), 37, S733 (1996).

J. Yang, X. Qi, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Modeling pedestal experiments with amplitude instead of contrast,” Vision Res. 35, 1979–1989 (1995).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
[CrossRef] [PubMed]

Makous, W. L.

McFarlane, D. K.

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

Morgan, M. J.

J. Ross, H. D. Speed, M. J. Morgan, “The effects of adaptation and masking on incremental thresholds for contrast,” Vision Res. 33, 2051–2056 (1993).
[CrossRef] [PubMed]

Movshon, J. A.

J. A. Movshon, I. D. Thompson, D. J. Tolhurst, “Spatial and temporal contrast sensitivity of neurones in areas 17 and 18 of the cat’s visual cortex,” J. Physiol. (London) 283, 101–120 (1978).

Nachmias, J.

J. Nachmias, “Masked detection of gratings: the standard model revised,” Vision Res. 33, 1359–1365 (1993).
[CrossRef] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

Nordby, K.

M. W. Greenlee, S. Magnussen, K. Nordby, “Spatial vision of the achromat: spatial frequency and orientation-specific adaptation,” J. Physiol. (London) 395, 661–678 (1988).

Olzak, L. A.

L. A. Olzak, J. P. Thomas, “Seeing spatial patterns,” in Handbook of Perception and Human Performance, Vol. 1, Sensory Processes and Perception, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), Chap. 7.

Pantle, A.

A. Pantle, R. Sekuler, “Size-detecting mechanisms in human vision,” Science 162, 1146–1148 (1968).
[CrossRef] [PubMed]

Pelli, D. G.

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

Peterzell, D. H.

D. H. Peterzell, D. Y. Teller, “Individual differences in contrast sensitivity functions: the lowest spatial frequency channels,” Vision Res. 36, 3077–3085 (1996).
[CrossRef] [PubMed]

Phillips, G. C.

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

Qi, X.

J. Yang, X. Qi, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

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. (London) 197, 551–566 (1968).

Ross, J.

J. Ross, H. D. Speed, M. J. Morgan, “The effects of adaptation and masking on incremental thresholds for contrast,” Vision Res. 33, 2051–2056 (1993).
[CrossRef] [PubMed]

J. Ross, H. D. Speed, “Contrast adaptation and contrast masking in human vision,” Proc. R. Soc. London, Ser. B 246, 61–69 (1991).
[CrossRef]

Sekuler, R.

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Ann. Rev. Neurosci. (1)

R. Shapley, P. Lennie, “Spatial frequency analysis in the visual system,” Ann. Rev. Neurosci. 8, 547–583 (1985).
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Invest. Ophthalmol. Visual Sci. (Suppl.) (1)

J. Yang, W. Makous, “Three theories of the low frequency cut,” Invest. Ophthalmol. Visual Sci. (Suppl.), 37, S733 (1996).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (4)

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

M. S. Silverman, D. H. Grosof, R. L. De Valois, S. D. Elfar, “Spatial-frequency organization in primate striate cortex,” Proc. Natl. Acad. Sci. USA 86, 711–715 (1989).
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Proc. R. Soc. London, Ser. B (1)

J. Ross, H. D. Speed, “Contrast adaptation and contrast masking in human vision,” Proc. R. Soc. London, Ser. B 246, 61–69 (1991).
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Psychol. Rev. (1)

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[CrossRef] [PubMed]

J. Yang, W. Makous, “Spatiotemporal separability in contrast sensitivity,” Vision Res. 34, 2569–2576 (1994).
[CrossRef] [PubMed]

J. Yang, X. Qi, W. Makous, “Zero frequency masking and a model of contrast sensitivity,” Vision Res. 35, 1965–1978 (1995).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Modeling pedestal experiments with amplitude instead of contrast,” Vision Res. 35, 1979–1989 (1995).
[CrossRef] [PubMed]

C. F. Stromeyer, S. Klein, B. M. Dawson, L. Spillmann, “Low spatial-frequency channels in human vision: adaptation and masking,” Vision Res. 22, 225–233 (1982).
[CrossRef] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

N. Graham, “Spatial frequency channels in the human visual system: effects of luminance and pattern drift rate,” Vision Res. 12, 53–68 (1972).
[CrossRef] [PubMed]

J. Yang, W. Makous, “Implicit masking constrained by spatial inhomogeneities,” Vision Res. 37, 1917–1927 (1997).
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Other (3)

N. V. S. Graham, Visual Pattern Analyzers (Oxford U. Press, Oxford, 1989).

R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, Oxford, 1988).

L. A. Olzak, J. P. Thomas, “Seeing spatial patterns,” in Handbook of Perception and Human Performance, Vol. 1, Sensory Processes and Perception, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), Chap. 7.

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Figures (9)

Fig. 1
Fig. 1

Masking by a 3-c/deg grating of 15% contrast. Threshold elevation is plotted against test frequency for observers QW, SBS, and JY. Error bars represent +1 standard error of the data and are shown in just one direction for clarity. The solid curve represents geometrical mean over the three observers. The arrow points to the mask frequency.

Fig. 2
Fig. 2

Masking by a 3-c/deg grating of 15% contrast in the case in which both masking and baseline conditions had an extra background grating of 2 c/deg and 20% contrast. Threshold elevation is plotted against test frequency for observers QW, SBS, and JY. Error bars represent +1 standard error of the mean for each subject. The solid curve represents the geometric mean over the three observers. The arrows point to the mask frequencies.

Fig. 3
Fig. 3

Masking by a 0.25-c/deg grating of 15% contrast. Threshold elevation is plotted against test frequency for observers QW, SBS, and JY. Error bars represent +1 standard error of the mean for each subject. The solid curve represents the geometric mean over the three observers. The arrow points to the mask frequency.

Fig. 4
Fig. 4

Masking by a 0.5-c/deg grating of 15% contrast. Threshold elevation is plotted against test frequency for observers QW, SBS, and JY. Error bars represent +1 standard error of the mean for each subject. The solid curve represents the geometric mean over the three observers. The arrow points to the mask frequency.

Fig. 5
Fig. 5

Mean contrast sensitivity functions for unmasked (filled squares) and in the presence of a mask frequency of 0.25 c/deg (open circles), 0.5 c/deg (filled triangles), 2 c/deg (open diamonds), 3 c/deg (open squares), and both 2 and 3 c/deg (filled circles). The mask contrast was 15% for all but the 2-c/deg masker, which had a contrast of 20%. Error bars represent +1 standard error of the mean over three observers. The solid curves are the model fits. The data for 2-c/deg masking (open diamonds) served as the baseline function for the threshold elevations plotted in Fig. 2 and the solid curve (3+2) in Fig. 6. For all other cases, the unmasked data (filled squares) were used for the baseline.

Fig. 6
Fig. 6

Model-based threshold-elevation curves with mask frequency of 0.25, 0.5, 2, 3, or 2 and 3 c/deg. The contrast of the mask was 15% except for the 2-c/deg masker which had a contrast of 20%. The arrows point to the mask frequencies.

Fig. 7
Fig. 7

Simulation of the change in peak shift by (a) varying masking strength or (b) varying the half-width of the zero-frequency spread. Parameter values, other than that shown in the figure, were the same as those shown in Table 1 of the current study. The arrows point to the mask frequencies.

Fig. 8
Fig. 8

Geometrically averaged experimental data over three subjects (symbols) and the model predictions (curves) of threshold-elevation curve versus mask frequency for test frequency of 0.25 c/deg (open circles, dotted curve), 0.5 c/deg (filled triangles, dashed curve), 3 c/deg (open squares, dotted–dashed curve) and 3 c/deg with an extra masker at 2 c/deg (filled circles, solid curve). The contrast of the maskers was 10% except for the extra masker, which had a contrast of 5%. Error bars represent +1 standard error of the mean over three observers. The arrows point to the test frequencies.

Fig. 9
Fig. 9

Comparison of the model predictions (curves) and the masking data (symbols) of Legge (Fig. 7 of Ref. 28), for test frequency of 0.125 c/deg (open squares, dotted–dashed curve), 0.25 c/deg (filled circles, solid curve), 1 c/deg (stars, long-dashed curve), 4 c/deg (open circles, short-dashed curve), and 16 c/deg (open triangles, dotted curve) c/deg. The contrast of the maskers was 19%, and the field size was 13 deg for test frequencies of 1 c/deg and below and 3.25 deg for test frequencies of 4 and 16 deg. The predictions were based on the same five parameter values as those used in Fig. 8. The threshold elevation is calculated as the ratio between the contrast thresholds obtained with and without a masker, which is slightly different from the definition used in the Legge paper.

Tables (1)

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Table 1 Estimated Model Parametersa

Equations (11)

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s(y)=L{1+sin(2πωt)[Cm cos(2πfmy)+C cos(2πfy)]},
Cth=exp(αf)(N+E0+Em)-ρmG(f, fm),
E0=η0σ02/(f2+σ02),
Em=Cm exp(-αfm)ηmG(f, fm),
G(f, fm)=σm2/[(fm-f )2+σm2].
ρm=CmG(f, fm)C02/[Cm2G(f, fm)2+C02],
C0=exp(αf)(N+E0).
Cth=exp(αf)(N+E0+Em)-ρmG(f, fm);
G(f, fm)=(fm/f )0.5σm2/[(fm-f )2+σm2]
σm=σ0+kfm,
σ0=0.042+0.64/field_size.

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