Abstract

Two-alternative forced-choice procedures were used to measure the detectability of bright and dark bars at various locations across luminance patterns that produced Mach bands. Detection performance was significantly affected by both dark and bright Mach bands: poor detection performance was observed at locations near, but not in, the Mach bands; relatively good detection performance at locations within the Mach bands was caused by reliable changes in the width, depth, or symmetry of the bands produced by the signal bars. The changes were apparent with signals of lower luminance than that needed for detection in the plateau regions far from the bands, but, because the cues were not sufficiently reliable to allow errorless performance, unusually shaped psychometric functions were obtained.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  33. D. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
    [CrossRef] [PubMed]
  34. J. P. Thomas, “Brightness variations in stimuli with ramp-like contours,” J. Opt. Soc. Am. 56, 238–242 (1966).
    [CrossRef] [PubMed]
  35. M. V. Levine, “Transformations that render curves parallel,” J. Math. Psychol. 7, 410–443 (1970).
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    [CrossRef]
  38. A. Vassilev, “Contrast sensitivity near borders: significance of test stimulus form, size and duration,” Vision Res. 13, 719–730 (1973).
    [CrossRef] [PubMed]
  39. K.-I. Naka, W. A. H. Rushton, “S-potentials from luminosity units in the retina of fish (Cyprinicae),” J. Physiol. (London) 185, 587–599 (1966).
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    [CrossRef] [PubMed]
  42. J. Nachmias, “Contrast modulated maskers: test of a late nonlinearity hypothesis,” Vision Res. 29, 137–142 (1989).
    [CrossRef] [PubMed]
  43. I. Fine, Department of Psychology, University of California, San Diego, La Jolla, Calif. 92093 (personal cummunication, 1993).

1997 (1)

1996 (1)

M. W. Cannon, S. C. Fullenkamp, “A model for inhibitory lateral interaction effects in perceived contrast,” Vision Res. 36, 1115–1125 (1996).
[CrossRef] [PubMed]

1995 (2)

L. Pessoa, E. Mignolla, H. Neumann, “A contrast- and luminance-driven multiscale network model of brightness,” Vision Res. 35, 2201–2223 (1995).
[CrossRef] [PubMed]

P. T. Kortum, W. S. Geisler, “Adaptation mechanisms in spatial vision—II. Flash thresholds and background adaptation,” Vision Res. 35, 1595–1609 (1995).
[CrossRef] [PubMed]

1994 (1)

J. M. H. du Buf, “Ramp edges, Mach bands, and the functional significance of the simple cell assembly,” Biol. Cybern. 70, 449–461 (1994).
[CrossRef]

1992 (1)

F. Kingdom, B. Moulden, “A multi-channel approach to brightness coding,” Vision Res. 32, 1565–1582 (1992).
[CrossRef] [PubMed]

1991 (1)

D. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

1989 (3)

D. B. Hamilton, D. C. Albrecht, W. S. Geisler, “Visual cortical receptive fields in monkey and cat: spatial and temporal phase transfer function,” Vision Res. 29, 1285–1308 (1989).
[CrossRef] [PubMed]

J. I. Yellott, “Constant volume operators and lateral inhibition,” J. Math. Psychol. 33, 1–35 (1989).
[CrossRef]

J. Nachmias, “Contrast modulated maskers: test of a late nonlinearity hypothesis,” Vision Res. 29, 137–142 (1989).
[CrossRef] [PubMed]

1988 (1)

M. C. Morrone, D. C. Burr, “Feature detection in human vision: a phase dependent energy model,” Proc. R. Soc. London B 235, 221–245 (1988).
[CrossRef]

1987 (1)

E. L. Arend, R. Goldstein, “Lightness models, gradient illusions and curl,” Percept. Psychophys. 42, 65–80 (1987).
[CrossRef] [PubMed]

1986 (1)

1985 (2)

J. I. Yellott, T. Cornsweet, S. Reuman, “Intensity dependent spatial summation and lateral inhibition,” Invest. Ophthalmol. Visual Sci. 26, 138 (1985).

T. Cornsweet, J. I. Yellott, “Intensity dependent spatial summation,” J. Opt. Soc. Am. A 2, 1769–1786 (1985).
[CrossRef] [PubMed]

1984 (1)

F. Ratliff, “Why Mach bands are not seen at the edges of a step,” Vision Res. 24, 163–165 (1984).
[CrossRef] [PubMed]

1983 (1)

F. Ratliff, N. Milkman, N. Rennert, “Attenuation of Mach bands by adjacent stimuli,” Proc. Natl. Acad. Sci. USA 80, 4554–4558 (1983).
[CrossRef] [PubMed]

1981 (3)

J. Ross, J. J. Holt, J. R. Johnstone, “High frequency limitations on Mach bands,” Vision Res. 21, 1165–1167 (1981).
[CrossRef] [PubMed]

A. M. Derrington, G. B. Henning, “Pattern discrimination with flickering stimuli,” Vision Res. 21, 597–602 (1981).
[CrossRef] [PubMed]

J. O. Limb, U. Tulunay-Keesey, “Spatiotemporal characteristics of thresholds adjacent to a luminance edge,” J. Opt. Soc. Am. 71, 1209–1219 (1981).
[CrossRef]

1973 (1)

A. Vassilev, “Contrast sensitivity near borders: significance of test stimulus form, size and duration,” Vision Res. 13, 719–730 (1973).
[CrossRef] [PubMed]

1971 (1)

1970 (1)

M. V. Levine, “Transformations that render curves parallel,” J. Math. Psychol. 7, 410–443 (1970).
[CrossRef]

1968 (1)

1966 (6)

1963 (1)

1961 (1)

1960 (1)

1959 (1)

F. Ratliff, H. K. Hartline, “The response of Limulus optic nerve fibers to patterns of illumination on the receptor mosaic,” J. Gen. Physiol. 42, 1241–1255 (1959).
[CrossRef] [PubMed]

1957 (1)

A. Fiorentini, T. Radici, “Binocular measurements of brightness on a field presenting a luminance gradient,” Atti Fond. Giorgio Ronchi 12, 453–461 (1957).

1955 (2)

C. McCollough, “The variation in width and position of Mach bands as a function of luminance,” J. Exp. Psychol. 49, 141–152 (1955).
[CrossRef] [PubMed]

A. Fiorentini, M. Jeanne, G. Toraldo di Francia, “Mésures photometriques visuelles sur un champ a gradient d’éclairement variable,” Opt. Acta 1, 192–193 (1955).
[CrossRef]

1948 (1)

G. A. Fry, “Mechanisms subserving simultaneous brightness contrast,” Am. J. Optom. Arch. Am. Acad. Optom. 25, 162–178 (1948).
[CrossRef] [PubMed]

Albrecht, D. C.

D. B. Hamilton, D. C. Albrecht, W. S. Geisler, “Visual cortical receptive fields in monkey and cat: spatial and temporal phase transfer function,” Vision Res. 29, 1285–1308 (1989).
[CrossRef] [PubMed]

Arend, E. L.

E. L. Arend, R. Goldstein, “Lightness models, gradient illusions and curl,” Percept. Psychophys. 42, 65–80 (1987).
[CrossRef] [PubMed]

Burkhardt, D. A.

Burr, D. C.

M. C. Morrone, D. C. Burr, “Feature detection in human vision: a phase dependent energy model,” Proc. R. Soc. London B 235, 221–245 (1988).
[CrossRef]

D. C. Burr, M. C. Morrone, “The role of features in structuring visual images,” in Higher-Order Processing in the Visual System, Ciba Foundation Symposium No. 184 (Wiley, Chichester, UK, 1994), pp. 129–146.

Cannon, M. W.

M. W. Cannon, S. C. Fullenkamp, “A model for inhibitory lateral interaction effects in perceived contrast,” Vision Res. 36, 1115–1125 (1996).
[CrossRef] [PubMed]

Cornsweet, T.

Davidson, M. L.

DePalma, J. J.

Derrington, A. M.

A. M. Derrington, G. B. Henning, “Pattern discrimination with flickering stimuli,” Vision Res. 21, 597–602 (1981).
[CrossRef] [PubMed]

du Buf, J. M. H.

J. M. H. du Buf, “Ramp edges, Mach bands, and the functional significance of the simple cell assembly,” Biol. Cybern. 70, 449–461 (1994).
[CrossRef]

Fine, I.

I. Fine, Department of Psychology, University of California, San Diego, La Jolla, Calif. 92093 (personal cummunication, 1993).

Fiorentini, A.

A. Fiorentini, M. T. Zoli, “Detection of a target superimposed to a step pattern of illumination,” Atti Fond. Giorgio Ronchi 21, 338–356 (1966).

A. Fiorentini, T. Radici, “Binocular measurements of brightness on a field presenting a luminance gradient,” Atti Fond. Giorgio Ronchi 12, 453–461 (1957).

A. Fiorentini, M. Jeanne, G. Toraldo di Francia, “Mésures photometriques visuelles sur un champ a gradient d’éclairement variable,” Opt. Acta 1, 192–193 (1955).
[CrossRef]

Fry, G. A.

G. A. Fry, “Mechanisms subserving simultaneous brightness contrast,” Am. J. Optom. Arch. Am. Acad. Optom. 25, 162–178 (1948).
[CrossRef] [PubMed]

Fullenkamp, S. C.

M. W. Cannon, S. C. Fullenkamp, “A model for inhibitory lateral interaction effects in perceived contrast,” Vision Res. 36, 1115–1125 (1996).
[CrossRef] [PubMed]

Geisler, W. S.

P. T. Kortum, W. S. Geisler, “Adaptation mechanisms in spatial vision—II. Flash thresholds and background adaptation,” Vision Res. 35, 1595–1609 (1995).
[CrossRef] [PubMed]

D. B. Hamilton, D. C. Albrecht, W. S. Geisler, “Visual cortical receptive fields in monkey and cat: spatial and temporal phase transfer function,” Vision Res. 29, 1285–1308 (1989).
[CrossRef] [PubMed]

Goldstein, R.

E. L. Arend, R. Goldstein, “Lightness models, gradient illusions and curl,” Percept. Psychophys. 42, 65–80 (1987).
[CrossRef] [PubMed]

Hamilton, D. B.

D. B. Hamilton, D. C. Albrecht, W. S. Geisler, “Visual cortical receptive fields in monkey and cat: spatial and temporal phase transfer function,” Vision Res. 29, 1285–1308 (1989).
[CrossRef] [PubMed]

Hartline, H. K.

F. Ratliff, H. K. Hartline, “The response of Limulus optic nerve fibers to patterns of illumination on the receptor mosaic,” J. Gen. Physiol. 42, 1241–1255 (1959).
[CrossRef] [PubMed]

Henning, G. B.

A. M. Derrington, G. B. Henning, “Pattern discrimination with flickering stimuli,” Vision Res. 21, 597–602 (1981).
[CrossRef] [PubMed]

Holt, J. J.

J. Ross, J. J. Holt, J. R. Johnstone, “High frequency limitations on Mach bands,” Vision Res. 21, 1165–1167 (1981).
[CrossRef] [PubMed]

Jeanne, M.

A. Fiorentini, M. Jeanne, G. Toraldo di Francia, “Mésures photometriques visuelles sur un champ a gradient d’éclairement variable,” Opt. Acta 1, 192–193 (1955).
[CrossRef]

Johnstone, J. R.

J. Ross, J. J. Holt, J. R. Johnstone, “High frequency limitations on Mach bands,” Vision Res. 21, 1165–1167 (1981).
[CrossRef] [PubMed]

Kingdom, F.

F. Kingdom, B. Moulden, “A multi-channel approach to brightness coding,” Vision Res. 32, 1565–1582 (1992).
[CrossRef] [PubMed]

Kortum, P. T.

P. T. Kortum, W. S. Geisler, “Adaptation mechanisms in spatial vision—II. Flash thresholds and background adaptation,” Vision Res. 35, 1595–1609 (1995).
[CrossRef] [PubMed]

Levine, M. V.

M. V. Levine, “Transformations that render curves parallel,” J. Math. Psychol. 7, 410–443 (1970).
[CrossRef]

Limb, J. O.

Lowry, E. M.

Mach, E.

E. Mach, “Über die Wirkung der räumlichen Vertheilung des Lichtreizes auf die Netzhaut” (1865), translated in Ref. 1, pp. 253–271.

Makous, W. L.

Marimont, R. B.

Matthews, M. L.

McCollough, C.

C. McCollough, “The variation in width and position of Mach bands as a function of luminance,” J. Exp. Psychol. 49, 141–152 (1955).
[CrossRef] [PubMed]

Mignolla, E.

L. Pessoa, E. Mignolla, H. Neumann, “A contrast- and luminance-driven multiscale network model of brightness,” Vision Res. 35, 2201–2223 (1995).
[CrossRef] [PubMed]

Milkman, N.

F. Ratliff, N. Milkman, N. Rennert, “Attenuation of Mach bands by adjacent stimuli,” Proc. Natl. Acad. Sci. USA 80, 4554–4558 (1983).
[CrossRef] [PubMed]

Morrone, M. C.

M. C. Morrone, D. C. Burr, “Feature detection in human vision: a phase dependent energy model,” Proc. R. Soc. London B 235, 221–245 (1988).
[CrossRef]

D. C. Burr, M. C. Morrone, “The role of features in structuring visual images,” in Higher-Order Processing in the Visual System, Ciba Foundation Symposium No. 184 (Wiley, Chichester, UK, 1994), pp. 129–146.

Moulden, B.

F. Kingdom, B. Moulden, “A multi-channel approach to brightness coding,” Vision Res. 32, 1565–1582 (1992).
[CrossRef] [PubMed]

Nachmias, J.

J. Nachmias, “Contrast modulated maskers: test of a late nonlinearity hypothesis,” Vision Res. 29, 137–142 (1989).
[CrossRef] [PubMed]

J. Nachmias, “Signal detection theory and its application to problems in vision,” in Handbook of Sensory Physiology, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, Berlin, 1972), Vol. VIII.

Naka, K.-I.

K.-I. Naka, W. A. H. Rushton, “S-potentials from luminosity units in the retina of fish (Cyprinicae),” J. Physiol. (London) 185, 587–599 (1966).

Neumann, H.

L. Pessoa, E. Mignolla, H. Neumann, “A contrast- and luminance-driven multiscale network model of brightness,” Vision Res. 35, 2201–2223 (1995).
[CrossRef] [PubMed]

Pelli, D.

D. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

Pessoa, L.

L. Pessoa, E. Mignolla, H. Neumann, “A contrast- and luminance-driven multiscale network model of brightness,” Vision Res. 35, 2201–2223 (1995).
[CrossRef] [PubMed]

Radici, T.

A. Fiorentini, T. Radici, “Binocular measurements of brightness on a field presenting a luminance gradient,” Atti Fond. Giorgio Ronchi 12, 453–461 (1957).

Ratliff, F.

F. Ratliff, “Why Mach bands are not seen at the edges of a step,” Vision Res. 24, 163–165 (1984).
[CrossRef] [PubMed]

F. Ratliff, N. Milkman, N. Rennert, “Attenuation of Mach bands by adjacent stimuli,” Proc. Natl. Acad. Sci. USA 80, 4554–4558 (1983).
[CrossRef] [PubMed]

F. Ratliff, H. K. Hartline, “The response of Limulus optic nerve fibers to patterns of illumination on the receptor mosaic,” J. Gen. Physiol. 42, 1241–1255 (1959).
[CrossRef] [PubMed]

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

Rennert, N.

F. Ratliff, N. Milkman, N. Rennert, “Attenuation of Mach bands by adjacent stimuli,” Proc. Natl. Acad. Sci. USA 80, 4554–4558 (1983).
[CrossRef] [PubMed]

Reuman, S.

J. I. Yellott, T. Cornsweet, S. Reuman, “Intensity dependent spatial summation and lateral inhibition,” Invest. Ophthalmol. Visual Sci. 26, 138 (1985).

Ross, J.

J. Ross, J. J. Holt, J. R. Johnstone, “High frequency limitations on Mach bands,” Vision Res. 21, 1165–1167 (1981).
[CrossRef] [PubMed]

Rushton, W. A. H.

K.-I. Naka, W. A. H. Rushton, “S-potentials from luminosity units in the retina of fish (Cyprinicae),” J. Physiol. (London) 185, 587–599 (1966).

Thomas, J. P.

Toraldo di Francia, G.

A. Fiorentini, M. Jeanne, G. Toraldo di Francia, “Mésures photometriques visuelles sur un champ a gradient d’éclairement variable,” Opt. Acta 1, 192–193 (1955).
[CrossRef]

Tulunay-Keesey, U.

Vassilev, A.

A. Vassilev, “Contrast sensitivity near borders: significance of test stimulus form, size and duration,” Vision Res. 13, 719–730 (1973).
[CrossRef] [PubMed]

von Békésy, G.

Watrasiewicz, B. M.

Whiteside, J. A.

Yellott, J. I.

J. I. Yellott, “Constant volume operators and lateral inhibition,” J. Math. Psychol. 33, 1–35 (1989).
[CrossRef]

T. Cornsweet, J. I. Yellott, “Intensity dependent spatial summation: errata,” J. Opt. Soc. Am. A 3, 165 (1986).
[CrossRef]

J. I. Yellott, T. Cornsweet, S. Reuman, “Intensity dependent spatial summation and lateral inhibition,” Invest. Ophthalmol. Visual Sci. 26, 138 (1985).

T. Cornsweet, J. I. Yellott, “Intensity dependent spatial summation,” J. Opt. Soc. Am. A 2, 1769–1786 (1985).
[CrossRef] [PubMed]

Zhang, L.

D. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

Zoli, M. T.

A. Fiorentini, M. T. Zoli, “Detection of a target superimposed to a step pattern of illumination,” Atti Fond. Giorgio Ronchi 21, 338–356 (1966).

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

G. A. Fry, “Mechanisms subserving simultaneous brightness contrast,” Am. J. Optom. Arch. Am. Acad. Optom. 25, 162–178 (1948).
[CrossRef] [PubMed]

Atti Fond. Giorgio Ronchi (2)

A. Fiorentini, T. Radici, “Binocular measurements of brightness on a field presenting a luminance gradient,” Atti Fond. Giorgio Ronchi 12, 453–461 (1957).

A. Fiorentini, M. T. Zoli, “Detection of a target superimposed to a step pattern of illumination,” Atti Fond. Giorgio Ronchi 21, 338–356 (1966).

Biol. Cybern. (1)

J. M. H. du Buf, “Ramp edges, Mach bands, and the functional significance of the simple cell assembly,” Biol. Cybern. 70, 449–461 (1994).
[CrossRef]

Invest. Ophthalmol. Visual Sci. (1)

J. I. Yellott, T. Cornsweet, S. Reuman, “Intensity dependent spatial summation and lateral inhibition,” Invest. Ophthalmol. Visual Sci. 26, 138 (1985).

J. Exp. Psychol. (1)

C. McCollough, “The variation in width and position of Mach bands as a function of luminance,” J. Exp. Psychol. 49, 141–152 (1955).
[CrossRef] [PubMed]

J. Gen. Physiol. (1)

F. Ratliff, H. K. Hartline, “The response of Limulus optic nerve fibers to patterns of illumination on the receptor mosaic,” J. Gen. Physiol. 42, 1241–1255 (1959).
[CrossRef] [PubMed]

J. Math. Psychol. (2)

J. I. Yellott, “Constant volume operators and lateral inhibition,” J. Math. Psychol. 33, 1–35 (1989).
[CrossRef]

M. V. Levine, “Transformations that render curves parallel,” J. Math. Psychol. 7, 410–443 (1970).
[CrossRef]

J. Opt. Soc. Am. (10)

J. O. Limb, U. Tulunay-Keesey, “Spatiotemporal characteristics of thresholds adjacent to a luminance edge,” J. Opt. Soc. Am. 71, 1209–1219 (1981).
[CrossRef]

R. B. Marimont, “Linearity and the Mach phenomenon,” J. Opt. Soc. Am. 53, 400–401 (1963).
[CrossRef] [PubMed]

J. P. Thomas, “Brightness variations in stimuli with ramp-like contours,” J. Opt. Soc. Am. 56, 238–242 (1966).
[CrossRef] [PubMed]

G. von Békésy, “Neural inhibitory units of the eye and skin. Quantitative description of contrast phenomena,” J. Opt. Soc. Am. 50, 1060–1070 (1960).
[CrossRef]

G. von Békésy, “Brightness distribution across the Mach bands measured with flicker photometry, and the linearity of sensory nervous interaction,” J. Opt. Soc. Am. 58, 1–8 (1968).
[CrossRef] [PubMed]

D. A. Burkhardt, “Brightness and the increment threshold,” J. Opt. Soc. Am. 56, 979–981 (1966).
[CrossRef] [PubMed]

E. M. Lowry, J. J. DePalma, “Sine-wave response of the visual system. 1. The Mach phenomenon,” J. Opt. Soc. Am. 51, 740–746 (1961).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Psychometric functions—the percentage of correct responses as a function of the size of the signal increment (cd/m2 on a logarithmic scale). The results are for the detection of increments at the different locations along the Mach-band pattern for a single observer [RWM in (a) and GBH in (b)]. Location, measured from the topmost edge of the horizontally oriented dark plateau, is indicated (in degrees) by the symbol shown in the inset. The filled symbols show data from locations in the darker regions; open symbols those for locations in the brighter regions. The error bars at the left-hand edge of the figure give the range ±1 standard deviation around 60%, 75%, and 90% correct on the assumption that the number correct in 100 observations was binomially distributed.

Fig. 2
Fig. 2

Percentage of correct responses as a function of the signal increment (cd/m2 on a linear scale) for a location in the center of the dark plateau (0.66 deg) and for a location near the center of the dark Mach band (1.33 deg) [for RWM (a) and GBH (b)]. Each data point is based on 100 observations, and the error bars at the left-hand edge of the figures give the range ±1 standard deviation around 60%, 75%, and 90% correct on the assumption that the number correct in 100 observations was binomially distributed.

Fig. 3
Fig. 3

Logarithm of the increment levels corresponding to (a) 60%, (b) 75%, and (c) 90% correct for locations along the Mach-band pattern. The increment values are taken from linear interpolation in the psychometric functions for observer RWM. The closed rectangle below the x axis near 1.33 deg represents the location of the dark Mach band, and the open rectangle near 2.67 deg represents the location of the bright Mach band.

Fig. 4
Fig. 4

Same as Fig. 3 but for GBH.

Fig. 5
Fig. 5

Absolute value of luminance decrements corresponding to 60%, 75%, and 90% correct as a function of location along the Mach-band pattern. The size of the decrement [cd/m2 on a linear scale in (a) for RWM; the logarithm of the size of the decrement in (b) for GBH] are linearly interpolated from the psychometric functions. The closed rectangle below the x axis near 1.33 deg represents the location of the dark Mach band, and the open rectangle near 2.67 deg represents the location of the bright Mach band.

Fig. 6
Fig. 6

Logarithm of the increments corresponding to 60%, 75%, and 90% correct for locations along a step pattern. The step (from 40.25 to 114.75 cd/m2) occurred in the center of the display at 2 deg. The increment values were linearly interpolated from the psychometric functions (100 observations per point) for observer GBH. (b) Same as (a) but for RWM.

Fig. 7
Fig. 7

Increment levels corresponding to 60%, 75%, and 90% correct for locations along a pattern producing the Cornsweet illusion. The increment values were linearly interpolated from the psychometric functions of observer RWM. (b) Same as (a) but for GBH.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

R[I(y)]=RmaxIn(y)/[In(y)+αn],
window(y)=4|y|(W/2-y2)1/2 sin-1(2|y|/W)/πW
R[I(y)]=Rmax{m[I(y)-s]}n/({m[Iint(y)-s]}n+αn),
s=gIint(y),
m=b0/[Iint(y)+b0],

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