Abstract

Color vision is useful for detecting surface boundaries and identifying objects. Are the signals used to perform these two functions processed by common mechanisms, or has the visual system optimized its processing separately for each task? We measured the effect of mean chromaticity and luminance on color discriminability and on color appearance under well-matched stimulus conditions. In the discrimination experiments, a pedestal spot was presented in one interval and a pedestal + test in a second. Observers indicated which interval contained the test. In the appearance experiments, observers matched the appearance of test spots across a change in background. We analyzed the data using a variant of Fechner’s proposal, that the rate of apparent stimulus change is proportional to visual sensitivity. We found that saturating visual response functions together with a model of adaptation that included multiplicative gain control and a subtractive term accounted for data from both tasks. This result suggests that effects of the contexts we studied on color appearance and discriminability are controlled by the same underlying mechanism. © 2005 Optical Society of America

© 2005 Optical Society of America

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  44. Note that matches varied along only the color direction of the test for this and other conditions examined in this paper. Thus, plotting intensity is sufficient.
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  55. This linking hypothesis is equivalent to assuming that performance is limited by additive noise of fixed variance following the nonlinearity. An alternative model includes signal-dependent noise. For a subset of the data, we examined parametric fits to the discrimination and appearance data that included signal-dependent noise (with variance proportional to the expected response). The precise shape of the inferred nonlinearity is different for a signal-dependent noise model, but the quality of the fits to the discrimination and appearance data was not affected (see Ref. [56] for an analysis of the power of discrimination data to test these alternative noise models).
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    [CrossRef] [PubMed]
  61. In the literature on subtractive adaptation, some authors apply the subtractive term to the incremental/decremental stimulus, as we have done here. Others apply it to the sum of the background and the increment/decrement. These two formulations are equivalent except in the interpretation of what a subtractive term of zero means.
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    [CrossRef] [PubMed]
  70. C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial symmetry,” Science 236, 597–582 (1987).
    [CrossRef]

2004 (1)

J. M. Hillis, D. H. Brainard, “A shadowy dissociation between discriminability and identity,” J. Vision 4, 56a (2004).
[CrossRef]

2003 (2)

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, F. J. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vision Res. 43, 1765–1775 (2003).
[CrossRef] [PubMed]

D. H. Foster, “Does colour constancy exist?” Trends Cogn. Sci. 7, 493–443 (2003).
[CrossRef]

2002 (1)

A. R. Wade, B. A. Wandell, “Chromatic light adaptation measured using functional magnetic resonance imaging,” J. Neurosci. 22, 8148–8157 (2002).
[PubMed]

2001 (1)

F. W. Wichmann, N. J. Hill, “The psychometric function: II. Bootstrap-based confidence intervals and sampling,” Percept. Psychophys. 63, 1314–1329 (2001).
[CrossRef]

2000 (4)

C. C. Chen, J. M. Foley, D. H. Brainard, “Detection of chromoluminance patterns on chromoluminance pedestals I: Threshold measurements,” Vision Res. 40, 773–788 (2000).
[CrossRef] [PubMed]

C. C. Chen, J. M. Foley, D. H. Brainard, “Detection of chromoluminance patterns on chromoluminance pedestals II: Model,” Vision Res. 40, 789–803 (2000).
[CrossRef] [PubMed]

P. B. Delahunt, D. H. Brainard, “Control of chromatic adaptation: signals from separate cone classes interact,” Vision Res. 40, 2885–2903 (2000).
[CrossRef] [PubMed]

O. Rinner, K. R. Gegenfurtner, “Time course of chromatic adaptation for color appearance and discrimination,” Vision Res. 40, 1813–1826 (2000).
[CrossRef] [PubMed]

1999 (1)

A. Stockman, L. T. Sharpe, C. C. Fach, “The spectral sensitivity of the human short-wavelength cones,” Vision Res. 39, 2901–2927 (1999).
[CrossRef] [PubMed]

1997 (1)

R. O. Brown, D. I.A. MacLeod, “Color appearance depends on the variance of surround colors,” Curr. Biol. 7, 844–849 (1997).
[CrossRef]

1996 (2)

M. A. Webster, “Human colour perception and its adaptation,” Network Comput. Neural Syst. 7, 587–634 (1996).
[CrossRef]

S. M. Wuerger, “Color appearance changes resulting from iso-luminant chromatic adaptation,” Vision Res. 36, 3107–3118 (1996).
[CrossRef] [PubMed]

1995 (1)

E. J. Chichilnisky, B. A. Wandell, “Photoreceptor sensitivity changes explain color appearance shifts induced by large uniform backgrounds in dichoptic matching,” Vision Res. 35, 239–254 (1995).
[CrossRef] [PubMed]

1994 (1)

1993 (2)

Q. Zaidi, A. G. Shapiro, “Adaptive orthogonalization of opponent-color signals,” Biol. Cybern. 69, 415–428 (1993).
[CrossRef] [PubMed]

J. L. Nerger, T. P. Piantanida, J. Larimer, “Color appearance of filled-in backgrounds affects hue cancellation, but not detection thresholds,” Vision Res. 33, 165–172 (1993).
[CrossRef] [PubMed]

1992 (4)

A. G. Shapiro, Q. Zaidi, “The effects of prolonged temporal modulation on the differential response of color mechanisms,” Vision Res. 32, 2065–2075 (1992).
[CrossRef] [PubMed]

R. A. Bone, J. T. Landrum, A. Cains, “Optical density spectra of the macular pigment invivo and invitro,” Vision Res. 32, 105–110 (1992).
[CrossRef] [PubMed]

J. Krauskopf, K. Gegenfurtner, “Color discrimination and adaptation,” Vision Res. 32, 2165–2175 (1992).
[CrossRef] [PubMed]

P. Whittle, “Brightness, discriminability and the `crispening effect',” Vision Res. 32, 1493–1507 (1992).
[CrossRef] [PubMed]

1991 (1)

M. A. Webster, J. D. Mollon, “Changes in colour appearance following post-receptoral adaptation,” Nature (London) 349, 235–238 (1991).
[CrossRef]

1988 (1)

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
[PubMed]

1987 (2)

C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial symmetry,” Science 236, 597–582 (1987).
[CrossRef]

G. E. Legge, D. Kerstein, A. E. Burgess, “Contrast discrimination in noise,” J. Opt. Soc. Am. A 4, 391–404 (1987).
[CrossRef] [PubMed]

1986 (2)

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher order color mechanisms,” Vision Res. 26, 23–32 (1986).
[CrossRef] [PubMed]

P. Whittle, “Increments and decrements: luminance discrimination,” Vision Res. 26, 1677–1691 (1986).
[CrossRef] [PubMed]

1983 (2)

W. S. Geisler, “Mechanisms of visual sensitivity: backgrounds and early dark adaptation,” Vision Res. 23, 1423–1432 (1983).
[CrossRef] [PubMed]

M. J. Valeton, D. v. Norren, “Light adaptation of primate cones: an analysis based on extracellular data,” Vision Res. 23, 1539–1547 (1983).
[CrossRef] [PubMed]

1982 (2)

E. H. Adelson, “Saturation and adaptation in the rod system,” Vision Res. 22, 1299–1312 (1982).
[CrossRef] [PubMed]

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef] [PubMed]

1981 (2)

J. Walraven, “Perceived color under conditions of chromatic adaptation: Evidence for again control by π- mechanisms,” Vision Res. 21, 611–620 (1981).
[CrossRef]

J. M. Foley, G. E. Legge, “Contrast detection and near-threshold discrimination in human vision,” Vision Res. 21, 1041–1053 (1981).
[CrossRef] [PubMed]

1980 (3)

E. N. Pugh, J. Larimer, “Test of the identity of the site of blue/yellow hue cancellation and the site of chromatic antagonism in the π1 pathway,” Vision Res. 20, 779–788 (1980).
[CrossRef]

G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).
[CrossRef] [PubMed]

S. K. Shevell, “Unambiguous evidence for the additive effect in chromatic adaptation,” Vision Res. 20, 637–639 (1980).
[CrossRef] [PubMed]

1979 (1)

J. M. Loomis, T. Berger, “Effects of chromatic adaptation on color discrimination and color appearance,” Vision Res. 19, 891–901 (1979).
[CrossRef] [PubMed]

1976 (1)

J. Walraven, “Discounting the background: The missing link in the explanation of chromatic induction,” Vision Res. 16, 289–295 (1976).
[CrossRef]

1975 (1)

V. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[CrossRef] [PubMed]

1974 (1)

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

1971 (1)

D. H. Krantz, “Integration of just-noticeable differences,” J. Math. Psychol. 8, 591–599 (1971).
[CrossRef]

1969 (1)

P. Whittle, P. D.C. Challands, “The effect of background luminance on the brightness of flashes,” Vision Res. 9, 1095–1110 (1969).
[CrossRef] [PubMed]

1967 (1)

W. S. Stiles, “Mechanism concepts in colour theory,” J. Colour Group 11, 106–123 (1967).

1966 (2)

K. I. Naka, W. A. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

H. Takasaki, “Lightness change of grays induced by change in reflectance of gray background,” J. Opt. Soc. Am. 56, 504–509 (1966).
[CrossRef] [PubMed]

1961 (1)

E. G. Heinemann, “The relation of apparent brightness to the threshold for differences in luminance,” J. Exp. Psychol. 61, 389–399 (1961).
[CrossRef] [PubMed]

1959 (1)

W. S. Stiles, “Color vision: the approach through increment threshold sensitivity,” Proc. Natl. Acad. Sci. U.S.A. 45, 100–114 (1959).
[CrossRef]

1958 (1)

R. D. Luce, W. Edwards, “The derivation of subjective scales from just noticeable differences,” Psychol. Rev. 65, 222–236 (1958).
[CrossRef] [PubMed]

1957 (2)

Adelson, E. H.

E. H. Adelson, “Saturation and adaptation in the rod system,” Vision Res. 22, 1299–1312 (1982).
[CrossRef] [PubMed]

Berger, T.

J. M. Loomis, T. Berger, “Effects of chromatic adaptation on color discrimination and color appearance,” Vision Res. 19, 891–901 (1979).
[CrossRef] [PubMed]

Bird, A. C.

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, F. J. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vision Res. 43, 1765–1775 (2003).
[CrossRef] [PubMed]

Bone, R. A.

R. A. Bone, J. T. Landrum, A. Cains, “Optical density spectra of the macular pigment invivo and invitro,” Vision Res. 32, 105–110 (1992).
[CrossRef] [PubMed]

Boynton, R. M.

P. K. Kaiser, R. M. Boynton, Human Color Vision, 2nd ed. (Optical Society of America, 1996).

Brainard, D. H.

J. M. Hillis, D. H. Brainard, “A shadowy dissociation between discriminability and identity,” J. Vision 4, 56a (2004).
[CrossRef]

C. C. Chen, J. M. Foley, D. H. Brainard, “Detection of chromoluminance patterns on chromoluminance pedestals II: Model,” Vision Res. 40, 789–803 (2000).
[CrossRef] [PubMed]

P. B. Delahunt, D. H. Brainard, “Control of chromatic adaptation: signals from separate cone classes interact,” Vision Res. 40, 2885–2903 (2000).
[CrossRef] [PubMed]

C. C. Chen, J. M. Foley, D. H. Brainard, “Detection of chromoluminance patterns on chromoluminance pedestals I: Threshold measurements,” Vision Res. 40, 773–788 (2000).
[CrossRef] [PubMed]

D. H. Brainard, “Cone contrast and opponent modulation color spaces,” in Human Color Vision, 2nd ed., P. K. Kaiser and R. M. Boynton, eds. (Optical Society of America, 1996), pp. 563–579.

D. H. Brainard, D. G. Pelli, T. Robson, “Display characterization,” in Encylopedia of Imaging Science and Technology, J. Hornak, ed. (Wiley, 2002), pp. 72–188.

D. H. Brainard, “Color vision theory,” in International Encyclopedia of the Social and Behavioral Sciences, N. J. Smelser and B. P. Baltas, eds. (Elsevier, 2001), pp. 2256–2263.
[CrossRef]

D. H. Brainard, “Color Constancy,” in The Visual Neurosciences, L. Chalupa and J. Werner, eds. (MIT Press, 2004), pp. 948–961.

Brown, A. M.

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher order color mechanisms,” Vision Res. 26, 23–32 (1986).
[CrossRef] [PubMed]

Brown, R. O.

R. O. Brown, D. I.A. MacLeod, “Color appearance depends on the variance of surround colors,” Curr. Biol. 7, 844–849 (1997).
[CrossRef]

Burgess, A. E.

Burnham, R. W.

Cains, A.

R. A. Bone, J. T. Landrum, A. Cains, “Optical density spectra of the macular pigment invivo and invitro,” Vision Res. 32, 105–110 (1992).
[CrossRef] [PubMed]

Challands, P. D.C.

P. Whittle, P. D.C. Challands, “The effect of background luminance on the brightness of flashes,” Vision Res. 9, 1095–1110 (1969).
[CrossRef] [PubMed]

Chen, C. C.

C. C. Chen, J. M. Foley, D. H. Brainard, “Detection of chromoluminance patterns on chromoluminance pedestals II: Model,” Vision Res. 40, 789–803 (2000).
[CrossRef] [PubMed]

C. C. Chen, J. M. Foley, D. H. Brainard, “Detection of chromoluminance patterns on chromoluminance pedestals I: Threshold measurements,” Vision Res. 40, 773–788 (2000).
[CrossRef] [PubMed]

Chichilnisky, E. J.

E. J. Chichilnisky, B. A. Wandell, “Photoreceptor sensitivity changes explain color appearance shifts induced by large uniform backgrounds in dichoptic matching,” Vision Res. 35, 239–254 (1995).
[CrossRef] [PubMed]

Curcio, C. A.

C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial symmetry,” Science 236, 597–582 (1987).
[CrossRef]

D’Zmura, M.

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J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher order color mechanisms,” Vision Res. 26, 23–32 (1986).
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J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
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J. M. Loomis, T. Berger, “Effects of chromatic adaptation on color discrimination and color appearance,” Vision Res. 19, 891–901 (1979).
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R. O. Brown, D. I.A. MacLeod, “Color appearance depends on the variance of surround colors,” Curr. Biol. 7, 844–849 (1997).
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J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher order color mechanisms,” Vision Res. 26, 23–32 (1986).
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R. T. Eskew, J. S. McLellan, F. Giulian, “Chromatic detection and discrimination,” in Color Vision: From Molecular Genetics to Perception, K. Gegenfurtner and L. T. Sharpe, eds. (Cambridge U. Press, 1999), pp. 345–368.

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M. A. Webster, J. D. Mollon, “Changes in colour appearance following post-receptoral adaptation,” Nature (London) 349, 235–238 (1991).
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A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, F. J. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vision Res. 43, 1765–1775 (2003).
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A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, F. J. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vision Res. 43, 1765–1775 (2003).
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J. L. Nerger, T. P. Piantanida, J. Larimer, “Color appearance of filled-in backgrounds affects hue cancellation, but not detection thresholds,” Vision Res. 33, 165–172 (1993).
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M. J. Valeton, D. v. Norren, “Light adaptation of primate cones: an analysis based on extracellular data,” Vision Res. 23, 1539–1547 (1983).
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A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, F. J. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vision Res. 43, 1765–1775 (2003).
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E. N. Pugh, J. Larimer, “Test of the identity of the site of blue/yellow hue cancellation and the site of chromatic antagonism in the π1 pathway,” Vision Res. 20, 779–788 (1980).
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O. Rinner, K. R. Gegenfurtner, “Time course of chromatic adaptation for color appearance and discrimination,” Vision Res. 40, 1813–1826 (2000).
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A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, F. J. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vision Res. 43, 1765–1775 (2003).
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K. I. Naka, W. A. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

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A. G. Shapiro, Q. Zaidi, “The effects of prolonged temporal modulation on the differential response of color mechanisms,” Vision Res. 32, 2065–2075 (1992).
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C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial symmetry,” Science 236, 597–582 (1987).
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Q. Zaidi, A. G. Shapiro, “Adaptive orthogonalization of opponent-color signals,” Biol. Cybern. 69, 415–428 (1993).
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Q. Zaidi, A. G. Shapiro, “Adaptive orthogonalization of opponent-color signals,” Biol. Cybern. 69, 415–428 (1993).
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Crit. Rev. Neurobiol. (1)

P. Lennie, M. D’Zmura, “Mechanisms of color vision,” Crit. Rev. Neurobiol. 3, 333–400 (1988).
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R. O. Brown, D. I.A. MacLeod, “Color appearance depends on the variance of surround colors,” Curr. Biol. 7, 844–849 (1997).
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W. S. Stiles, “Mechanism concepts in colour theory,” J. Colour Group 11, 106–123 (1967).

J. Exp. Psychol. (1)

E. G. Heinemann, “The relation of apparent brightness to the threshold for differences in luminance,” J. Exp. Psychol. 61, 389–399 (1961).
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J. Math. Psychol. (1)

D. H. Krantz, “Integration of just-noticeable differences,” J. Math. Psychol. 8, 591–599 (1971).
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J. Neurosci. (1)

A. R. Wade, B. A. Wandell, “Chromatic light adaptation measured using functional magnetic resonance imaging,” J. Neurosci. 22, 8148–8157 (2002).
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J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

J. Physiol. (London) (1)

K. I. Naka, W. A. Rushton, “S-potentials from colour units in the retina of fish (Cyprinidae),” J. Physiol. (London) 185, 536–555 (1966).

J. Vision (1)

J. M. Hillis, D. H. Brainard, “A shadowy dissociation between discriminability and identity,” J. Vision 4, 56a (2004).
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Nature (London) (1)

M. A. Webster, J. D. Mollon, “Changes in colour appearance following post-receptoral adaptation,” Nature (London) 349, 235–238 (1991).
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Network Comput. Neural Syst. (1)

M. A. Webster, “Human colour perception and its adaptation,” Network Comput. Neural Syst. 7, 587–634 (1996).
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Percept. Psychophys. (1)

F. W. Wichmann, N. J. Hill, “The psychometric function: II. Bootstrap-based confidence intervals and sampling,” Percept. Psychophys. 63, 1314–1329 (2001).
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Proc. Natl. Acad. Sci. U.S.A. (1)

W. S. Stiles, “Color vision: the approach through increment threshold sensitivity,” Proc. Natl. Acad. Sci. U.S.A. 45, 100–114 (1959).
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Psychol. Rev. (2)

L. M. Hurvich, D. Jameson, “An opponent-process theory of color vision,” Psychol. Rev. 64, 384–404 (1957).
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R. D. Luce, W. Edwards, “The derivation of subjective scales from just noticeable differences,” Psychol. Rev. 65, 222–236 (1958).
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Science (1)

C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial symmetry,” Science 236, 597–582 (1987).
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Trends Cogn. Sci. (1)

D. H. Foster, “Does colour constancy exist?” Trends Cogn. Sci. 7, 493–443 (2003).
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Vision Res. (28)

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982).
[CrossRef] [PubMed]

J. Krauskopf, D. R. Williams, M. B. Mandler, A. M. Brown, “Higher order color mechanisms,” Vision Res. 26, 23–32 (1986).
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E. H. Adelson, “Saturation and adaptation in the rod system,” Vision Res. 22, 1299–1312 (1982).
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W. S. Geisler, “Mechanisms of visual sensitivity: backgrounds and early dark adaptation,” Vision Res. 23, 1423–1432 (1983).
[CrossRef] [PubMed]

C. C. Chen, J. M. Foley, D. H. Brainard, “Detection of chromoluminance patterns on chromoluminance pedestals II: Model,” Vision Res. 40, 789–803 (2000).
[CrossRef] [PubMed]

P. B. Delahunt, D. H. Brainard, “Control of chromatic adaptation: signals from separate cone classes interact,” Vision Res. 40, 2885–2903 (2000).
[CrossRef] [PubMed]

J. M. Loomis, T. Berger, “Effects of chromatic adaptation on color discrimination and color appearance,” Vision Res. 19, 891–901 (1979).
[CrossRef] [PubMed]

E. N. Pugh, J. Larimer, “Test of the identity of the site of blue/yellow hue cancellation and the site of chromatic antagonism in the π1 pathway,” Vision Res. 20, 779–788 (1980).
[CrossRef]

J. Walraven, “Perceived color under conditions of chromatic adaptation: Evidence for again control by π- mechanisms,” Vision Res. 21, 611–620 (1981).
[CrossRef]

J. Walraven, “Discounting the background: The missing link in the explanation of chromatic induction,” Vision Res. 16, 289–295 (1976).
[CrossRef]

S. K. Shevell, “Unambiguous evidence for the additive effect in chromatic adaptation,” Vision Res. 20, 637–639 (1980).
[CrossRef] [PubMed]

A. Stockman, L. T. Sharpe, C. C. Fach, “The spectral sensitivity of the human short-wavelength cones,” Vision Res. 39, 2901–2927 (1999).
[CrossRef] [PubMed]

R. A. Bone, J. T. Landrum, A. Cains, “Optical density spectra of the macular pigment invivo and invitro,” Vision Res. 32, 105–110 (1992).
[CrossRef] [PubMed]

A. G. Robson, J. D. Moreland, D. Pauleikhoff, T. Morrissey, G. E. Holder, F. W. Fitzke, A. C. Bird, F. J. van Kuijk, “Macular pigment density and distribution: comparison of fundus autofluorescence with minimum motion photometry,” Vision Res. 43, 1765–1775 (2003).
[CrossRef] [PubMed]

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Other (20)

This linking hypothesis is equivalent to assuming that performance is limited by additive noise of fixed variance following the nonlinearity. An alternative model includes signal-dependent noise. For a subset of the data, we examined parametric fits to the discrimination and appearance data that included signal-dependent noise (with variance proportional to the expected response). The precise shape of the inferred nonlinearity is different for a signal-dependent noise model, but the quality of the fits to the discrimination and appearance data was not affected (see Ref. [56] for an analysis of the power of discrimination data to test these alternative noise models).

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Note that matches varied along only the color direction of the test for this and other conditions examined in this paper. Thus, plotting intensity is sufficient.

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In the literature on subtractive adaptation, some authors apply the subtractive term to the incremental/decremental stimulus, as we have done here. Others apply it to the sum of the background and the increment/decrement. These two formulations are equivalent except in the interpretation of what a subtractive term of zero means.

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Figures (12)

Fig. 1
Fig. 1

Two hypothetical response functions. Each function corresponds to a different context (e.g., different chromaticity of background) and plots a mechanism’s response as a function of stimulus strength (e.g., test spot contrast). Equality of appearance across the context change is predicted by equality of mechanism response, so that the stimuli indicated by the downward arrows would be predicted to match in appearance. Discrimination thresholds (i.e., test increment required to discriminate between a pedestal presented alone and a pedestal plus the test) are predicted to be inversely proportional to response function slope.

Fig. 2
Fig. 2

Intensity response model with expected asymmetric matches and discrimination performance. The x axes in panels A,C,D, and E test stimulus intensity. Panel C shows the response model [Eq. (2)]. The y axis is the magnitude of the response. The two curves in Panel C are the response functions for one mechanism in two adapted states. The gray curve represents expected response in a gray context and the black curve represents expected response in a green context. The difference between the two curves is a difference in the gain-and-subtractive parameters [g and s in Eq. (2)]. Panel B shows the Gaussian response distributions for four test intensities ( I 1 , I 1 + Δ I 1 , 75 , I 2 , I 2 + Δ I 2 , 75 where Δ I i , 75 is the incremental intensity that yields 75% correct performance) presented in the green context. The x and y axes are probability and response magnitude, respectively. Panel D shows two psychometric curves for pedestals I 1 and I 2 . These curves are the expected discrimination performance derived from the model characterized in panels B and C for the response function adapted to the green context. Panel E shows the increments expected to yield 75% correct (JNDs) as a function of pedestal intensity derived from the response model in B and C. Finally, Panel A shows the expected performance in an asymmetric matching task with the tests presented in the green context and the matches set in the gray context. The height of the shaded rectangle running the width of the x axis represents absolute threshold for a spot presented against a gray background ( JND gray 0 , which is equivalent to the point where the JND gray curve in Panel E intersects the y axis). The width of the shaded rectangle running the height of the y axis represents absolute threshold for a spot presented against the green background JND green 0 . Any test-match pairs in this gray shaded region would be extremely difficult to obtain.

Fig. 3
Fig. 3

Spatial and temporal profiles of test spots. The top panel shows the spatial profile of test spots in the discrimination and matching experiments. The bottom panel shows the temporal parameters of a trial in the discrimination experiment. The small white spots indicate frame timing (vertical blanking). The temporal profile in the matching experiment was the same except that only one interval was used.

Fig. 4
Fig. 4

JMH’s results from discrimination and matching experiments for LM tests and backgrounds that varied in their LM input. The top six panels are discrimination thresholds (JNDs) plotted as a function of pedestal intensity. The three left panels are JNDs for decrements and the three right panels are JNDs for increments presented on, from top to bottom, the Gray + LM , Gray and Gray LM backgrounds. Error bars are 95% confidence intervals. The bottom panel shows asymmetric matching data for the same set of conditions. The x axis is the test excursion (i.e., the number of isomerizations expected from the test independent of the background) against the Gray + LM (circles) and the Gray LM (triangles) backgrounds. The y axis is the match excursion from the gray background against which the matches were set. Error bars are standard error of the mean. Dashed and solid lines are results of model fits with parameters selected on the basis of both discrimination and matching data. These are fits for the gain-and-subtractive model of adaptation. Increments and decrements were fit independently but the p , q , and M parameters in Eq. (2) were yoked across adapting conditions. The raw psychometric and matching data underlying the points and model fits shown in this figure and Figs. 4, 5, 6, 7 can be obtained at http://color.psych.upenn.edu/supplements/com_uniform/.

Fig. 5
Fig. 5

QRS’s results from discrimination and matching experiments for LM tests and adapting fields that varied in their LM input. Results are plotted in the same format as Fig. 4.

Fig. 6
Fig. 6

JMH’s results from discrimination and matching experiments for S-cone tests and adapting fields that varied in their S-cone input. Results are plotted in the same format as Fig. 4 except that values correspond to expected S-cone isomerizations.

Fig. 7
Fig. 7

QRS’s results from discrimination and matching experiments for S-cone tests and adapting fields that varied in their S-cone input. Results are plotted in the same format as Figs. 4, 5, 6.

Fig. 8
Fig. 8

Error trade-off analysis for JMH’s LM test data in the Gray and Gray + LM adapting condtions. Central panel are results of the error trade-off analysis described in the text for the gain-and-subtractive model of adaptation. The x axis is the normalized negative log likelihood ( LL ) of model parameters given the full complement of discrimination data from the Gray and Gray + LM adapting conditions (we plot the negative log likelihood so small values correspond to better fits, consistent with the sum-of-squared error metric used as a criterion for the matching data). The y axis is the normalized least-squared error (LSE) of model fits for the matching data in the same adapting conditions. The two left panels show the data that underlie the analysis presented in the central panel and are replotted from Fig. 4. The two right panels show the same data. The model fits in the two left panels are fits where model parameters were determined exclusively by the discrimination data. The gray star in the central error trade-off panel is the LL , LSE combination corresponding to these fits. The model fits in the two right panels are fits where model parameters were determined exclusively by the matching data. The gray diamond in the central error trade-off panel is the LL , LSE combination corresponding to these fits. The filled gray circles in the central panel are LL , LSE combinations where both data sets were used to determine the model parameters. Each gray circle represents a LL , LSE combination for a specific combination of weights to the matching and discrimination error. Higher points in the graph are from fits where more weight was given to maximize the likelihood of the parameters given the discrimination data than to minimize the sum-of-squared error for the model parameters given the matching data. Similarly, the more rightward points are from fits where more weight was given to minimize the sum-of-squared error for the model parameters given the matching data than to maximizing the likelihood of the parameters given the discrimination data.

Fig. 9
Fig. 9

Error trade-off analysis for LM tests and adapting fields that varied only in their LM component. The top two panels are, from left to right, JMH’s results from + LM tests on Gray and Gray LM adapting fields and LM tests on Gray and Gray + LM adapting fields. The bottom two panels are from the same conditions for QRS. Plotting conventions are the same as those for the central panel in Fig. 8. We have included results of the error trade-off analysis for the gain-only (open white symbols) model as well as the gain-and-subtractive (gray symbols) model.

Fig. 10
Fig. 10

Same as Fig. 8 except for S-cone tests and adapting fields that varied only in their S-cone component.

Fig. 11
Fig. 11

JMH’s JND ratios for the split field versus uniform field conditions for LM increments presented against Gray and Gray LM backgrounds. The x axis is isomerizations of the pedestal (same as lower right and middle right panels in Fig. 4). The y axis is the JND ratio for discrimination data collected on a uniform and split field. Open circles are JND ratios from the Gray adapting field and filled gray circles are ratios from the Gray LM adapting field. Error bars are 95% confidence intervals determined by a bootstrap analysis.

Fig. 12
Fig. 12

JMH’s detection and matching results for LM-cone tests presented on adapting fields that varied only in their S component and S-cone tests presented on adapting fields that varied only in their LM component. The top two panels are detection thresholds plotted as a function of background intensity. The bottom two panels are results of the asymmetric matching task. The two left panels are results from LM-cone tests presented on backgrounds that varied only in the S-cone components. The two right panels are results from S-cone tests presented on backgrounds that varied only in their LM-cone component. The x axis in the top left panel is the expected number of S-cone isomerizations from the background light for the same area and temporal interval as the test stimuli, and the y axis is the expected number of isomerizations for an LM-cone test. Similarly, the x axis in the top right panel represents background LM-cone isomerizations and the y axis S-cone test isomerizations. Data points in these top two panels are the 75% thresholds determined by fitting the detection data with a cumulative normal. The x axis in the bottom left panel is the expected number of isomerizations for fixed LM-cone tests presented on either the Gray + S , Gray, or Gray S adapting fields. The y axis is S-cone isomerizations for JMH’s match settings against the gray background. Filled squares are from the symmetric matching conditions (where both the fixed test and adjustable match were presented on the Gray background). Open circles and filled diamonds are conditions where the fixed tests were presented against the Gray + LM and Gray LM conditions, respectively. Error bars are standard errors of the mean. The convention for the bottom right panel is the same as for the bottom left panel except that the axes correspond to the expected isomerizations of S-cone tests.

Tables (2)

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Table 1   Properties of Test Backgrounds

Tables Icon

Table 2   Conventions Used to Estimate Isomerizations

Equations (8)

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p ( R green ( I 1 ) < R green ( I 1 + Δ ) ) = p ( R green ( I 1 ) R green ( I 1 + Δ ) < 0 ) = p ( n ( r ¯ green 1 , σ 2 ) n ( r ¯ green 1 + Δ , σ 2 ) < 0 ) = p ( n ( r ¯ green 1 r ¯ green 1 + Δ , 2 σ 2 ) < 0 ) = 0 n ( r ¯ green 1 r ¯ green 1 + Δ , 2 σ 2 ) ,
R = M ( g I + s ) p ( g I + s ) q + 1 .
P ( ϵ ) = { 0 for ϵ < 1.5 1 3 for 1.5 < ϵ < 1.5 0 for ϵ > 1.5 }
C = test isomerizations background isomerizations .
C L = 2 3 I test I bg , L , C M = 1 3 I test I bg , M ,
L = i = 1 N 1 × N ped ( N i trials N i correct ) p i N i correct ( 1 p i ) N i trials N i correct ,
JND 1 R = 1 M [ ( g I + S ) q + 1 ] 2 g { ( g I + S ) p 1 [ ( g I + S ) q ( p q ) + p ] } .
R i A = R i B M A ( g A I + s A ) p ( g A I + s A ) q + 1 = M B ( g B I + s B ) p ( g B I + s B ) q + 1 .

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