Abstract

Across many scenes, local contrast provides a valid cue to surface reflectance, but it is not the only such cue. To generalize beyond theories of lightness that rely exclusively on local contrast, we need to know which other potential cues matter. We had observers make lightness matches between two scene locations, and varied the surface slant and local surround reflectance of one of the locations. When local contrast was a valid cue to reflectance, all observers were approximately lightness constant. When it was not, observers’ lightness matches were intermediate between contrast matching and lightness constancy. For most observers, surface slant exerted an effect on perceived lightness beyond that explainable by local contrast.

© 2009 Optical Society of America

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  1. H. Helson and V. B. Jeffers, “Fundamental problems in color vision, ii. hue, lightness, and saturation of selective samples in chromatic illumination,” J. Exp. Psychol. 26, 1-27 (1940).
    [CrossRef]
  2. E. J. Breneman, “Corresponding chromaticities for different states of adaptation to complex visual fields,” J. Opt. Soc. Am. A 4, 1115-1129 (1987).
    [CrossRef] [PubMed]
  3. J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in retinex theory. A comparison between theoretical predictions and observer responses to the “color Mondrian” experiments,” Vision Res. 16, 445-458 (1976).
    [CrossRef] [PubMed]
  4. L. Arend and A. Reeves, “Simultaneous color constancy,” J. Opt. Soc. Am. A 3, 1743-1751 (1986).
    [CrossRef] [PubMed]
  5. D. H. Brainard, W. A. Brunt, and J. M. Speigle, “Color constancy in the nearly natural image. I Asymmetric matches,” J. Opt. Soc. Am. A 14, 2091-2110 (1997).
    [CrossRef]
  6. D. H. Brainard, “Color constancy in the nearly natural image. II. Achromatic loci,” J. Opt. Soc. Am. A 15, 307-325 (1998).
    [CrossRef]
  7. E. H. Land and J. J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Am. 61, 1-11 (1971).
    [CrossRef] [PubMed]
  8. M. H. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473-478 (1978).
    [CrossRef] [PubMed]
  9. M. H. Brill, “Further features of the illuminant-invariant trichromatic photosensor,” J. Theor. Biol. 78, 305-308 (1979).
    [CrossRef] [PubMed]
  10. G. West and M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaptation to give color constancy,” J. Math. Biol. 15, 249-258 (1982).
    [CrossRef] [PubMed]
  11. J. A. Worthey and M. H. Brill, “Heuristic analysis of von Kries color constancy,” J. Opt. Soc. Am. A 3, 1708-1712 (1986).
    [CrossRef] [PubMed]
  12. D. H. Brainard and B. A. Wandell, “Analysis of the retinex theory of color vision,” J. Opt. Soc. Am. A 3, 1651-1661 (1986).
    [CrossRef] [PubMed]
  13. D. H. Foster and S. M. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London 257, 115-121 (1994).
    [CrossRef]
  14. H. Wallach, “Brightness constancy and the nature of achromatic colors,” J. Exp. Psychol. 38, 310-324 (1948).
    [CrossRef] [PubMed]
  15. T. N. Cornsweet, Visual Perception (Academic, 1970).
  16. E. H. Land, “Recent advances in retinex theory,” Vision Res. 26, 7-21 (1986).
    [CrossRef] [PubMed]
  17. J. Walraven, “Discounting the background-the missing link in the explanation of chromatic induction,” Vision Res. 16, 289-295 (1976).
    [CrossRef] [PubMed]
  18. S. K. Shevell, “The dual role of chromatic backgrounds in color perception,” Vision Res. 18, 1649-1661 (1978).
    [CrossRef] [PubMed]
  19. A. Gilchrist, Seeing Black and White (Oxford U. Press, 2006).
    [CrossRef]
  20. E. H. Adelson, “Lightness perception and lightness illusions,” in The New Cognitive Neurosciences, M.Gazzaniga, ed., 2nd ed. (MIT Press, 1999).
  21. R. Shapley, “The importance of contrast for the activity of single neurons, the vep and perception,” Vision Res. 26, 45-61 (1986).
    [CrossRef] [PubMed]
  22. D. Katz, The World of Colour (Kegan Paul, Trench, Trubner, 1935).
  23. L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 2. reflectance variation,” Percept. Psychophys. 54, 457-468 (1993).
    [CrossRef] [PubMed]
  24. J. M. Kraft and D. H. Brainard, “Mechanisms of color constancy under nearly natural viewing,” Proc. Natl. Acad. Sci. U.S.A. 96, 307-312 (1999).
    [CrossRef] [PubMed]
  25. P. B. Delahunt and D. H. Brainard, “Does human color constancy incorporate the statistical regularity of natural daylight?” J. Vision 4, 57-81 (2004).
    [CrossRef]
  26. J. E. Hochberg and J. Beck, “Apparent spatial arrangement and perceived brightness,” J. Exp. Psychol. 47, 263-266 (1954).
    [CrossRef] [PubMed]
  27. A. L. Gilchrist, “Perceived lightness depends on perceived spatial arrangement,” Science 195, 185-187 (1977).
    [CrossRef] [PubMed]
  28. A. L. Gilchrist, “When does perceived lightness depend on perceived spatial arrangement?” Percept. Psychophys. 28, 527-538 (1980).
    [CrossRef] [PubMed]
  29. M. G. Bloj, D. Kersten, and A. C. Hurlbert, “Perception of three-dimensional shape influences colour perception through mutual illumination,” Nature (London) 402, 877-879 (1999).
  30. H. Boyaci, K. Doerschner, J. L. Snyder, and L. T. Maloney, “Surface color perception in three-dimensional scenes,” Visual Neurosci. 23, 311-321 (2006).
    [CrossRef]
  31. C. Ripamonti, M. Bloj, R. Hauck, M. Kiran, S. Greenwald, S. I. Maloney, and D. H. Brainard, “Measurements of the effect of surface slant on perceived lightness,” J. Vision 4, 747-763 (2004).
    [CrossRef]
  32. K. Doerschner, H. Boyaci, and L. T. Maloney, “Human observers compensate for secondary illumination originating in nearby chromatic surfaces,” J. Vision 4, 92-105 (2004).
    [CrossRef]
  33. M. Bloj, C. Ripamonti, K. Mitha, R. Hauck, S. Greenwald, and D. H. Brainard, “An equivalent illuminant model for the effect of surface slant on perceived lightness,” J. Vision 4, 735-746 (2004).
    [CrossRef]
  34. D. H. Brainard, “The psychophysics toolbox,” Spatial Vis. 10, 433-436 (1997).
    [CrossRef]
  35. A. B. Watson and D. G. Pelli, “Quest: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113-120 (1983).
    [CrossRef] [PubMed]
  36. F. A. Wichmann and N. J. Hill, “The psychometric function: I. Fitting, sampling, and goodness-of-fit,” Percept. Psychophys. 63, 1293-1313 (2001).
    [CrossRef]
  37. P. Whittle and P. D. Challands, “The effect of background luminance on the brightness of flashes,” Vision Res. 9, 1095-1110 (1969).
    [CrossRef] [PubMed]
  38. H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716-723 (1974).
    [CrossRef]
  39. K. P. Burnham and D. R. Anderson, Model Selection and Multi-Model Inference (Springer, 2002).
  40. L. E. Arend and R. Goldstein, “Simultaneous constancy, lightness, and brightness,” J. Opt. Soc. Am. A 4, 2281-2285 (1987).
    [CrossRef] [PubMed]
  41. K. H. Bauml, “Simultaneous color constancy: how surface color perception varies with the illuminant,” Vision Res. 39, 1531-1550 (1999).
    [CrossRef] [PubMed]
  42. L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 1. Illuminance variation,” Percept. Psychophys. 54, 446-456 (1993).
    [CrossRef] [PubMed]
  43. B. Blakeslee, D. Reetz, and M. E. McCourt, “Coming to terms with lightness and brightness: effects of stimulus configuration and instructions on brightness and lightness judgments,” J. Vision 8, 1-14 (2008).
    [CrossRef]
  44. A. J. Reeves, K. Amano, and D. H. Foster, “Color constancy: phenomenal or projective?” Percept. Psychophys. 70, 219-228 (2008).
    [CrossRef] [PubMed]
  45. Z. Pylyshyn, “Is vision continuous with cognition? the case for cognitive impenetrability of visual perception,” Behav. Brain Sci. 22, 341-365; discussion, pp. 366-423 (1999).
    [PubMed]
  46. A. D. Logvinenko, K. Petrini, and L. T. Maloney, “A scaling analysis of the snake lightness illusion,” Percept. Psychophys. 70, 828-840 (2008).
    [CrossRef] [PubMed]
  47. J. M. Hillis and D. H. Brainard, “Distinct mechanisms mediate visual detection and identification,” Curr. Biol. 17, 1714-1719 (2007).
    [CrossRef] [PubMed]
  48. A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
    [CrossRef] [PubMed]

2008 (3)

B. Blakeslee, D. Reetz, and M. E. McCourt, “Coming to terms with lightness and brightness: effects of stimulus configuration and instructions on brightness and lightness judgments,” J. Vision 8, 1-14 (2008).
[CrossRef]

A. J. Reeves, K. Amano, and D. H. Foster, “Color constancy: phenomenal or projective?” Percept. Psychophys. 70, 219-228 (2008).
[CrossRef] [PubMed]

A. D. Logvinenko, K. Petrini, and L. T. Maloney, “A scaling analysis of the snake lightness illusion,” Percept. Psychophys. 70, 828-840 (2008).
[CrossRef] [PubMed]

2007 (1)

J. M. Hillis and D. H. Brainard, “Distinct mechanisms mediate visual detection and identification,” Curr. Biol. 17, 1714-1719 (2007).
[CrossRef] [PubMed]

2006 (1)

H. Boyaci, K. Doerschner, J. L. Snyder, and L. T. Maloney, “Surface color perception in three-dimensional scenes,” Visual Neurosci. 23, 311-321 (2006).
[CrossRef]

2004 (4)

C. Ripamonti, M. Bloj, R. Hauck, M. Kiran, S. Greenwald, S. I. Maloney, and D. H. Brainard, “Measurements of the effect of surface slant on perceived lightness,” J. Vision 4, 747-763 (2004).
[CrossRef]

K. Doerschner, H. Boyaci, and L. T. Maloney, “Human observers compensate for secondary illumination originating in nearby chromatic surfaces,” J. Vision 4, 92-105 (2004).
[CrossRef]

M. Bloj, C. Ripamonti, K. Mitha, R. Hauck, S. Greenwald, and D. H. Brainard, “An equivalent illuminant model for the effect of surface slant on perceived lightness,” J. Vision 4, 735-746 (2004).
[CrossRef]

P. B. Delahunt and D. H. Brainard, “Does human color constancy incorporate the statistical regularity of natural daylight?” J. Vision 4, 57-81 (2004).
[CrossRef]

2001 (1)

F. A. Wichmann and N. J. Hill, “The psychometric function: I. Fitting, sampling, and goodness-of-fit,” Percept. Psychophys. 63, 1293-1313 (2001).
[CrossRef]

1999 (4)

M. G. Bloj, D. Kersten, and A. C. Hurlbert, “Perception of three-dimensional shape influences colour perception through mutual illumination,” Nature (London) 402, 877-879 (1999).

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

J. M. Kraft and D. H. Brainard, “Mechanisms of color constancy under nearly natural viewing,” Proc. Natl. Acad. Sci. U.S.A. 96, 307-312 (1999).
[CrossRef] [PubMed]

K. H. Bauml, “Simultaneous color constancy: how surface color perception varies with the illuminant,” Vision Res. 39, 1531-1550 (1999).
[CrossRef] [PubMed]

1998 (1)

1997 (2)

1994 (1)

D. H. Foster and S. M. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London 257, 115-121 (1994).
[CrossRef]

1993 (2)

L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 2. reflectance variation,” Percept. Psychophys. 54, 457-468 (1993).
[CrossRef] [PubMed]

L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 1. Illuminance variation,” Percept. Psychophys. 54, 446-456 (1993).
[CrossRef] [PubMed]

1987 (2)

1986 (5)

1983 (1)

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

1982 (1)

G. West and M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaptation to give color constancy,” J. Math. Biol. 15, 249-258 (1982).
[CrossRef] [PubMed]

1980 (1)

A. L. Gilchrist, “When does perceived lightness depend on perceived spatial arrangement?” Percept. Psychophys. 28, 527-538 (1980).
[CrossRef] [PubMed]

1979 (1)

M. H. Brill, “Further features of the illuminant-invariant trichromatic photosensor,” J. Theor. Biol. 78, 305-308 (1979).
[CrossRef] [PubMed]

1978 (2)

M. H. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473-478 (1978).
[CrossRef] [PubMed]

S. K. Shevell, “The dual role of chromatic backgrounds in color perception,” Vision Res. 18, 1649-1661 (1978).
[CrossRef] [PubMed]

1977 (1)

A. L. Gilchrist, “Perceived lightness depends on perceived spatial arrangement,” Science 195, 185-187 (1977).
[CrossRef] [PubMed]

1976 (2)

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

J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in retinex theory. A comparison between theoretical predictions and observer responses to the “color Mondrian” experiments,” Vision Res. 16, 445-458 (1976).
[CrossRef] [PubMed]

1974 (1)

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716-723 (1974).
[CrossRef]

1971 (1)

1969 (1)

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

1954 (1)

J. E. Hochberg and J. Beck, “Apparent spatial arrangement and perceived brightness,” J. Exp. Psychol. 47, 263-266 (1954).
[CrossRef] [PubMed]

1948 (1)

H. Wallach, “Brightness constancy and the nature of achromatic colors,” J. Exp. Psychol. 38, 310-324 (1948).
[CrossRef] [PubMed]

1940 (1)

H. Helson and V. B. Jeffers, “Fundamental problems in color vision, ii. hue, lightness, and saturation of selective samples in chromatic illumination,” J. Exp. Psychol. 26, 1-27 (1940).
[CrossRef]

Adelson, E. H.

E. H. Adelson, “Lightness perception and lightness illusions,” in The New Cognitive Neurosciences, M.Gazzaniga, ed., 2nd ed. (MIT Press, 1999).

Agostini, T.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

Akaike, H.

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716-723 (1974).
[CrossRef]

Amano, K.

A. J. Reeves, K. Amano, and D. H. Foster, “Color constancy: phenomenal or projective?” Percept. Psychophys. 70, 219-228 (2008).
[CrossRef] [PubMed]

Anderson, D. R.

K. P. Burnham and D. R. Anderson, Model Selection and Multi-Model Inference (Springer, 2002).

Annan, V.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

Arend, L.

Arend, L. E.

L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 1. Illuminance variation,” Percept. Psychophys. 54, 446-456 (1993).
[CrossRef] [PubMed]

L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 2. reflectance variation,” Percept. Psychophys. 54, 457-468 (1993).
[CrossRef] [PubMed]

L. E. Arend and R. Goldstein, “Simultaneous constancy, lightness, and brightness,” J. Opt. Soc. Am. A 4, 2281-2285 (1987).
[CrossRef] [PubMed]

Bauml, K. H.

K. H. Bauml, “Simultaneous color constancy: how surface color perception varies with the illuminant,” Vision Res. 39, 1531-1550 (1999).
[CrossRef] [PubMed]

Beck, J.

J. E. Hochberg and J. Beck, “Apparent spatial arrangement and perceived brightness,” J. Exp. Psychol. 47, 263-266 (1954).
[CrossRef] [PubMed]

Blakeslee, B.

B. Blakeslee, D. Reetz, and M. E. McCourt, “Coming to terms with lightness and brightness: effects of stimulus configuration and instructions on brightness and lightness judgments,” J. Vision 8, 1-14 (2008).
[CrossRef]

Bloj, M.

M. Bloj, C. Ripamonti, K. Mitha, R. Hauck, S. Greenwald, and D. H. Brainard, “An equivalent illuminant model for the effect of surface slant on perceived lightness,” J. Vision 4, 735-746 (2004).
[CrossRef]

C. Ripamonti, M. Bloj, R. Hauck, M. Kiran, S. Greenwald, S. I. Maloney, and D. H. Brainard, “Measurements of the effect of surface slant on perceived lightness,” J. Vision 4, 747-763 (2004).
[CrossRef]

Bloj, M. G.

M. G. Bloj, D. Kersten, and A. C. Hurlbert, “Perception of three-dimensional shape influences colour perception through mutual illumination,” Nature (London) 402, 877-879 (1999).

Bonato, F.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

Boyaci, H.

H. Boyaci, K. Doerschner, J. L. Snyder, and L. T. Maloney, “Surface color perception in three-dimensional scenes,” Visual Neurosci. 23, 311-321 (2006).
[CrossRef]

K. Doerschner, H. Boyaci, and L. T. Maloney, “Human observers compensate for secondary illumination originating in nearby chromatic surfaces,” J. Vision 4, 92-105 (2004).
[CrossRef]

Brainard, D. H.

J. M. Hillis and D. H. Brainard, “Distinct mechanisms mediate visual detection and identification,” Curr. Biol. 17, 1714-1719 (2007).
[CrossRef] [PubMed]

P. B. Delahunt and D. H. Brainard, “Does human color constancy incorporate the statistical regularity of natural daylight?” J. Vision 4, 57-81 (2004).
[CrossRef]

M. Bloj, C. Ripamonti, K. Mitha, R. Hauck, S. Greenwald, and D. H. Brainard, “An equivalent illuminant model for the effect of surface slant on perceived lightness,” J. Vision 4, 735-746 (2004).
[CrossRef]

C. Ripamonti, M. Bloj, R. Hauck, M. Kiran, S. Greenwald, S. I. Maloney, and D. H. Brainard, “Measurements of the effect of surface slant on perceived lightness,” J. Vision 4, 747-763 (2004).
[CrossRef]

J. M. Kraft and D. H. Brainard, “Mechanisms of color constancy under nearly natural viewing,” Proc. Natl. Acad. Sci. U.S.A. 96, 307-312 (1999).
[CrossRef] [PubMed]

D. H. Brainard, “Color constancy in the nearly natural image. II. Achromatic loci,” J. Opt. Soc. Am. A 15, 307-325 (1998).
[CrossRef]

D. H. Brainard, “The psychophysics toolbox,” Spatial Vis. 10, 433-436 (1997).
[CrossRef]

D. H. Brainard, W. A. Brunt, and J. M. Speigle, “Color constancy in the nearly natural image. I Asymmetric matches,” J. Opt. Soc. Am. A 14, 2091-2110 (1997).
[CrossRef]

D. H. Brainard and B. A. Wandell, “Analysis of the retinex theory of color vision,” J. Opt. Soc. Am. A 3, 1651-1661 (1986).
[CrossRef] [PubMed]

Breneman, E. J.

Brill, M. H.

J. A. Worthey and M. H. Brill, “Heuristic analysis of von Kries color constancy,” J. Opt. Soc. Am. A 3, 1708-1712 (1986).
[CrossRef] [PubMed]

G. West and M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaptation to give color constancy,” J. Math. Biol. 15, 249-258 (1982).
[CrossRef] [PubMed]

M. H. Brill, “Further features of the illuminant-invariant trichromatic photosensor,” J. Theor. Biol. 78, 305-308 (1979).
[CrossRef] [PubMed]

M. H. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473-478 (1978).
[CrossRef] [PubMed]

Brunt, W. A.

Burnham, K. P.

K. P. Burnham and D. R. Anderson, Model Selection and Multi-Model Inference (Springer, 2002).

Cataliotti, J.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

Challands, P. D.

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

Cornsweet, T. N.

T. N. Cornsweet, Visual Perception (Academic, 1970).

Delahunt, P. B.

P. B. Delahunt and D. H. Brainard, “Does human color constancy incorporate the statistical regularity of natural daylight?” J. Vision 4, 57-81 (2004).
[CrossRef]

Doerschner, K.

H. Boyaci, K. Doerschner, J. L. Snyder, and L. T. Maloney, “Surface color perception in three-dimensional scenes,” Visual Neurosci. 23, 311-321 (2006).
[CrossRef]

K. Doerschner, H. Boyaci, and L. T. Maloney, “Human observers compensate for secondary illumination originating in nearby chromatic surfaces,” J. Vision 4, 92-105 (2004).
[CrossRef]

Economou, E.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

Foster, D. H.

A. J. Reeves, K. Amano, and D. H. Foster, “Color constancy: phenomenal or projective?” Percept. Psychophys. 70, 219-228 (2008).
[CrossRef] [PubMed]

D. H. Foster and S. M. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London 257, 115-121 (1994).
[CrossRef]

Gilchrist, A.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

A. Gilchrist, Seeing Black and White (Oxford U. Press, 2006).
[CrossRef]

Gilchrist, A. L.

A. L. Gilchrist, “When does perceived lightness depend on perceived spatial arrangement?” Percept. Psychophys. 28, 527-538 (1980).
[CrossRef] [PubMed]

A. L. Gilchrist, “Perceived lightness depends on perceived spatial arrangement,” Science 195, 185-187 (1977).
[CrossRef] [PubMed]

Goldstein, R.

Greenwald, S.

M. Bloj, C. Ripamonti, K. Mitha, R. Hauck, S. Greenwald, and D. H. Brainard, “An equivalent illuminant model for the effect of surface slant on perceived lightness,” J. Vision 4, 735-746 (2004).
[CrossRef]

C. Ripamonti, M. Bloj, R. Hauck, M. Kiran, S. Greenwald, S. I. Maloney, and D. H. Brainard, “Measurements of the effect of surface slant on perceived lightness,” J. Vision 4, 747-763 (2004).
[CrossRef]

Hauck, R.

C. Ripamonti, M. Bloj, R. Hauck, M. Kiran, S. Greenwald, S. I. Maloney, and D. H. Brainard, “Measurements of the effect of surface slant on perceived lightness,” J. Vision 4, 747-763 (2004).
[CrossRef]

M. Bloj, C. Ripamonti, K. Mitha, R. Hauck, S. Greenwald, and D. H. Brainard, “An equivalent illuminant model for the effect of surface slant on perceived lightness,” J. Vision 4, 735-746 (2004).
[CrossRef]

Helson, H.

H. Helson and V. B. Jeffers, “Fundamental problems in color vision, ii. hue, lightness, and saturation of selective samples in chromatic illumination,” J. Exp. Psychol. 26, 1-27 (1940).
[CrossRef]

Hill, N. J.

F. A. Wichmann and N. J. Hill, “The psychometric function: I. Fitting, sampling, and goodness-of-fit,” Percept. Psychophys. 63, 1293-1313 (2001).
[CrossRef]

Hillis, J. M.

J. M. Hillis and D. H. Brainard, “Distinct mechanisms mediate visual detection and identification,” Curr. Biol. 17, 1714-1719 (2007).
[CrossRef] [PubMed]

Hochberg, J. E.

J. E. Hochberg and J. Beck, “Apparent spatial arrangement and perceived brightness,” J. Exp. Psychol. 47, 263-266 (1954).
[CrossRef] [PubMed]

Hurlbert, A. C.

M. G. Bloj, D. Kersten, and A. C. Hurlbert, “Perception of three-dimensional shape influences colour perception through mutual illumination,” Nature (London) 402, 877-879 (1999).

Jeffers, V. B.

H. Helson and V. B. Jeffers, “Fundamental problems in color vision, ii. hue, lightness, and saturation of selective samples in chromatic illumination,” J. Exp. Psychol. 26, 1-27 (1940).
[CrossRef]

Katz, D.

D. Katz, The World of Colour (Kegan Paul, Trench, Trubner, 1935).

Kersten, D.

M. G. Bloj, D. Kersten, and A. C. Hurlbert, “Perception of three-dimensional shape influences colour perception through mutual illumination,” Nature (London) 402, 877-879 (1999).

Kiran, M.

C. Ripamonti, M. Bloj, R. Hauck, M. Kiran, S. Greenwald, S. I. Maloney, and D. H. Brainard, “Measurements of the effect of surface slant on perceived lightness,” J. Vision 4, 747-763 (2004).
[CrossRef]

Kossyfidis, C.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

Kraft, J. M.

J. M. Kraft and D. H. Brainard, “Mechanisms of color constancy under nearly natural viewing,” Proc. Natl. Acad. Sci. U.S.A. 96, 307-312 (1999).
[CrossRef] [PubMed]

Land, E. H.

Li, X.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

Logvinenko, A. D.

A. D. Logvinenko, K. Petrini, and L. T. Maloney, “A scaling analysis of the snake lightness illusion,” Percept. Psychophys. 70, 828-840 (2008).
[CrossRef] [PubMed]

Maloney, L. T.

A. D. Logvinenko, K. Petrini, and L. T. Maloney, “A scaling analysis of the snake lightness illusion,” Percept. Psychophys. 70, 828-840 (2008).
[CrossRef] [PubMed]

H. Boyaci, K. Doerschner, J. L. Snyder, and L. T. Maloney, “Surface color perception in three-dimensional scenes,” Visual Neurosci. 23, 311-321 (2006).
[CrossRef]

K. Doerschner, H. Boyaci, and L. T. Maloney, “Human observers compensate for secondary illumination originating in nearby chromatic surfaces,” J. Vision 4, 92-105 (2004).
[CrossRef]

Maloney, S. I.

C. Ripamonti, M. Bloj, R. Hauck, M. Kiran, S. Greenwald, S. I. Maloney, and D. H. Brainard, “Measurements of the effect of surface slant on perceived lightness,” J. Vision 4, 747-763 (2004).
[CrossRef]

McCann, J. J.

J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in retinex theory. A comparison between theoretical predictions and observer responses to the “color Mondrian” experiments,” Vision Res. 16, 445-458 (1976).
[CrossRef] [PubMed]

E. H. Land and J. J. McCann, “Lightness and retinex theory,” J. Opt. Soc. Am. 61, 1-11 (1971).
[CrossRef] [PubMed]

McCourt, M. E.

B. Blakeslee, D. Reetz, and M. E. McCourt, “Coming to terms with lightness and brightness: effects of stimulus configuration and instructions on brightness and lightness judgments,” J. Vision 8, 1-14 (2008).
[CrossRef]

McKee, S. P.

J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in retinex theory. A comparison between theoretical predictions and observer responses to the “color Mondrian” experiments,” Vision Res. 16, 445-458 (1976).
[CrossRef] [PubMed]

Mitha, K.

M. Bloj, C. Ripamonti, K. Mitha, R. Hauck, S. Greenwald, and D. H. Brainard, “An equivalent illuminant model for the effect of surface slant on perceived lightness,” J. Vision 4, 735-746 (2004).
[CrossRef]

Nascimento, S. M.

D. H. Foster and S. M. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London 257, 115-121 (1994).
[CrossRef]

Pelli, D. G.

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

Petrini, K.

A. D. Logvinenko, K. Petrini, and L. T. Maloney, “A scaling analysis of the snake lightness illusion,” Percept. Psychophys. 70, 828-840 (2008).
[CrossRef] [PubMed]

Pylyshyn, Z.

Z. Pylyshyn, “Is vision continuous with cognition? the case for cognitive impenetrability of visual perception,” Behav. Brain Sci. 22, 341-365; discussion, pp. 366-423 (1999).
[PubMed]

Reetz, D.

B. Blakeslee, D. Reetz, and M. E. McCourt, “Coming to terms with lightness and brightness: effects of stimulus configuration and instructions on brightness and lightness judgments,” J. Vision 8, 1-14 (2008).
[CrossRef]

Reeves, A.

Reeves, A. J.

A. J. Reeves, K. Amano, and D. H. Foster, “Color constancy: phenomenal or projective?” Percept. Psychophys. 70, 219-228 (2008).
[CrossRef] [PubMed]

Ripamonti, C.

M. Bloj, C. Ripamonti, K. Mitha, R. Hauck, S. Greenwald, and D. H. Brainard, “An equivalent illuminant model for the effect of surface slant on perceived lightness,” J. Vision 4, 735-746 (2004).
[CrossRef]

C. Ripamonti, M. Bloj, R. Hauck, M. Kiran, S. Greenwald, S. I. Maloney, and D. H. Brainard, “Measurements of the effect of surface slant on perceived lightness,” J. Vision 4, 747-763 (2004).
[CrossRef]

Shapley, R.

R. Shapley, “The importance of contrast for the activity of single neurons, the vep and perception,” Vision Res. 26, 45-61 (1986).
[CrossRef] [PubMed]

Shevell, S. K.

S. K. Shevell, “The dual role of chromatic backgrounds in color perception,” Vision Res. 18, 1649-1661 (1978).
[CrossRef] [PubMed]

Snyder, J. L.

H. Boyaci, K. Doerschner, J. L. Snyder, and L. T. Maloney, “Surface color perception in three-dimensional scenes,” Visual Neurosci. 23, 311-321 (2006).
[CrossRef]

Spehar, B.

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 2. reflectance variation,” Percept. Psychophys. 54, 457-468 (1993).
[CrossRef] [PubMed]

L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 1. Illuminance variation,” Percept. Psychophys. 54, 446-456 (1993).
[CrossRef] [PubMed]

Speigle, J. M.

Taylor, T. H.

J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in retinex theory. A comparison between theoretical predictions and observer responses to the “color Mondrian” experiments,” Vision Res. 16, 445-458 (1976).
[CrossRef] [PubMed]

Wallach, H.

H. Wallach, “Brightness constancy and the nature of achromatic colors,” J. Exp. Psychol. 38, 310-324 (1948).
[CrossRef] [PubMed]

Walraven, J.

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

Wandell, B. A.

Watson, A. B.

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

West, G.

G. West and M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaptation to give color constancy,” J. Math. Biol. 15, 249-258 (1982).
[CrossRef] [PubMed]

Whittle, P.

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

Wichmann, F. A.

F. A. Wichmann and N. J. Hill, “The psychometric function: I. Fitting, sampling, and goodness-of-fit,” Percept. Psychophys. 63, 1293-1313 (2001).
[CrossRef]

Worthey, J. A.

Behav. Brain Sci. (1)

Z. Pylyshyn, “Is vision continuous with cognition? the case for cognitive impenetrability of visual perception,” Behav. Brain Sci. 22, 341-365; discussion, pp. 366-423 (1999).
[PubMed]

Curr. Biol. (1)

J. M. Hillis and D. H. Brainard, “Distinct mechanisms mediate visual detection and identification,” Curr. Biol. 17, 1714-1719 (2007).
[CrossRef] [PubMed]

IEEE Trans. Autom. Control (1)

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716-723 (1974).
[CrossRef]

J. Exp. Psychol. (3)

H. Helson and V. B. Jeffers, “Fundamental problems in color vision, ii. hue, lightness, and saturation of selective samples in chromatic illumination,” J. Exp. Psychol. 26, 1-27 (1940).
[CrossRef]

H. Wallach, “Brightness constancy and the nature of achromatic colors,” J. Exp. Psychol. 38, 310-324 (1948).
[CrossRef] [PubMed]

J. E. Hochberg and J. Beck, “Apparent spatial arrangement and perceived brightness,” J. Exp. Psychol. 47, 263-266 (1954).
[CrossRef] [PubMed]

J. Math. Biol. (1)

G. West and M. H. Brill, “Necessary and sufficient conditions for von Kries chromatic adaptation to give color constancy,” J. Math. Biol. 15, 249-258 (1982).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

J. Theor. Biol. (2)

M. H. Brill, “A device performing illuminant-invariant assessment of chromatic relations,” J. Theor. Biol. 71, 473-478 (1978).
[CrossRef] [PubMed]

M. H. Brill, “Further features of the illuminant-invariant trichromatic photosensor,” J. Theor. Biol. 78, 305-308 (1979).
[CrossRef] [PubMed]

J. Vision (5)

P. B. Delahunt and D. H. Brainard, “Does human color constancy incorporate the statistical regularity of natural daylight?” J. Vision 4, 57-81 (2004).
[CrossRef]

C. Ripamonti, M. Bloj, R. Hauck, M. Kiran, S. Greenwald, S. I. Maloney, and D. H. Brainard, “Measurements of the effect of surface slant on perceived lightness,” J. Vision 4, 747-763 (2004).
[CrossRef]

K. Doerschner, H. Boyaci, and L. T. Maloney, “Human observers compensate for secondary illumination originating in nearby chromatic surfaces,” J. Vision 4, 92-105 (2004).
[CrossRef]

M. Bloj, C. Ripamonti, K. Mitha, R. Hauck, S. Greenwald, and D. H. Brainard, “An equivalent illuminant model for the effect of surface slant on perceived lightness,” J. Vision 4, 735-746 (2004).
[CrossRef]

B. Blakeslee, D. Reetz, and M. E. McCourt, “Coming to terms with lightness and brightness: effects of stimulus configuration and instructions on brightness and lightness judgments,” J. Vision 8, 1-14 (2008).
[CrossRef]

Nature (London) (1)

M. G. Bloj, D. Kersten, and A. C. Hurlbert, “Perception of three-dimensional shape influences colour perception through mutual illumination,” Nature (London) 402, 877-879 (1999).

Percept. Psychophys. (7)

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

F. A. Wichmann and N. J. Hill, “The psychometric function: I. Fitting, sampling, and goodness-of-fit,” Percept. Psychophys. 63, 1293-1313 (2001).
[CrossRef]

A. L. Gilchrist, “When does perceived lightness depend on perceived spatial arrangement?” Percept. Psychophys. 28, 527-538 (1980).
[CrossRef] [PubMed]

L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 2. reflectance variation,” Percept. Psychophys. 54, 457-468 (1993).
[CrossRef] [PubMed]

A. J. Reeves, K. Amano, and D. H. Foster, “Color constancy: phenomenal or projective?” Percept. Psychophys. 70, 219-228 (2008).
[CrossRef] [PubMed]

A. D. Logvinenko, K. Petrini, and L. T. Maloney, “A scaling analysis of the snake lightness illusion,” Percept. Psychophys. 70, 828-840 (2008).
[CrossRef] [PubMed]

L. E. Arend and B. Spehar, “Lightness, brightness, and brightness contrast: 1. Illuminance variation,” Percept. Psychophys. 54, 446-456 (1993).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. M. Kraft and D. H. Brainard, “Mechanisms of color constancy under nearly natural viewing,” Proc. Natl. Acad. Sci. U.S.A. 96, 307-312 (1999).
[CrossRef] [PubMed]

Proc. R. Soc. London (1)

D. H. Foster and S. M. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London 257, 115-121 (1994).
[CrossRef]

Psychol. Rev. (1)

A. Gilchrist, C. Kossyfidis, F. Bonato, T. Agostini, J. Cataliotti, X. Li, B. Spehar, V. Annan, and E. Economou, “An anchoring theory of lightness perception,” Psychol. Rev. 106, 795-834 (1999).
[CrossRef] [PubMed]

Science (1)

A. L. Gilchrist, “Perceived lightness depends on perceived spatial arrangement,” Science 195, 185-187 (1977).
[CrossRef] [PubMed]

Spatial Vis. (1)

D. H. Brainard, “The psychophysics toolbox,” Spatial Vis. 10, 433-436 (1997).
[CrossRef]

Vision Res. (7)

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

R. Shapley, “The importance of contrast for the activity of single neurons, the vep and perception,” Vision Res. 26, 45-61 (1986).
[CrossRef] [PubMed]

J. J. McCann, S. P. McKee, and T. H. Taylor, “Quantitative studies in retinex theory. A comparison between theoretical predictions and observer responses to the “color Mondrian” experiments,” Vision Res. 16, 445-458 (1976).
[CrossRef] [PubMed]

E. H. Land, “Recent advances in retinex theory,” Vision Res. 26, 7-21 (1986).
[CrossRef] [PubMed]

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

S. K. Shevell, “The dual role of chromatic backgrounds in color perception,” Vision Res. 18, 1649-1661 (1978).
[CrossRef] [PubMed]

K. H. Bauml, “Simultaneous color constancy: how surface color perception varies with the illuminant,” Vision Res. 39, 1531-1550 (1999).
[CrossRef] [PubMed]

Visual Neurosci. (1)

H. Boyaci, K. Doerschner, J. L. Snyder, and L. T. Maloney, “Surface color perception in three-dimensional scenes,” Visual Neurosci. 23, 311-321 (2006).
[CrossRef]

Other (5)

D. Katz, The World of Colour (Kegan Paul, Trench, Trubner, 1935).

A. Gilchrist, Seeing Black and White (Oxford U. Press, 2006).
[CrossRef]

E. H. Adelson, “Lightness perception and lightness illusions,” in The New Cognitive Neurosciences, M.Gazzaniga, ed., 2nd ed. (MIT Press, 1999).

T. N. Cornsweet, Visual Perception (Academic, 1970).

K. P. Burnham and D. R. Anderson, Model Selection and Multi-Model Inference (Springer, 2002).

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Figures (11)

Fig. 1
Fig. 1

Observer’s view of experimental setup. The circular stages on which the cards rested could be rotated.

Fig. 2
Fig. 2

Example psychometric function for observer DBH. On each trial, the reference spot reflectance was 0.32, the reference surround reflectance was 0.16, the reference slant was 0°, the match surround reflectance was 0.16, and the match slant was 0°. The match spot reflectance was selected on each of 30 trials by the staircase procedure. For visualization purposes, the 30 trials have been divided into six bins of five trials each. In each bin, the reflectance values and responses were averaged to get the x and y values for each plotted data point. The horizontal bars show the standard error of the mean match spot reflectance for that bin. The black curve represents the best-fit cumulative Gaussian to the data. The black vertical line represents the extracted point of subjective equality (PSE), or where the best fit curve reaches 50%.

Fig. 3
Fig. 3

PSE as a function of reference spot reflectance for all six observers in one condition (reflectance of match surround = 0.16 , match slant = 0 ° ). Error bars represent standard error of the mean across sessions. Solid curves represent PSE predictions for both contrast matching and lightness constancy, which coincide for this condition. Dotted curves represent luminance matching predictions. The error-based constancy index is reported in the lower right corner of each panel.

Fig. 4
Fig. 4

PSE as a function of reference spot reflectance for all six observers in one condition (reflectance of match surround = 0.16 , match slant = 10 ° ). Error bars represent SEM across sessions. Solid curves represent PSE predictions for contrast matching and lightness constancy, which coincide for this condition. Dotted curves represent luminance matching predictions. The error-based constancy index is reported in the lower right corner of each panel.

Fig. 5
Fig. 5

PSE as a function of reference spot reflectance for all six observers in one condition (reflectance of match surround = 0.16 , match slant = 20 ° ). Error bars represent SEM across sessions. Solid curves represent PSE predictions for contrast matching and lightness constancy, which coincide for this condition. Dotted curves represent luminance matching predictions. The error-based constancy index is reported in the lower right corner of each panel.

Fig. 6
Fig. 6

Normalized PSE as a function of match slant for all six observers. Each color represents a different reference spot reflectance. Reference surround was equal to match surround (0.16). At each slant, the PSE was normalized by the PSE at slant 0. Colored curves represent the best-fit line through the data points when the curve was constrained to go through the point (0, 1). Horizontal dashed black curves represent predictions of lightness constancy and contrast matching, which are the same for this condition. Angled dashed black curves show predictions of luminance matching. Constancy index values are calculated using normalized PSEs.

Fig. 7
Fig. 7

Normalized PSE as a function of match surround reflectance for all six observers when match slant was equal to reference slant (0°). Each color represents a different reference spot reflectance. At each match surround, the PSE was normalized by the PSE obtained in the condition where match surround and reference surround were of equal reflectance (0.16). Colored curves represent the best-fit line through the data points, when the curve was constrained to go through the point (0.16, 1). Horizontal dashed black curves represent predictions of lightness constancy and luminance matching, which are the same for this condition. Angled dashed black curves show predictions from contrast. Constancy index values are calculated using normalized PSEs.

Fig. 8
Fig. 8

Constancy index (CI) values for each subject. Each panel represents CI values calculated in across a different condition. Top left: match slant and surround reflectance are the same as reference slant and surround reflectance. Values reported in Fig. 3. Top right: match surround reflectance and reference surround reflectance are the same, match slant is varied. Values reported in Fig. 6. Bottom left: match slant and reference slant are the same, match surround reflectance is varied. Values reported in Fig. 7.

Fig. 9
Fig. 9

Difference in the AIC score between a model in which normalized PSEs for all reference spots are predicted by one line and a model in which normalized PSEs are predicted by five lines, one for each reference spot. Each bar is a different subject. Δ AICs are shown for slant manipulation (left panel) and match surround reflectance manipulation (right panel). Horizontal black line indicates a Δ AIC of 10.

Fig. 10
Fig. 10

PSE as a function of match surround luminance for three observers for the lowest reflectance reference spot (top panels, reference spot reflectance = 0.16 ) and the highest reflectance reference spot (bottom panels, reference spot reflectance = 0.32 ). Each color represents a different slant ( red = 0 ° ; blue = 10 ° ; green = 20 ° ) and each symbol represents a different match surround reflectance ( cross = 0.16 ; circle = 0.25 ; star = 0.34 ; diamond = 0.44 ; square = 0.56 ). Black solid curves are predictions from contrast matching, and colored solid curves are predictions for full lightness constancy at each slant. Dashed curves represent maximum-likelihood fits of the data to the modified Naka–Rushton function. Colored dashed curves fit data separately by slant, black dashed curves fit data from all slants simultaneously.

Fig. 11
Fig. 11

Difference in AIC score between the two models for each reference spot reflectance (dark blue = 0.18 , light blue = 0.20 , green = 0.22 , orange = 0.26 , red = 0.32 ) and each observer. Higher bars indicate that nine parameters were required to fit the data. Horizontal black bar represents Δ AIC of 10.

Equations (5)

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

R match ̱ spot ( PSE ) = R reference ̱ spot ,
L match ̱ spot ( PSE ) = L reference ̱ spot ,
CI error = ϵ luminance 2 ϵ luminance 2 + ϵ constancy 2 .
AIC = 2 ln [ L ( θ y ) ] + 2 K .
L match ̱ spot ( PSE ) = M ( g L match ̱ surround I ) n ( g L match ̱ surround ) n + 1 .

Metrics