Abstract

The perception of brightness of unrelated self-luminous colored stimuli of the same luminance has been investigated. The Helmholtz–Kohlrausch (H-K) effect, i.e., an increase in brightness perception due to an increase in saturation, is clearly observed. This brightness perception is compared with the calculated brightness according to six existing vision models, color appearance models, and models based on the concept of equivalent luminance. Although these models included the H-K effect and half of them were developed to work with unrelated colors, none of the models seemed to be able to fully predict the perceived brightness. A tentative solution to increase the prediction accuracy of the color appearance model CAM97u, developed by Hunt, is presented.

© 2013 Optical Society of America

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References

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  1. CIE, International Lighting Vocabulary (CIE Central Bureau, 2011).
  2. C. L. Sanders and G. Wyszecki, “Correlate for brightness in terms of CIE color matching data,” in CIE Proceedings 15th Session (CIE Central Bureau, 1963).
  3. Y. Nayatani, “Simple estimation methods for the Helmholtz—Kohlrausch effect,” Color Res. Appl. 22, 385–401 (1997).
    [CrossRef]
  4. CIE, Supplementary System of Photometry (CIE Central Bureau, 2011).
  5. CIE, Testing of Supplementary Systems of Photometry (CIE Central Bureau, 2001).
  6. G. Wyszecki and W. S. Stiles, Color Science, 2nd ed. (Wiley, 1982), p. 410.
  7. S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vis. Res. 9, 537–575 (1969).
    [CrossRef]
  8. S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
    [CrossRef]
  9. R. M. Boynton and P. K. Kaiser, “Vision: the additivity law made to work for heterochromatic photometry with bipartite fields,” Science 161, 366–368 (1968).
    [CrossRef]
  10. G. Wagner and R. M. Boynton, “Comparison of four methods of heterochromatic photometry,” J. Opt. Soc. Am. 62, 1508–1515 (1972).
    [CrossRef]
  11. P. K. Kaiser and G. Wyszecki, “Additivity failures in heterochromatic brightness matching,” Color Res. Appl. 3, 177–182 (1978).
    [CrossRef]
  12. S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
    [CrossRef]
  13. H. Yaguchi and M. Ikeda, “Subadditivity and superadditivity in heterochromatic brightness matching,” Vis. Res. 23, 1711–1718 (1983).
    [CrossRef]
  14. M. D. Fairchild, Color Appearance Models, 2nd ed., Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2005).
  15. R. W. G. Hunt and M. R. Pointer, Measuring Colour, 4th ed., Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2011).
  16. R. W. G. Hunt, “Revised colour-appearance model for related and unrelated colours,” Color Res. Appl. 16, 146–165 (1991).
    [CrossRef]
  17. S. L. Guth, “ATD01 model for color appearances, color differences and chromatic adaptation,” Proc. SPIE 4421, 303–3062002).
    [CrossRef]
  18. C. Fu, C. Li, G. Cui, M. R. Luo, R. W. G. Hunt, and M. R. Pointer, “An investigation of colour appearance for unrelated colours under photopic and mesopic vision,” Color Res. Appl. 37, 238–254 (2012).
    [CrossRef]
  19. R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain, 1998), pp. 239–246.
  20. M. R. Luo and R. W. G. Hunt, “The structure of the CIE 1997 Colour Appearance Model (CIECAM97s),” Color Res. Appl. 23, 138–146 (1998).
    [CrossRef]
  21. CIE, A Colour Appearance Model for Colour Management Systems: CIECAM02 (CIE Central Bureau, 2004).
  22. P. Capilla, M. J. Luque, J. Gómez, and A. Palomares, “On saturation and related parameters following Guth’s ATD colour-vision model,” Color Res. Appl. 26, 305–321 (2001).
    [CrossRef]
  23. M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. R. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. Lutchi colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
    [CrossRef]
  24. K. Sagawa and K. Takeichi, “System of mesopic photometry for evaluating lights in terms of comparative brightness relationships,” J. Opt. Soc. Am. A 9, 1240–1246 (1992).
    [CrossRef]
  25. Y. Nakano, “A model for brightness perception and its application to individual data,” Jpn. J. Opt. 21, 705–716 (1992).
  26. D. A. Palmer, “Standard observer for large-field photometry at any level,” J. Opt. Soc. Am. 58, 1296–1298 (1968).
    [CrossRef]
  27. CIE, Colorimetry (CIE Central Bureau, 2004).
  28. T. N. Cornsweet, Visual Perception (Academic, 1970).
  29. F. B. Leloup, M. R. Pointer, P. Dutré, and P. Hanselaer, “Luminance-based specular gloss characterization,” J. Opt. Soc. Am. A 28, 1322–1330 (2011).
    [CrossRef]
  30. G. A. Gescheider, “Psychophysical scaling,” Annual Rev. Psych. 39, 169–200 (1988).
    [CrossRef]
  31. W. S. Torgerson, Theory and Methods of Scaling (Wiley, 1958).
  32. ASTM International, ASTM Standard E1697-05(2012)e1, “Standard Test Method for Unipolar Magnitude Estimation of Sensory Attributes” (ASTM International, 2012).
  33. P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
    [CrossRef]
  34. A. Field, Discovering Statistics Using SPSS, 3rd ed. (SAGE, 2009).

2012 (1)

C. Fu, C. Li, G. Cui, M. R. Luo, R. W. G. Hunt, and M. R. Pointer, “An investigation of colour appearance for unrelated colours under photopic and mesopic vision,” Color Res. Appl. 37, 238–254 (2012).
[CrossRef]

2011 (1)

F. B. Leloup, M. R. Pointer, P. Dutré, and P. Hanselaer, “Luminance-based specular gloss characterization,” J. Opt. Soc. Am. A 28, 1322–1330 (2011).
[CrossRef]

2007 (1)

P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[CrossRef]

2002 (1)

S. L. Guth, “ATD01 model for color appearances, color differences and chromatic adaptation,” Proc. SPIE 4421, 303–3062002).
[CrossRef]

2001 (1)

P. Capilla, M. J. Luque, J. Gómez, and A. Palomares, “On saturation and related parameters following Guth’s ATD colour-vision model,” Color Res. Appl. 26, 305–321 (2001).
[CrossRef]

1998 (1)

M. R. Luo and R. W. G. Hunt, “The structure of the CIE 1997 Colour Appearance Model (CIECAM97s),” Color Res. Appl. 23, 138–146 (1998).
[CrossRef]

1997 (1)

Y. Nayatani, “Simple estimation methods for the Helmholtz—Kohlrausch effect,” Color Res. Appl. 22, 385–401 (1997).
[CrossRef]

1992 (2)

K. Sagawa and K. Takeichi, “System of mesopic photometry for evaluating lights in terms of comparative brightness relationships,” J. Opt. Soc. Am. A 9, 1240–1246 (1992).
[CrossRef]

Y. Nakano, “A model for brightness perception and its application to individual data,” Jpn. J. Opt. 21, 705–716 (1992).

1991 (2)

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. R. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. Lutchi colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

R. W. G. Hunt, “Revised colour-appearance model for related and unrelated colours,” Color Res. Appl. 16, 146–165 (1991).
[CrossRef]

1988 (1)

G. A. Gescheider, “Psychophysical scaling,” Annual Rev. Psych. 39, 169–200 (1988).
[CrossRef]

1983 (1)

H. Yaguchi and M. Ikeda, “Subadditivity and superadditivity in heterochromatic brightness matching,” Vis. Res. 23, 1711–1718 (1983).
[CrossRef]

1978 (1)

P. K. Kaiser and G. Wyszecki, “Additivity failures in heterochromatic brightness matching,” Color Res. Appl. 3, 177–182 (1978).
[CrossRef]

1973 (1)

S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
[CrossRef]

1972 (1)

G. Wagner and R. M. Boynton, “Comparison of four methods of heterochromatic photometry,” J. Opt. Soc. Am. 62, 1508–1515 (1972).
[CrossRef]

1969 (1)

S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vis. Res. 9, 537–575 (1969).
[CrossRef]

1968 (2)

R. M. Boynton and P. K. Kaiser, “Vision: the additivity law made to work for heterochromatic photometry with bipartite fields,” Science 161, 366–368 (1968).
[CrossRef]

D. A. Palmer, “Standard observer for large-field photometry at any level,” J. Opt. Soc. Am. 58, 1296–1298 (1968).
[CrossRef]

1957 (1)

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
[CrossRef]

Boynton, R. M.

G. Wagner and R. M. Boynton, “Comparison of four methods of heterochromatic photometry,” J. Opt. Soc. Am. 62, 1508–1515 (1972).
[CrossRef]

R. M. Boynton and P. K. Kaiser, “Vision: the additivity law made to work for heterochromatic photometry with bipartite fields,” Science 161, 366–368 (1968).
[CrossRef]

Capilla, P.

P. Capilla, M. J. Luque, J. Gómez, and A. Palomares, “On saturation and related parameters following Guth’s ATD colour-vision model,” Color Res. Appl. 26, 305–321 (2001).
[CrossRef]

Clarke, A. A.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. R. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. Lutchi colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Cornsweet, T. N.

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

Cui, G.

C. Fu, C. Li, G. Cui, M. R. Luo, R. W. G. Hunt, and M. R. Pointer, “An investigation of colour appearance for unrelated colours under photopic and mesopic vision,” Color Res. Appl. 37, 238–254 (2012).
[CrossRef]

P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[CrossRef]

Donley, N. J.

S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vis. Res. 9, 537–575 (1969).
[CrossRef]

Dutré, P.

F. B. Leloup, M. R. Pointer, P. Dutré, and P. Hanselaer, “Luminance-based specular gloss characterization,” J. Opt. Soc. Am. A 28, 1322–1330 (2011).
[CrossRef]

Fairchild, M. D.

M. D. Fairchild, Color Appearance Models, 2nd ed., Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2005).

Field, A.

A. Field, Discovering Statistics Using SPSS, 3rd ed. (SAGE, 2009).

Fu, C.

C. Fu, C. Li, G. Cui, M. R. Luo, R. W. G. Hunt, and M. R. Pointer, “An investigation of colour appearance for unrelated colours under photopic and mesopic vision,” Color Res. Appl. 37, 238–254 (2012).
[CrossRef]

García, P. A.

P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[CrossRef]

Gescheider, G. A.

G. A. Gescheider, “Psychophysical scaling,” Annual Rev. Psych. 39, 169–200 (1988).
[CrossRef]

Gómez, J.

P. Capilla, M. J. Luque, J. Gómez, and A. Palomares, “On saturation and related parameters following Guth’s ATD colour-vision model,” Color Res. Appl. 26, 305–321 (2001).
[CrossRef]

Guth, S. L.

S. L. Guth, “ATD01 model for color appearances, color differences and chromatic adaptation,” Proc. SPIE 4421, 303–3062002).
[CrossRef]

S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
[CrossRef]

S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vis. Res. 9, 537–575 (1969).
[CrossRef]

Hanselaer, P.

F. B. Leloup, M. R. Pointer, P. Dutré, and P. Hanselaer, “Luminance-based specular gloss characterization,” J. Opt. Soc. Am. A 28, 1322–1330 (2011).
[CrossRef]

Huertas, R.

P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[CrossRef]

Hunt, R. W. G.

C. Fu, C. Li, G. Cui, M. R. Luo, R. W. G. Hunt, and M. R. Pointer, “An investigation of colour appearance for unrelated colours under photopic and mesopic vision,” Color Res. Appl. 37, 238–254 (2012).
[CrossRef]

M. R. Luo and R. W. G. Hunt, “The structure of the CIE 1997 Colour Appearance Model (CIECAM97s),” Color Res. Appl. 23, 138–146 (1998).
[CrossRef]

R. W. G. Hunt, “Revised colour-appearance model for related and unrelated colours,” Color Res. Appl. 16, 146–165 (1991).
[CrossRef]

R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain, 1998), pp. 239–246.

R. W. G. Hunt and M. R. Pointer, Measuring Colour, 4th ed., Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2011).

Ikeda, M.

H. Yaguchi and M. Ikeda, “Subadditivity and superadditivity in heterochromatic brightness matching,” Vis. Res. 23, 1711–1718 (1983).
[CrossRef]

Kaiser, P. K.

P. K. Kaiser and G. Wyszecki, “Additivity failures in heterochromatic brightness matching,” Color Res. Appl. 3, 177–182 (1978).
[CrossRef]

R. M. Boynton and P. K. Kaiser, “Vision: the additivity law made to work for heterochromatic photometry with bipartite fields,” Science 161, 366–368 (1968).
[CrossRef]

Leloup, F. B.

F. B. Leloup, M. R. Pointer, P. Dutré, and P. Hanselaer, “Luminance-based specular gloss characterization,” J. Opt. Soc. Am. A 28, 1322–1330 (2011).
[CrossRef]

Li, C.

C. Fu, C. Li, G. Cui, M. R. Luo, R. W. G. Hunt, and M. R. Pointer, “An investigation of colour appearance for unrelated colours under photopic and mesopic vision,” Color Res. Appl. 37, 238–254 (2012).
[CrossRef]

Lodge, H. R.

S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
[CrossRef]

Luo, M. R.

C. Fu, C. Li, G. Cui, M. R. Luo, R. W. G. Hunt, and M. R. Pointer, “An investigation of colour appearance for unrelated colours under photopic and mesopic vision,” Color Res. Appl. 37, 238–254 (2012).
[CrossRef]

M. R. Luo and R. W. G. Hunt, “The structure of the CIE 1997 Colour Appearance Model (CIECAM97s),” Color Res. Appl. 23, 138–146 (1998).
[CrossRef]

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. R. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. Lutchi colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Luque, M. J.

P. Capilla, M. J. Luque, J. Gómez, and A. Palomares, “On saturation and related parameters following Guth’s ATD colour-vision model,” Color Res. Appl. 26, 305–321 (2001).
[CrossRef]

Marrocco, R. T.

S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vis. Res. 9, 537–575 (1969).
[CrossRef]

Melgosa, M.

P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[CrossRef]

Nakano, Y.

Y. Nakano, “A model for brightness perception and its application to individual data,” Jpn. J. Opt. 21, 705–716 (1992).

Nayatani, Y.

Y. Nayatani, “Simple estimation methods for the Helmholtz—Kohlrausch effect,” Color Res. Appl. 22, 385–401 (1997).
[CrossRef]

Palmer, D. A.

D. A. Palmer, “Standard observer for large-field photometry at any level,” J. Opt. Soc. Am. 58, 1296–1298 (1968).
[CrossRef]

Palomares, A.

P. Capilla, M. J. Luque, J. Gómez, and A. Palomares, “On saturation and related parameters following Guth’s ATD colour-vision model,” Color Res. Appl. 26, 305–321 (2001).
[CrossRef]

Pointer, M. R.

C. Fu, C. Li, G. Cui, M. R. Luo, R. W. G. Hunt, and M. R. Pointer, “An investigation of colour appearance for unrelated colours under photopic and mesopic vision,” Color Res. Appl. 37, 238–254 (2012).
[CrossRef]

F. B. Leloup, M. R. Pointer, P. Dutré, and P. Hanselaer, “Luminance-based specular gloss characterization,” J. Opt. Soc. Am. A 28, 1322–1330 (2011).
[CrossRef]

R. W. G. Hunt and M. R. Pointer, Measuring Colour, 4th ed., Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2011).

Rhodes, P. A.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. R. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. Lutchi colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Sagawa, K.

K. Sagawa and K. Takeichi, “System of mesopic photometry for evaluating lights in terms of comparative brightness relationships,” J. Opt. Soc. Am. A 9, 1240–1246 (1992).
[CrossRef]

Sanders, C. L.

C. L. Sanders and G. Wyszecki, “Correlate for brightness in terms of CIE color matching data,” in CIE Proceedings 15th Session (CIE Central Bureau, 1963).

Schappo, A.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. R. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. Lutchi colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Scrivener, S. A. R.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. R. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. Lutchi colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Stevens, S. S.

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
[CrossRef]

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science, 2nd ed. (Wiley, 1982), p. 410.

Tait, C. J.

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. R. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. Lutchi colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Takeichi, K.

K. Sagawa and K. Takeichi, “System of mesopic photometry for evaluating lights in terms of comparative brightness relationships,” J. Opt. Soc. Am. A 9, 1240–1246 (1992).
[CrossRef]

Torgerson, W. S.

W. S. Torgerson, Theory and Methods of Scaling (Wiley, 1958).

Wagner, G.

G. Wagner and R. M. Boynton, “Comparison of four methods of heterochromatic photometry,” J. Opt. Soc. Am. 62, 1508–1515 (1972).
[CrossRef]

Wyszecki, G.

P. K. Kaiser and G. Wyszecki, “Additivity failures in heterochromatic brightness matching,” Color Res. Appl. 3, 177–182 (1978).
[CrossRef]

G. Wyszecki and W. S. Stiles, Color Science, 2nd ed. (Wiley, 1982), p. 410.

C. L. Sanders and G. Wyszecki, “Correlate for brightness in terms of CIE color matching data,” in CIE Proceedings 15th Session (CIE Central Bureau, 1963).

Yaguchi, H.

H. Yaguchi and M. Ikeda, “Subadditivity and superadditivity in heterochromatic brightness matching,” Vis. Res. 23, 1711–1718 (1983).
[CrossRef]

Annual Rev. Psych. (1)

G. A. Gescheider, “Psychophysical scaling,” Annual Rev. Psych. 39, 169–200 (1988).
[CrossRef]

Color Res. Appl. (7)

C. Fu, C. Li, G. Cui, M. R. Luo, R. W. G. Hunt, and M. R. Pointer, “An investigation of colour appearance for unrelated colours under photopic and mesopic vision,” Color Res. Appl. 37, 238–254 (2012).
[CrossRef]

M. R. Luo and R. W. G. Hunt, “The structure of the CIE 1997 Colour Appearance Model (CIECAM97s),” Color Res. Appl. 23, 138–146 (1998).
[CrossRef]

P. Capilla, M. J. Luque, J. Gómez, and A. Palomares, “On saturation and related parameters following Guth’s ATD colour-vision model,” Color Res. Appl. 26, 305–321 (2001).
[CrossRef]

M. R. Luo, A. A. Clarke, P. A. Rhodes, A. Schappo, S. A. R. Scrivener, and C. J. Tait, “Quantifying colour appearance. Part I. Lutchi colour appearance data,” Color Res. Appl. 16, 166–180 (1991).
[CrossRef]

Y. Nayatani, “Simple estimation methods for the Helmholtz—Kohlrausch effect,” Color Res. Appl. 22, 385–401 (1997).
[CrossRef]

P. K. Kaiser and G. Wyszecki, “Additivity failures in heterochromatic brightness matching,” Color Res. Appl. 3, 177–182 (1978).
[CrossRef]

R. W. G. Hunt, “Revised colour-appearance model for related and unrelated colours,” Color Res. Appl. 16, 146–165 (1991).
[CrossRef]

J. Opt. Soc. Am. (3)

G. Wagner and R. M. Boynton, “Comparison of four methods of heterochromatic photometry,” J. Opt. Soc. Am. 62, 1508–1515 (1972).
[CrossRef]

S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity, and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
[CrossRef]

D. A. Palmer, “Standard observer for large-field photometry at any level,” J. Opt. Soc. Am. 58, 1296–1298 (1968).
[CrossRef]

J. Opt. Soc. Am. A (3)

P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[CrossRef]

F. B. Leloup, M. R. Pointer, P. Dutré, and P. Hanselaer, “Luminance-based specular gloss characterization,” J. Opt. Soc. Am. A 28, 1322–1330 (2011).
[CrossRef]

K. Sagawa and K. Takeichi, “System of mesopic photometry for evaluating lights in terms of comparative brightness relationships,” J. Opt. Soc. Am. A 9, 1240–1246 (1992).
[CrossRef]

Jpn. J. Opt. (1)

Y. Nakano, “A model for brightness perception and its application to individual data,” Jpn. J. Opt. 21, 705–716 (1992).

Proc. SPIE (1)

S. L. Guth, “ATD01 model for color appearances, color differences and chromatic adaptation,” Proc. SPIE 4421, 303–3062002).
[CrossRef]

Psychol. Rev. (1)

S. S. Stevens, “On the psychophysical law,” Psychol. Rev. 64, 153–181 (1957).
[CrossRef]

Science (1)

R. M. Boynton and P. K. Kaiser, “Vision: the additivity law made to work for heterochromatic photometry with bipartite fields,” Science 161, 366–368 (1968).
[CrossRef]

Vis. Res. (2)

H. Yaguchi and M. Ikeda, “Subadditivity and superadditivity in heterochromatic brightness matching,” Vis. Res. 23, 1711–1718 (1983).
[CrossRef]

S. L. Guth, N. J. Donley, and R. T. Marrocco, “On luminance additivity and related topics,” Vis. Res. 9, 537–575 (1969).
[CrossRef]

Other (14)

M. D. Fairchild, Color Appearance Models, 2nd ed., Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2005).

R. W. G. Hunt and M. R. Pointer, Measuring Colour, 4th ed., Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2011).

CIE, International Lighting Vocabulary (CIE Central Bureau, 2011).

C. L. Sanders and G. Wyszecki, “Correlate for brightness in terms of CIE color matching data,” in CIE Proceedings 15th Session (CIE Central Bureau, 1963).

CIE, Supplementary System of Photometry (CIE Central Bureau, 2011).

CIE, Testing of Supplementary Systems of Photometry (CIE Central Bureau, 2001).

G. Wyszecki and W. S. Stiles, Color Science, 2nd ed. (Wiley, 1982), p. 410.

CIE, A Colour Appearance Model for Colour Management Systems: CIECAM02 (CIE Central Bureau, 2004).

R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain, 1998), pp. 239–246.

A. Field, Discovering Statistics Using SPSS, 3rd ed. (SAGE, 2009).

CIE, Colorimetry (CIE Central Bureau, 2004).

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

W. S. Torgerson, Theory and Methods of Scaling (Wiley, 1958).

ASTM International, ASTM Standard E1697-05(2012)e1, “Standard Test Method for Unipolar Magnitude Estimation of Sensory Attributes” (ASTM International, 2012).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Experimental room and (b) example of a stimulus under dark viewing conditions.

Fig. 2.
Fig. 2.

Chromaticity coordinates of the 58 stimuli plotted in the CIE 1976 u10, v10 chromaticity diagram.

Fig. 3.
Fig. 3.

Average observer brightness (Qgeom) with SE error bars, calculated for each individual stimulus from all observer answers, plotted against the CIE 1976 u10, v10saturation (suv,10) of the stimuli with the yellow, green, blue, and red stimuli highlighted.

Fig. 4.
Fig. 4.

Average observer brightness (Qgeom) with SE error bars plotted against the brightness predictions of (a) CAM97u, (b) ATD01, and (c) CAMFu and the predictions of the equivalent luminance of Nayatani [VAC (d) and VCC (e)], and (f) CIE. The blue, green, red, and yellow stimuli are highlighted.

Fig. 5.
Fig. 5.

Average observer brightness (Qgeom) with SE error bars plotted against the colorfulness predictions of CAM97u. The blue, green, red, and yellow stimuli are highlighted.

Tables (3)

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Table 1. Evaluation of Inter-observer Agreement by Calculation of the Coefficient of Variation (CV)

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Table 2. Values of the Geometric Mean of the Observer Brightness (Qgeom), CIE 1976 u10, v10 Saturation (suv,10), and CIE 1976 u10, v10 Hue-Angle (huv,10) of All the 58 Stimuli Ordered by Hue

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Table 3. Overview of the Correlation between the Average Brightness Data of the Observers and the Predictions of the Vision Models Together with the One-Way ANOVA of the 11 Hue Series

Equations (9)

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QCAM97u=[(1.1)(ACAM97u+MCAM97u100)]0.9,
QATD=(A2+T2+D2)0.5.
QCAMFu=ACAMFu+MCAMFu100,
γVAC=Leq,Nay(VAC)L=0.4462[1+{0.1340q(θ)+0.0872KBr(La)}suv(x,y)+0.3086]3,
γVCC=Leq,Nay(VCC)L=0.4462[1+{0.8660q(θ)+0.0872KBr(La)}suv(x,y)+0.3086]3.
Leq,CIE=(L)a.(L)1a.10c.
CV=1001ni=1n(Qgeom,ifQobs,i)2Q¯geom2withf=i=1nQgeom,iQobs,ii=1nQobs,i2.
huv,10=arctan[v10vn,10u10un,10],
suv,10=13[(u10un,10)2+(v10vn,10)2]12,

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