Abstract

We present a systematic algorithm capable of searching for optimal colors for any lightness L* (between 0 and 100), any illuminant (D65, F2, F7, F11, etc.), and any light source reported by CIE. Color solids are graphed in some color spaces (CIELAB, SVF, DIN99d, and CIECAM02) by horizontal (constant lightness) and transversal (constant hue angle) sections. Color solids plotted in DIN99d and CIECAM02 color spaces look more spherical or homogeneous than the ones plotted in CIELAB and SVF color spaces. Depending on the spectrum of the light source or illuminant, the shape of its color solid and its content (variety of distinguishable colors, with or without color correspondence) change drastically, particularly with sources whose spectrum is discontinuous and/or very peaked, with correlated color temperature lower than 5500K. This could be used to propose an absolute colorimetric quality index for light sources comparing the volumes of their gamuts, in a uniform color space.

© 2007 Optical Society of America

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References

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  1. R. G. Kuehni, Color Space and Its Divisions: Color Order from Antiquity to the Present (Wiley, 2003).
  2. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 179-184.
  3. R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).
  4. D. L. MacAdam, "Maximum visual efficiency of colored materials," J. Opt. Soc. Am. 25, 316-367 (1935).
  5. D. L. MacAdam, "Theory of the maximum visual efficiency of colored materials," J. Opt. Soc. Am. 25, 249-252 (1935).
    [CrossRef]
  6. E. Schrödinger, "Theorie der Pigmente von grösster Leuchtkraft," Ann. Phys. 62, 603-622 (1920).
    [CrossRef]
  7. S. Rösch, "Fortschritte der Mineral," Kristallogr. Petrogr. 13, 143 (1929).
  8. R. G. Kuehni, Color Space and Its Divisions: Color Order from Antiquity to the Present (Wiley, 2003), pp. 91, 359.
  9. R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000), pp. 62, 143.
  10. R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Wiley, 2004), pp. 88-90.
  11. T. Seim and A. Valberg, "Towards a uniform color space: a better formula to describe the Munsell and OSA color scales," Color Res. Appl. 11, 11-24 (1986).
    [CrossRef]
  12. G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, "Uniform colour spaces based on the DIN99 colour-difference formula," Color Res. Appl. 27, 282-290 (2002).
    [CrossRef]
  13. CIE, A Colour Appearance Model for Colour Management Systems: CIECAM02, CIE 159:2004 (Commission Internationale de l'Eclairage, 2004).
  14. M. R. Pointer, "The gamut of real surface colours," Color Res. Appl. 5, 145-155 (1980).
    [CrossRef]
  15. M. R. Pointer, "Request for real surface colours," Color Res. Appl. 27, 374 (2002).
    [CrossRef]
  16. N. Ohta and A. Robertson, Colorimetry: Fundamentals and Applications (Wiley, 2005), pp. 215.
  17. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 725-735.
  18. CIE, Recommended Practice for Tabulating Spectral Data for Use in Colour Computations, CIE 167:2005 (Commission Internationale de l'Eclairage, 2005).
  19. CIE, Colorimetry, 3rd ed., CIE 15:2004 (Commission Internationale de l'Eclairage, 2004).
  20. CIE, Method of Measuring and Specifying Colour Rendering Properties of Light Sources, CIE 13.3:1995 (Commission Internationale de l'Eclairage, 1995).
  21. CIE, CIE Collection 1999, Vision and Colour, Physical Measurement of Light and Radiation, Research Note: Colour Rendering, TC 1-33 Closing Remarks, CIE 135/2:1999 (Commission Internationale de l'Eclairage, 1999).
    [PubMed]
  22. C. van Trigt, "Color rendering, a reassessment," Color Res. Appl. 24, 197-206 (1999).
    [CrossRef]
  23. J. A. Worthey, "Color rendering: asking the question," Color Res. Appl. 28, 403-412 (2003).
    [CrossRef]
  24. D. B. Judd and G. Wyszecki, Color in Business, Science, and Industry, 3rd ed. (Wiley, 1975), pp. 267.
  25. R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Wiley, 2004), pp. 162-163.
  26. R. G. Kuehni, Color Space and Its Divisions: Color Order from Antiquity to the Present (Wiley, 2003), pp. 202.
  27. S. D. Hordley and G. D. Finlayson, "Reevaluation of color constancy algorithm performance," J. Opt. Soc. Am. A 23, 1008-1020 (2006).
    [CrossRef]
  28. A. Lewis and L. Zhaoping, "Are cone sensitivities determined by natural color statistics?" J. Vision 6, 285-302 (2006).
    [CrossRef]
  29. Y. Nayatani, "Development of chromatic adaptation transforms and concept for their classification," Color Res. Appl. 31, 205-217 (2006).
    [CrossRef]
  30. S. D. Hordley, "Scene illuminant estimation: past, present, and future," Color Res. Appl. 31, 303-314 (2006).
    [CrossRef]
  31. D. H. Brainard, P. Longère, P. B. Delahunt, W. T. Freeman, J. M. Kraft, and V. Xiao, "Bayesian model of human color constancy," J. Vision 6, 1267-1281 (2006).
    [CrossRef]
  32. E. Perales, F. Martínez-Verdú, V. Viqueira, M. J. Luque, and P. Capilla, "Computing the number of distinguishable colors under several illuminants and light sources," in Proceedings of Third IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 414-419.
  33. J. Krauskopf, "Higher order color mechanisms," in Color Vision: From Genes to Perception, K.R.Gegenfurtner and L.T.Sharpe, eds. (Cambridge U. Press, 1999), pp. 310.
  34. U. Steingrímsson, K. Simon, W. Steiger, and K. Schläpfer, "The gamut obtainable with surface colors," in Proceedings of First IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2002), pp. 287-291.
  35. CIE, Criteria for the Evaluation of Extended-Gamut Colour Encodings, CIE 168:2005 (Commission Internationale de l'Eclairage, 2005).
  36. F. Martínez-Verdú, M. J. Luque, P. Capilla, and J. Pujol, "Concerning the calculation of the color gamut in a digital camera," Color Res. Appl. 31, 399-410 (2006).
    [CrossRef]

2006 (6)

A. Lewis and L. Zhaoping, "Are cone sensitivities determined by natural color statistics?" J. Vision 6, 285-302 (2006).
[CrossRef]

Y. Nayatani, "Development of chromatic adaptation transforms and concept for their classification," Color Res. Appl. 31, 205-217 (2006).
[CrossRef]

S. D. Hordley, "Scene illuminant estimation: past, present, and future," Color Res. Appl. 31, 303-314 (2006).
[CrossRef]

D. H. Brainard, P. Longère, P. B. Delahunt, W. T. Freeman, J. M. Kraft, and V. Xiao, "Bayesian model of human color constancy," J. Vision 6, 1267-1281 (2006).
[CrossRef]

F. Martínez-Verdú, M. J. Luque, P. Capilla, and J. Pujol, "Concerning the calculation of the color gamut in a digital camera," Color Res. Appl. 31, 399-410 (2006).
[CrossRef]

S. D. Hordley and G. D. Finlayson, "Reevaluation of color constancy algorithm performance," J. Opt. Soc. Am. A 23, 1008-1020 (2006).
[CrossRef]

2003 (1)

J. A. Worthey, "Color rendering: asking the question," Color Res. Appl. 28, 403-412 (2003).
[CrossRef]

2002 (2)

M. R. Pointer, "Request for real surface colours," Color Res. Appl. 27, 374 (2002).
[CrossRef]

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, "Uniform colour spaces based on the DIN99 colour-difference formula," Color Res. Appl. 27, 282-290 (2002).
[CrossRef]

1999 (1)

C. van Trigt, "Color rendering, a reassessment," Color Res. Appl. 24, 197-206 (1999).
[CrossRef]

1986 (1)

T. Seim and A. Valberg, "Towards a uniform color space: a better formula to describe the Munsell and OSA color scales," Color Res. Appl. 11, 11-24 (1986).
[CrossRef]

1980 (1)

M. R. Pointer, "The gamut of real surface colours," Color Res. Appl. 5, 145-155 (1980).
[CrossRef]

1935 (2)

D. L. MacAdam, "Maximum visual efficiency of colored materials," J. Opt. Soc. Am. 25, 316-367 (1935).

D. L. MacAdam, "Theory of the maximum visual efficiency of colored materials," J. Opt. Soc. Am. 25, 249-252 (1935).
[CrossRef]

1929 (1)

S. Rösch, "Fortschritte der Mineral," Kristallogr. Petrogr. 13, 143 (1929).

1920 (1)

E. Schrödinger, "Theorie der Pigmente von grösster Leuchtkraft," Ann. Phys. 62, 603-622 (1920).
[CrossRef]

Berns, R. S.

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000), pp. 62, 143.

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).

Brainard, D. H.

D. H. Brainard, P. Longère, P. B. Delahunt, W. T. Freeman, J. M. Kraft, and V. Xiao, "Bayesian model of human color constancy," J. Vision 6, 1267-1281 (2006).
[CrossRef]

Capilla, P.

F. Martínez-Verdú, M. J. Luque, P. Capilla, and J. Pujol, "Concerning the calculation of the color gamut in a digital camera," Color Res. Appl. 31, 399-410 (2006).
[CrossRef]

E. Perales, F. Martínez-Verdú, V. Viqueira, M. J. Luque, and P. Capilla, "Computing the number of distinguishable colors under several illuminants and light sources," in Proceedings of Third IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 414-419.

Cui, G.

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, "Uniform colour spaces based on the DIN99 colour-difference formula," Color Res. Appl. 27, 282-290 (2002).
[CrossRef]

Delahunt, P. B.

D. H. Brainard, P. Longère, P. B. Delahunt, W. T. Freeman, J. M. Kraft, and V. Xiao, "Bayesian model of human color constancy," J. Vision 6, 1267-1281 (2006).
[CrossRef]

Finlayson, G. D.

Freeman, W. T.

D. H. Brainard, P. Longère, P. B. Delahunt, W. T. Freeman, J. M. Kraft, and V. Xiao, "Bayesian model of human color constancy," J. Vision 6, 1267-1281 (2006).
[CrossRef]

Hordley, S. D.

S. D. Hordley and G. D. Finlayson, "Reevaluation of color constancy algorithm performance," J. Opt. Soc. Am. A 23, 1008-1020 (2006).
[CrossRef]

S. D. Hordley, "Scene illuminant estimation: past, present, and future," Color Res. Appl. 31, 303-314 (2006).
[CrossRef]

Hunt, R. W. G.

R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Wiley, 2004), pp. 88-90.

R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Wiley, 2004), pp. 162-163.

Judd, D. B.

D. B. Judd and G. Wyszecki, Color in Business, Science, and Industry, 3rd ed. (Wiley, 1975), pp. 267.

Kraft, J. M.

D. H. Brainard, P. Longère, P. B. Delahunt, W. T. Freeman, J. M. Kraft, and V. Xiao, "Bayesian model of human color constancy," J. Vision 6, 1267-1281 (2006).
[CrossRef]

Krauskopf, J.

J. Krauskopf, "Higher order color mechanisms," in Color Vision: From Genes to Perception, K.R.Gegenfurtner and L.T.Sharpe, eds. (Cambridge U. Press, 1999), pp. 310.

Kuehni, R. G.

R. G. Kuehni, Color Space and Its Divisions: Color Order from Antiquity to the Present (Wiley, 2003), pp. 91, 359.

R. G. Kuehni, Color Space and Its Divisions: Color Order from Antiquity to the Present (Wiley, 2003).

R. G. Kuehni, Color Space and Its Divisions: Color Order from Antiquity to the Present (Wiley, 2003), pp. 202.

Lewis, A.

A. Lewis and L. Zhaoping, "Are cone sensitivities determined by natural color statistics?" J. Vision 6, 285-302 (2006).
[CrossRef]

Longère, P.

D. H. Brainard, P. Longère, P. B. Delahunt, W. T. Freeman, J. M. Kraft, and V. Xiao, "Bayesian model of human color constancy," J. Vision 6, 1267-1281 (2006).
[CrossRef]

Luo, M. R.

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, "Uniform colour spaces based on the DIN99 colour-difference formula," Color Res. Appl. 27, 282-290 (2002).
[CrossRef]

Luque, M. J.

F. Martínez-Verdú, M. J. Luque, P. Capilla, and J. Pujol, "Concerning the calculation of the color gamut in a digital camera," Color Res. Appl. 31, 399-410 (2006).
[CrossRef]

E. Perales, F. Martínez-Verdú, V. Viqueira, M. J. Luque, and P. Capilla, "Computing the number of distinguishable colors under several illuminants and light sources," in Proceedings of Third IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 414-419.

MacAdam, D. L.

D. L. MacAdam, "Maximum visual efficiency of colored materials," J. Opt. Soc. Am. 25, 316-367 (1935).

D. L. MacAdam, "Theory of the maximum visual efficiency of colored materials," J. Opt. Soc. Am. 25, 249-252 (1935).
[CrossRef]

Martínez-Verdú, F.

F. Martínez-Verdú, M. J. Luque, P. Capilla, and J. Pujol, "Concerning the calculation of the color gamut in a digital camera," Color Res. Appl. 31, 399-410 (2006).
[CrossRef]

E. Perales, F. Martínez-Verdú, V. Viqueira, M. J. Luque, and P. Capilla, "Computing the number of distinguishable colors under several illuminants and light sources," in Proceedings of Third IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 414-419.

Nayatani, Y.

Y. Nayatani, "Development of chromatic adaptation transforms and concept for their classification," Color Res. Appl. 31, 205-217 (2006).
[CrossRef]

Ohta, N.

N. Ohta and A. Robertson, Colorimetry: Fundamentals and Applications (Wiley, 2005), pp. 215.

Perales, E.

E. Perales, F. Martínez-Verdú, V. Viqueira, M. J. Luque, and P. Capilla, "Computing the number of distinguishable colors under several illuminants and light sources," in Proceedings of Third IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 414-419.

Pointer, M. R.

M. R. Pointer, "Request for real surface colours," Color Res. Appl. 27, 374 (2002).
[CrossRef]

M. R. Pointer, "The gamut of real surface colours," Color Res. Appl. 5, 145-155 (1980).
[CrossRef]

Pujol, J.

F. Martínez-Verdú, M. J. Luque, P. Capilla, and J. Pujol, "Concerning the calculation of the color gamut in a digital camera," Color Res. Appl. 31, 399-410 (2006).
[CrossRef]

Rigg, B.

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, "Uniform colour spaces based on the DIN99 colour-difference formula," Color Res. Appl. 27, 282-290 (2002).
[CrossRef]

Robertson, A.

N. Ohta and A. Robertson, Colorimetry: Fundamentals and Applications (Wiley, 2005), pp. 215.

Roesler, G.

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, "Uniform colour spaces based on the DIN99 colour-difference formula," Color Res. Appl. 27, 282-290 (2002).
[CrossRef]

Rösch, S.

S. Rösch, "Fortschritte der Mineral," Kristallogr. Petrogr. 13, 143 (1929).

Schläpfer, K.

U. Steingrímsson, K. Simon, W. Steiger, and K. Schläpfer, "The gamut obtainable with surface colors," in Proceedings of First IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2002), pp. 287-291.

Schrödinger, E.

E. Schrödinger, "Theorie der Pigmente von grösster Leuchtkraft," Ann. Phys. 62, 603-622 (1920).
[CrossRef]

Seim, T.

T. Seim and A. Valberg, "Towards a uniform color space: a better formula to describe the Munsell and OSA color scales," Color Res. Appl. 11, 11-24 (1986).
[CrossRef]

Simon, K.

U. Steingrímsson, K. Simon, W. Steiger, and K. Schläpfer, "The gamut obtainable with surface colors," in Proceedings of First IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2002), pp. 287-291.

Steiger, W.

U. Steingrímsson, K. Simon, W. Steiger, and K. Schläpfer, "The gamut obtainable with surface colors," in Proceedings of First IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2002), pp. 287-291.

Steingrímsson, U.

U. Steingrímsson, K. Simon, W. Steiger, and K. Schläpfer, "The gamut obtainable with surface colors," in Proceedings of First IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2002), pp. 287-291.

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 179-184.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 725-735.

Valberg, A.

T. Seim and A. Valberg, "Towards a uniform color space: a better formula to describe the Munsell and OSA color scales," Color Res. Appl. 11, 11-24 (1986).
[CrossRef]

van Trigt, C.

C. van Trigt, "Color rendering, a reassessment," Color Res. Appl. 24, 197-206 (1999).
[CrossRef]

Viqueira, V.

E. Perales, F. Martínez-Verdú, V. Viqueira, M. J. Luque, and P. Capilla, "Computing the number of distinguishable colors under several illuminants and light sources," in Proceedings of Third IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 414-419.

Witt, K.

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, "Uniform colour spaces based on the DIN99 colour-difference formula," Color Res. Appl. 27, 282-290 (2002).
[CrossRef]

Worthey, J. A.

J. A. Worthey, "Color rendering: asking the question," Color Res. Appl. 28, 403-412 (2003).
[CrossRef]

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 179-184.

D. B. Judd and G. Wyszecki, Color in Business, Science, and Industry, 3rd ed. (Wiley, 1975), pp. 267.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 725-735.

Xiao, V.

D. H. Brainard, P. Longère, P. B. Delahunt, W. T. Freeman, J. M. Kraft, and V. Xiao, "Bayesian model of human color constancy," J. Vision 6, 1267-1281 (2006).
[CrossRef]

Zhaoping, L.

A. Lewis and L. Zhaoping, "Are cone sensitivities determined by natural color statistics?" J. Vision 6, 285-302 (2006).
[CrossRef]

Ann. Phys. (1)

E. Schrödinger, "Theorie der Pigmente von grösster Leuchtkraft," Ann. Phys. 62, 603-622 (1920).
[CrossRef]

Color Res. Appl. (9)

C. van Trigt, "Color rendering, a reassessment," Color Res. Appl. 24, 197-206 (1999).
[CrossRef]

J. A. Worthey, "Color rendering: asking the question," Color Res. Appl. 28, 403-412 (2003).
[CrossRef]

M. R. Pointer, "The gamut of real surface colours," Color Res. Appl. 5, 145-155 (1980).
[CrossRef]

M. R. Pointer, "Request for real surface colours," Color Res. Appl. 27, 374 (2002).
[CrossRef]

Y. Nayatani, "Development of chromatic adaptation transforms and concept for their classification," Color Res. Appl. 31, 205-217 (2006).
[CrossRef]

S. D. Hordley, "Scene illuminant estimation: past, present, and future," Color Res. Appl. 31, 303-314 (2006).
[CrossRef]

F. Martínez-Verdú, M. J. Luque, P. Capilla, and J. Pujol, "Concerning the calculation of the color gamut in a digital camera," Color Res. Appl. 31, 399-410 (2006).
[CrossRef]

T. Seim and A. Valberg, "Towards a uniform color space: a better formula to describe the Munsell and OSA color scales," Color Res. Appl. 11, 11-24 (1986).
[CrossRef]

G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, "Uniform colour spaces based on the DIN99 colour-difference formula," Color Res. Appl. 27, 282-290 (2002).
[CrossRef]

J. Opt. Soc. Am. (2)

D. L. MacAdam, "Maximum visual efficiency of colored materials," J. Opt. Soc. Am. 25, 316-367 (1935).

D. L. MacAdam, "Theory of the maximum visual efficiency of colored materials," J. Opt. Soc. Am. 25, 249-252 (1935).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Vision (2)

A. Lewis and L. Zhaoping, "Are cone sensitivities determined by natural color statistics?" J. Vision 6, 285-302 (2006).
[CrossRef]

D. H. Brainard, P. Longère, P. B. Delahunt, W. T. Freeman, J. M. Kraft, and V. Xiao, "Bayesian model of human color constancy," J. Vision 6, 1267-1281 (2006).
[CrossRef]

Kristallogr. Petrogr. (1)

S. Rösch, "Fortschritte der Mineral," Kristallogr. Petrogr. 13, 143 (1929).

Other (20)

R. G. Kuehni, Color Space and Its Divisions: Color Order from Antiquity to the Present (Wiley, 2003), pp. 91, 359.

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000), pp. 62, 143.

R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Wiley, 2004), pp. 88-90.

D. B. Judd and G. Wyszecki, Color in Business, Science, and Industry, 3rd ed. (Wiley, 1975), pp. 267.

R. W. G. Hunt, The Reproduction of Colour, 6th ed. (Wiley, 2004), pp. 162-163.

R. G. Kuehni, Color Space and Its Divisions: Color Order from Antiquity to the Present (Wiley, 2003), pp. 202.

N. Ohta and A. Robertson, Colorimetry: Fundamentals and Applications (Wiley, 2005), pp. 215.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 725-735.

CIE, Recommended Practice for Tabulating Spectral Data for Use in Colour Computations, CIE 167:2005 (Commission Internationale de l'Eclairage, 2005).

CIE, Colorimetry, 3rd ed., CIE 15:2004 (Commission Internationale de l'Eclairage, 2004).

CIE, Method of Measuring and Specifying Colour Rendering Properties of Light Sources, CIE 13.3:1995 (Commission Internationale de l'Eclairage, 1995).

CIE, CIE Collection 1999, Vision and Colour, Physical Measurement of Light and Radiation, Research Note: Colour Rendering, TC 1-33 Closing Remarks, CIE 135/2:1999 (Commission Internationale de l'Eclairage, 1999).
[PubMed]

E. Perales, F. Martínez-Verdú, V. Viqueira, M. J. Luque, and P. Capilla, "Computing the number of distinguishable colors under several illuminants and light sources," in Proceedings of Third IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 414-419.

J. Krauskopf, "Higher order color mechanisms," in Color Vision: From Genes to Perception, K.R.Gegenfurtner and L.T.Sharpe, eds. (Cambridge U. Press, 1999), pp. 310.

U. Steingrímsson, K. Simon, W. Steiger, and K. Schläpfer, "The gamut obtainable with surface colors," in Proceedings of First IS&T European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2002), pp. 287-291.

CIE, Criteria for the Evaluation of Extended-Gamut Colour Encodings, CIE 168:2005 (Commission Internationale de l'Eclairage, 2005).

R. G. Kuehni, Color Space and Its Divisions: Color Order from Antiquity to the Present (Wiley, 2003).

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 179-184.

R. S. Berns, Billmeyer and Saltzman's Principles of Color Technology, 3rd ed. (Wiley, 2000).

CIE, A Colour Appearance Model for Colour Management Systems: CIECAM02, CIE 159:2004 (Commission Internationale de l'Eclairage, 2004).

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Figures (14)

Fig. 1
Fig. 1

Six examples of optimal colors (left: type 1; right: type 2) with luminance factor Y = 20 % under illuminant E and the CIE 1931 X Y Z standard observer. The transition wavelengths λ 1 and λ 2 are, from left to right, as follows: 412.1–525.2, 540.0–562.0, 594.0–654.7, 428.0–596.0, 517.1–628.0, and 524.0 660.1 nm .

Fig. 2
Fig. 2

Scheme of our algorithm in column format. See text for more detail.

Fig. 3
Fig. 3

General diagram for obtaining the color solid in several color spaces.

Fig. 4
Fig. 4

Rösch–MacAdam color solid in the CIE- L * a * b * color space under the illuminant D65.

Fig. 5
Fig. 5

Effect of the luminance factor Y over the (calculated optimal color) symbol sampling of the MacAdam loci: the smaller MacAdam loci correspond to L * = 1 and L * = 98 , while the larger one corresponds to L * = 50 . It was clearly seen that in the larger locus the yellow–red quadrant is partially sampled, particularly for the red hues.

Fig. 6
Fig. 6

Rösch–MacAdam color solid in the CIE- L * a * b * color space under three fluorescent illuminants: F2 (left), F7 (center), and F11 (right).

Fig. 7
Fig. 7

Rösch–MacAdam color solid in the CIE- L * a * b * color space under three real lamps: HP1 (left), HP2 (center), and HP3 (right).

Fig. 8
Fig. 8

Rösch–MacAdam color solids for the CIE 1931 standard observer under the illuminant D65 in different perceptual color spaces: SVF (left), DIN99d (center), and CIECAM02 (right).

Fig. 9
Fig. 9

Rösch–MacAdam color solid under the illuminants D65 (left) and F11 (center) and the real lamp HP1 (right) in the color spaces CIE- L * a * b * , SVF, DIN99d, and CIECAM02. Sixty hue profiles have been taken to avoid aliasing.

Fig. 10
Fig. 10

Constant hue-angle profiles of the Rösch–MacAdam color solid under several illuminants in the CIE- L * a * b * ( C a b * , L * ) diagram (illuminant F11: solid curve; HP1: dashed curve; E: dotted curve; and D65: dashed–dotted–dotted curve).

Fig. 11
Fig. 11

Constant hue-angle profiles of the Rösch–MacAdam color solid under several illuminants in the CIECAM02 ( M , J ) diagram (illuminant F11: solid curve; HP1: dashed curve; E: dotted curve; and D65: dashed–dotted–dotted curve).

Fig. 12
Fig. 12

Top view of some color solids under several illuminants–lamps in the CIECAM02 color space with different chromatic adaptation degrees (left: D = 1 ; right: D = 0 ). (The MacAdam locus with the solid curve corresponds to the highest constant lightness plane.)

Fig. 13
Fig. 13

Top view of several color solids under several illuminants/lamps, with the same color correspondence to illuminant D65, in the DIN99d color space. From top to bottom and from left to right: lamp HP1 ( T C = 1960 K ) , illuminant A ( T C = 2856 K ) , illuminant F11 ( T C = 4000 K ) , illuminant E ( T C = 5500 K ) , illuminant D65 ( T C = 6500 K ) , and illuminant D100 ( T C = 10,000 K ) . (The MacAdam locus with the solid curve corresponds to the lowest constant lightness plane.)

Fig. 14
Fig. 14

Constant hue-angle profiles of the Rösch–MacAdam color solid under several illuminants, with the same color correspondence to illuminant D65, in the DIN99d ( C 99 , L 99 ) diagram (illuminant F11: solid curve; HP1: short-dashed curve; D65: dotted curve; A: dashed–dotted–dotted curve; and D100: long-dashed curve).

Tables (2)

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Table 1 Comparison between the Sampling of Optimal Colors, Using the Illuminant C and the CIE 1931 Standard Observer with the Same Spectral Sampling ( Δ λ = 0.1 nm ) , Obtained with MacAdam’s Algorithm[4] and Our Algorithm

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Table 2 Total Number of the Distinguishable Colors under Several Illuminants and Light Sources according to Several Packing Methods of Constant Lightness MacAdam Loci

Equations (4)

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L * = { 903.3 Y Y n , if Y Y n 0.008856 116 ( Y Y n ) 1 3 16 , if Y Y n > 0.008856 } ,
Δ Y = { 100 903.3 Δ L * , if Y ( % ) 0.8856 100 [ ( Δ L * 116 + ( Y 100 ) 1 3 ) 3 Y 100 ] , if Y ( % ) > 0.8856 } .
Type 1 : Y = 100 y ¯ S k = i j y ¯ ( λ k ) S ( λ k ) [ Y 0 Δ Y , Y 0 + Δ Y ] ,
Type 2 : Y = 100 y ¯ S ( k = 1 i y ¯ ( λ k ) S ( λ k ) + k = j N y ¯ ( λ k ) S ( λ k ) ) [ Y 0 Δ Y , Y 0 + Δ Y ] ,

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