Abstract

Recently there has been great interest in establishing the color gamut of solid colors or the optimum colors. The optimum colors are widely used for quantifying the quality of light sources and evaluating reproduction devices. An enumeration method was developed by Martinez-Verdu et al. [J. Opt. Soc. Am. A 24, 1501 (2007)] for finding optimum colors. However, it was found that the method is too time-costly. In this paper, a linear programming approach is proposed. The proposed method is simple and faster and has the advantage of keeping the characteristics of the true boundary. Comparison of the present method with the method of Martinez-Verdu et al. is also given.

© 2010 Optical Society of America

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  1. D. L. MacAdam, “The theory of the maximum visual efficiency of colored materials,” J. Opt. Soc. Am. 25, 249-252 (1935).
    [CrossRef]
  2. D. L. MacAdam, “Maximum visual efficiency of colored materials,” J. Opt. Soc. Am. 25, 316-367 (1935).
  3. G. Wyszeki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, 1982), pp. 179-184.
  4. F. Martinez-Verdu, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. A 24, 1501-1515 (2007).
    [CrossRef]
  5. ISO 10527:2007(E), CIE S 014-1/E: 2006, Colorimetry Part 1: CIE Standard Colorimetric Observers, CIE Central Bureau, Kegelgasse 27, A-1030 Vienna, Austria (2006).
  6. CIE Publication 15, Colorimetry, 3rd ed. (2004).
  7. CIE Publication 159, A colour appearance model for colour management systems, CIECAM02 (2004).
  8. G. Cui, M. R. Luo, B. Rigg, G. Roesler, and K. Witt, “Uniform colour spaces based on the DIN99 colour appearance formula,” Color Res. Appl. 27, 282-290 (2002).
    [CrossRef]
  9. E. Perales, F. Martinez-Verdu, V. Viqueira, M. J. Luque, and P. Capilla, “Computing the number of distinguishable colours under several illuminants and light sources,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 414-419.
  10. E. Perales, F. Martinez-Verdu, and V. Viqueira, “New contribution for the revision of colour rendering for light sources based on the colour gamut volume,” in Proceedings of the Ciencia y Tecnología del Color, Seminario 2007 de la Red Temática, J.Campos and R.Huertas, eds. (Red Temática, Ciencia y Tecnología del Color, 2007), pp. 43-46.
  11. E. Perales, F. Martinez-Verdu, V. Viqueira, “Calculation of number of distinguishable colors by real normal observers,” in Proceedings of IS&T 4th European Conference on Colors in Graphics, Imaging and Vision (CGIV, 2008), pp. 80-84.
  12. P. W. Trezona, “Individual observer data for the 1955 Stiles-Burch 2° pilot investigation,” J. Opt. Soc. Am. A 4, 769-782 (1987).
    [CrossRef] [PubMed]
  13. F. Martinez-Verdu, E. Perales, D. de Fez, and E. Chorro, “Calculation of the optimal colours of linear input devices,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 345-349.
  14. E. Perales, E. Chorro, V. Viqueira, F. Martinez-Verdu, S. Otero, and V. de Gracia, “New method for comparing colour gamut among printing technologies,” Imaging Sci. J. 56, 145-152 (2008).
    [CrossRef]
  15. E. Perales, F. Martinez-Verdu, J. Fernandez-Reche, J. A. Diaz, and J. Uroz, “Comparison of color gamuts among several types of paper with the same printing technology,” Color Res. Appl. 34, 330-336 (2009).
    [CrossRef]
  16. W. Ostwald and F. Birren, The Color Primer: A Basic Treatise on the Color System of Wilhelm Ostwald (Van Nostrand Reinhold, 1969).
  17. E. Schrodinger, “Der Theorie der Pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603-622 (1920).
    [CrossRef]
  18. X. Li, C. J. Li, M. R. Luo, M. R. Pointer, M. Cho, and J. Kim, “A new colour gamut for object colours,” in Proceedings of Fifth Colour Imaging Conference, November 5-9, 2007, Albuquerque, New Mexico, USA (2007).
  19. M. R. Pointer, “The gamut of real surface colours,” Color Res. Appl. 5, 145-155 (1980).
    [CrossRef]
  20. ISO/DIS 12640-3, Graphic technology--Prepress digital data exchange--Part 3: CIELAB standard colour image data (CIELAB/SCID) (2007).
  21. J. Holm, I. Tastl, and T. Johnson, “Definition and use of the ISO 12640-3 reference colour gamut,” in Proceedings of 14th Color Imaging Conference (IS&T/SID, 2006), pp. 62-68.
  22. C. J. Li, M. R. Luo, M. R. Pointer, X. Li, C. Li, and W. Ji, “A new method for quantifying colour rendering,” in Proceedings of the 26th Session of the CIE, Beijing, China, July 4-11, 2007, Vol. 1, D1-14-D1-17.
  23. J. Morovic, and P. Morovic, “Determining colour gamuts of digital cameras and scanners,” Color Res. Appl. 28, 59-68 (2003).
    [CrossRef]
  24. J. Morovic, “To develop a universal gamut mapping algorithm,” Ph.D. thesis (University of Derby, UK, 1998).
  25. A. D. Logvinenko, “An object-color space,” J. Vision 9, 1-23 (2009).
    [CrossRef]

2009 (2)

E. Perales, F. Martinez-Verdu, J. Fernandez-Reche, J. A. Diaz, and J. Uroz, “Comparison of color gamuts among several types of paper with the same printing technology,” Color Res. Appl. 34, 330-336 (2009).
[CrossRef]

A. D. Logvinenko, “An object-color space,” J. Vision 9, 1-23 (2009).
[CrossRef]

2008 (2)

E. Perales, E. Chorro, V. Viqueira, F. Martinez-Verdu, S. Otero, and V. de Gracia, “New method for comparing colour gamut among printing technologies,” Imaging Sci. J. 56, 145-152 (2008).
[CrossRef]

E. Perales, F. Martinez-Verdu, V. Viqueira, “Calculation of number of distinguishable colors by real normal observers,” in Proceedings of IS&T 4th European Conference on Colors in Graphics, Imaging and Vision (CGIV, 2008), pp. 80-84.

2007 (5)

E. Perales, F. Martinez-Verdu, and V. Viqueira, “New contribution for the revision of colour rendering for light sources based on the colour gamut volume,” in Proceedings of the Ciencia y Tecnología del Color, Seminario 2007 de la Red Temática, J.Campos and R.Huertas, eds. (Red Temática, Ciencia y Tecnología del Color, 2007), pp. 43-46.

X. Li, C. J. Li, M. R. Luo, M. R. Pointer, M. Cho, and J. Kim, “A new colour gamut for object colours,” in Proceedings of Fifth Colour Imaging Conference, November 5-9, 2007, Albuquerque, New Mexico, USA (2007).

F. Martinez-Verdu, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. A 24, 1501-1515 (2007).
[CrossRef]

ISO/DIS 12640-3, Graphic technology--Prepress digital data exchange--Part 3: CIELAB standard colour image data (CIELAB/SCID) (2007).

C. J. Li, M. R. Luo, M. R. Pointer, X. Li, C. Li, and W. Ji, “A new method for quantifying colour rendering,” in Proceedings of the 26th Session of the CIE, Beijing, China, July 4-11, 2007, Vol. 1, D1-14-D1-17.

2006 (4)

J. Holm, I. Tastl, and T. Johnson, “Definition and use of the ISO 12640-3 reference colour gamut,” in Proceedings of 14th Color Imaging Conference (IS&T/SID, 2006), pp. 62-68.

ISO 10527:2007(E), CIE S 014-1/E: 2006, Colorimetry Part 1: CIE Standard Colorimetric Observers, CIE Central Bureau, Kegelgasse 27, A-1030 Vienna, Austria (2006).

E. Perales, F. Martinez-Verdu, V. Viqueira, M. J. Luque, and P. Capilla, “Computing the number of distinguishable colours under several illuminants and light sources,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 414-419.

F. Martinez-Verdu, E. Perales, D. de Fez, and E. Chorro, “Calculation of the optimal colours of linear input devices,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 345-349.

2004 (2)

CIE Publication 15, Colorimetry, 3rd ed. (2004).

CIE Publication 159, A colour appearance model for colour management systems, CIECAM02 (2004).

2003 (1)

J. Morovic, and P. Morovic, “Determining colour gamuts of digital cameras and scanners,” Color Res. Appl. 28, 59-68 (2003).
[CrossRef]

2002 (1)

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

1998 (1)

J. Morovic, “To develop a universal gamut mapping algorithm,” Ph.D. thesis (University of Derby, UK, 1998).

1987 (1)

1982 (1)

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

1980 (1)

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

1969 (1)

W. Ostwald and F. Birren, The Color Primer: A Basic Treatise on the Color System of Wilhelm Ostwald (Van Nostrand Reinhold, 1969).

1935 (2)

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

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

1920 (1)

E. Schrodinger, “Der Theorie der Pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603-622 (1920).
[CrossRef]

Birren, F.

W. Ostwald and F. Birren, The Color Primer: A Basic Treatise on the Color System of Wilhelm Ostwald (Van Nostrand Reinhold, 1969).

Capilla, P.

E. Perales, F. Martinez-Verdu, V. Viqueira, M. J. Luque, and P. Capilla, “Computing the number of distinguishable colours under several illuminants and light sources,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 414-419.

Cho, M.

X. Li, C. J. Li, M. R. Luo, M. R. Pointer, M. Cho, and J. Kim, “A new colour gamut for object colours,” in Proceedings of Fifth Colour Imaging Conference, November 5-9, 2007, Albuquerque, New Mexico, USA (2007).

Chorro, E.

E. Perales, E. Chorro, V. Viqueira, F. Martinez-Verdu, S. Otero, and V. de Gracia, “New method for comparing colour gamut among printing technologies,” Imaging Sci. J. 56, 145-152 (2008).
[CrossRef]

F. Martinez-Verdu, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. A 24, 1501-1515 (2007).
[CrossRef]

F. Martinez-Verdu, E. Perales, D. de Fez, and E. Chorro, “Calculation of the optimal colours of linear input devices,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 345-349.

Cui, G.

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

de Fez, D.

F. Martinez-Verdu, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. A 24, 1501-1515 (2007).
[CrossRef]

F. Martinez-Verdu, E. Perales, D. de Fez, and E. Chorro, “Calculation of the optimal colours of linear input devices,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 345-349.

de Gracia, V.

E. Perales, E. Chorro, V. Viqueira, F. Martinez-Verdu, S. Otero, and V. de Gracia, “New method for comparing colour gamut among printing technologies,” Imaging Sci. J. 56, 145-152 (2008).
[CrossRef]

Diaz, J. A.

E. Perales, F. Martinez-Verdu, J. Fernandez-Reche, J. A. Diaz, and J. Uroz, “Comparison of color gamuts among several types of paper with the same printing technology,” Color Res. Appl. 34, 330-336 (2009).
[CrossRef]

Fernandez-Reche, J.

E. Perales, F. Martinez-Verdu, J. Fernandez-Reche, J. A. Diaz, and J. Uroz, “Comparison of color gamuts among several types of paper with the same printing technology,” Color Res. Appl. 34, 330-336 (2009).
[CrossRef]

Gilabert, E.

Holm, J.

J. Holm, I. Tastl, and T. Johnson, “Definition and use of the ISO 12640-3 reference colour gamut,” in Proceedings of 14th Color Imaging Conference (IS&T/SID, 2006), pp. 62-68.

Ji, W.

C. J. Li, M. R. Luo, M. R. Pointer, X. Li, C. Li, and W. Ji, “A new method for quantifying colour rendering,” in Proceedings of the 26th Session of the CIE, Beijing, China, July 4-11, 2007, Vol. 1, D1-14-D1-17.

Johnson, T.

J. Holm, I. Tastl, and T. Johnson, “Definition and use of the ISO 12640-3 reference colour gamut,” in Proceedings of 14th Color Imaging Conference (IS&T/SID, 2006), pp. 62-68.

Kim, J.

X. Li, C. J. Li, M. R. Luo, M. R. Pointer, M. Cho, and J. Kim, “A new colour gamut for object colours,” in Proceedings of Fifth Colour Imaging Conference, November 5-9, 2007, Albuquerque, New Mexico, USA (2007).

Li, C.

C. J. Li, M. R. Luo, M. R. Pointer, X. Li, C. Li, and W. Ji, “A new method for quantifying colour rendering,” in Proceedings of the 26th Session of the CIE, Beijing, China, July 4-11, 2007, Vol. 1, D1-14-D1-17.

Li, C. J.

C. J. Li, M. R. Luo, M. R. Pointer, X. Li, C. Li, and W. Ji, “A new method for quantifying colour rendering,” in Proceedings of the 26th Session of the CIE, Beijing, China, July 4-11, 2007, Vol. 1, D1-14-D1-17.

X. Li, C. J. Li, M. R. Luo, M. R. Pointer, M. Cho, and J. Kim, “A new colour gamut for object colours,” in Proceedings of Fifth Colour Imaging Conference, November 5-9, 2007, Albuquerque, New Mexico, USA (2007).

Li, X.

X. Li, C. J. Li, M. R. Luo, M. R. Pointer, M. Cho, and J. Kim, “A new colour gamut for object colours,” in Proceedings of Fifth Colour Imaging Conference, November 5-9, 2007, Albuquerque, New Mexico, USA (2007).

C. J. Li, M. R. Luo, M. R. Pointer, X. Li, C. Li, and W. Ji, “A new method for quantifying colour rendering,” in Proceedings of the 26th Session of the CIE, Beijing, China, July 4-11, 2007, Vol. 1, D1-14-D1-17.

Logvinenko, A. D.

A. D. Logvinenko, “An object-color space,” J. Vision 9, 1-23 (2009).
[CrossRef]

Luo, M. R.

C. J. Li, M. R. Luo, M. R. Pointer, X. Li, C. Li, and W. Ji, “A new method for quantifying colour rendering,” in Proceedings of the 26th Session of the CIE, Beijing, China, July 4-11, 2007, Vol. 1, D1-14-D1-17.

X. Li, C. J. Li, M. R. Luo, M. R. Pointer, M. Cho, and J. Kim, “A new colour gamut for object colours,” in Proceedings of Fifth Colour Imaging Conference, November 5-9, 2007, Albuquerque, New Mexico, USA (2007).

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

Luque, M. J.

E. Perales, F. Martinez-Verdu, V. Viqueira, M. J. Luque, and P. Capilla, “Computing the number of distinguishable colours under several illuminants and light sources,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 414-419.

MacAdam, D. L.

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

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

Martinez-Verdu, F.

E. Perales, F. Martinez-Verdu, J. Fernandez-Reche, J. A. Diaz, and J. Uroz, “Comparison of color gamuts among several types of paper with the same printing technology,” Color Res. Appl. 34, 330-336 (2009).
[CrossRef]

E. Perales, E. Chorro, V. Viqueira, F. Martinez-Verdu, S. Otero, and V. de Gracia, “New method for comparing colour gamut among printing technologies,” Imaging Sci. J. 56, 145-152 (2008).
[CrossRef]

E. Perales, F. Martinez-Verdu, V. Viqueira, “Calculation of number of distinguishable colors by real normal observers,” in Proceedings of IS&T 4th European Conference on Colors in Graphics, Imaging and Vision (CGIV, 2008), pp. 80-84.

E. Perales, F. Martinez-Verdu, and V. Viqueira, “New contribution for the revision of colour rendering for light sources based on the colour gamut volume,” in Proceedings of the Ciencia y Tecnología del Color, Seminario 2007 de la Red Temática, J.Campos and R.Huertas, eds. (Red Temática, Ciencia y Tecnología del Color, 2007), pp. 43-46.

F. Martinez-Verdu, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. A 24, 1501-1515 (2007).
[CrossRef]

E. Perales, F. Martinez-Verdu, V. Viqueira, M. J. Luque, and P. Capilla, “Computing the number of distinguishable colours under several illuminants and light sources,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 414-419.

F. Martinez-Verdu, E. Perales, D. de Fez, and E. Chorro, “Calculation of the optimal colours of linear input devices,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 345-349.

Morovic, J.

J. Morovic, and P. Morovic, “Determining colour gamuts of digital cameras and scanners,” Color Res. Appl. 28, 59-68 (2003).
[CrossRef]

J. Morovic, “To develop a universal gamut mapping algorithm,” Ph.D. thesis (University of Derby, UK, 1998).

Morovic, P.

J. Morovic, and P. Morovic, “Determining colour gamuts of digital cameras and scanners,” Color Res. Appl. 28, 59-68 (2003).
[CrossRef]

Ostwald, W.

W. Ostwald and F. Birren, The Color Primer: A Basic Treatise on the Color System of Wilhelm Ostwald (Van Nostrand Reinhold, 1969).

Otero, S.

E. Perales, E. Chorro, V. Viqueira, F. Martinez-Verdu, S. Otero, and V. de Gracia, “New method for comparing colour gamut among printing technologies,” Imaging Sci. J. 56, 145-152 (2008).
[CrossRef]

Perales, E.

E. Perales, F. Martinez-Verdu, J. Fernandez-Reche, J. A. Diaz, and J. Uroz, “Comparison of color gamuts among several types of paper with the same printing technology,” Color Res. Appl. 34, 330-336 (2009).
[CrossRef]

E. Perales, E. Chorro, V. Viqueira, F. Martinez-Verdu, S. Otero, and V. de Gracia, “New method for comparing colour gamut among printing technologies,” Imaging Sci. J. 56, 145-152 (2008).
[CrossRef]

E. Perales, F. Martinez-Verdu, V. Viqueira, “Calculation of number of distinguishable colors by real normal observers,” in Proceedings of IS&T 4th European Conference on Colors in Graphics, Imaging and Vision (CGIV, 2008), pp. 80-84.

E. Perales, F. Martinez-Verdu, and V. Viqueira, “New contribution for the revision of colour rendering for light sources based on the colour gamut volume,” in Proceedings of the Ciencia y Tecnología del Color, Seminario 2007 de la Red Temática, J.Campos and R.Huertas, eds. (Red Temática, Ciencia y Tecnología del Color, 2007), pp. 43-46.

F. Martinez-Verdu, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. A 24, 1501-1515 (2007).
[CrossRef]

E. Perales, F. Martinez-Verdu, V. Viqueira, M. J. Luque, and P. Capilla, “Computing the number of distinguishable colours under several illuminants and light sources,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 414-419.

F. Martinez-Verdu, E. Perales, D. de Fez, and E. Chorro, “Calculation of the optimal colours of linear input devices,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 2006), pp. 345-349.

Pointer, M. R.

X. Li, C. J. Li, M. R. Luo, M. R. Pointer, M. Cho, and J. Kim, “A new colour gamut for object colours,” in Proceedings of Fifth Colour Imaging Conference, November 5-9, 2007, Albuquerque, New Mexico, USA (2007).

C. J. Li, M. R. Luo, M. R. Pointer, X. Li, C. Li, and W. Ji, “A new method for quantifying colour rendering,” in Proceedings of the 26th Session of the CIE, Beijing, China, July 4-11, 2007, Vol. 1, D1-14-D1-17.

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

Rigg, B.

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

Roesler, G.

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

Schrodinger, E.

E. Schrodinger, “Der Theorie der Pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603-622 (1920).
[CrossRef]

Stiles, W. S.

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

Tastl, I.

J. Holm, I. Tastl, and T. Johnson, “Definition and use of the ISO 12640-3 reference colour gamut,” in Proceedings of 14th Color Imaging Conference (IS&T/SID, 2006), pp. 62-68.

Trezona, P. W.

Uroz, J.

E. Perales, F. Martinez-Verdu, J. Fernandez-Reche, J. A. Diaz, and J. Uroz, “Comparison of color gamuts among several types of paper with the same printing technology,” Color Res. Appl. 34, 330-336 (2009).
[CrossRef]

Viqueira, V.

E. Perales, F. Martinez-Verdu, V. Viqueira, “Calculation of number of distinguishable colors by real normal observers,” in Proceedings of IS&T 4th European Conference on Colors in Graphics, Imaging and Vision (CGIV, 2008), pp. 80-84.

E. Perales, E. Chorro, V. Viqueira, F. Martinez-Verdu, S. Otero, and V. de Gracia, “New method for comparing colour gamut among printing technologies,” Imaging Sci. J. 56, 145-152 (2008).
[CrossRef]

E. Perales, F. Martinez-Verdu, and V. Viqueira, “New contribution for the revision of colour rendering for light sources based on the colour gamut volume,” in Proceedings of the Ciencia y Tecnología del Color, Seminario 2007 de la Red Temática, J.Campos and R.Huertas, eds. (Red Temática, Ciencia y Tecnología del Color, 2007), pp. 43-46.

F. Martinez-Verdu, E. Perales, E. Chorro, D. de Fez, V. Viqueira, and E. Gilabert, “Computation and visualization of the MacAdam limits for any lightness, hue angle, and light source,” J. Opt. Soc. Am. A 24, 1501-1515 (2007).
[CrossRef]

E. Perales, F. Martinez-Verdu, V. Viqueira, M. J. Luque, and P. Capilla, “Computing the number of distinguishable colours under several illuminants and light sources,” in Proceedings of IS&T 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV, 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 appearance formula,” Color Res. Appl. 27, 282-290 (2002).
[CrossRef]

Wyszeki, G.

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

Ann. Phys. (1)

E. Schrodinger, “Der Theorie der Pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603-622 (1920).
[CrossRef]

Color Res. Appl. (4)

E. Perales, F. Martinez-Verdu, J. Fernandez-Reche, J. A. Diaz, and J. Uroz, “Comparison of color gamuts among several types of paper with the same printing technology,” Color Res. Appl. 34, 330-336 (2009).
[CrossRef]

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

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

J. Morovic, and P. Morovic, “Determining colour gamuts of digital cameras and scanners,” Color Res. Appl. 28, 59-68 (2003).
[CrossRef]

Imaging Sci. J. (1)

E. Perales, E. Chorro, V. Viqueira, F. Martinez-Verdu, S. Otero, and V. de Gracia, “New method for comparing colour gamut among printing technologies,” Imaging Sci. J. 56, 145-152 (2008).
[CrossRef]

J. Opt. Soc. Am. (2)

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

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

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

J. Vision (1)

A. D. Logvinenko, “An object-color space,” J. Vision 9, 1-23 (2009).
[CrossRef]

Other (14)

J. Morovic, “To develop a universal gamut mapping algorithm,” Ph.D. thesis (University of Derby, UK, 1998).

ISO/DIS 12640-3, Graphic technology--Prepress digital data exchange--Part 3: CIELAB standard colour image data (CIELAB/SCID) (2007).

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Figures (14)

Fig. 1
Fig. 1

Boundary (thick curve) of the X Z plane of the object color solid with L * = 99 ( Y = 97.4360 ) for the D50 and CIE1931 standard colorimetric observer.

Fig. 2
Fig. 2

Boundary (thick curve) of the X Z plane of the object color solid with L * = 99 ( Y = 97.4360 ) for the D50 and CIE1931 standard colorimetric observer. The ten points marked with stars were found using the new method with n = 4 .

Fig. 3
Fig. 3

Blow-up of part between P 4 and P 1 from Fig. 2.

Fig. 4
Fig. 4

Reflectance corresponding to the point P 2 in Fig. 2.

Fig. 5
Fig. 5

Reflectance corresponding to the point P 4 in Fig. 2.

Fig. 6
Fig. 6

X Z plane boundary with L * = 10 for the D 50 2 ° generated using the proposed method (full curve) and using the Martinez–Verdu et al. method [4] (dots for type 1 and stars for type 2).

Fig. 7
Fig. 7

Enlarged part of the top-right corner of Fig. 6. The solid boundary was found using the proposed method, and dots (black, type 1) and stars (black, type 2) were found using the Martinez–Verdu et al. method [4].

Fig. 8
Fig. 8

Enlarged part of the bottom-right corner of Fig. 6. The solid boundary was found using the proposed method, and dots (black, type 1) and stars (black, type 2) were found using the Martinez–Verdu et al. method [4].

Fig. 9
Fig. 9

X Z plane boundary with L * = 99 for the D 50 2 ° generated using the proposed method (full curve) and using the Martinez–Verdu et al. method [4] (dots for type 1 and stars for type 2).

Fig. 10
Fig. 10

Enlarged top-left corner of the boundary in Fig. 9. Solid curve (blue online) was found using the proposed method. Black points were found using the Martinez–Verdu et al. method.

Fig. 11
Fig. 11

Enlarged bottom corner of the boundary in Fig. 9. Solid curve (blue online) was found using the proposed method. Black points were found using the Martinez–Verdu et al. method.

Fig. 12
Fig. 12

Enlarged left side of the boundary in Fig. 9. Solid curve (blue online) was found using the proposed method. Black points were found using the Martinez–Verdu et al. method.

Fig. 13
Fig. 13

Enlarged right side of the boundary in Fig. 9. Solid curve (blue online) was found using the proposed method. Black points were found using the Martinez–Verdu et al. method.

Fig. 14
Fig. 14

Gamut boundaries in a * b * planes under D 50 2 ° with L * = 1 , 5 , 10 , , 90 , 95 , 99 , respectively.

Equations (18)

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X = k a b E ( λ ) x ¯ ( λ ) R ( λ ) d λ ,
Y = k a b E ( λ ) y ¯ ( λ ) R ( λ ) d λ ,
Z = k a b E ( λ ) z ¯ ( λ ) R ( λ ) d λ ,
0 X X W , 0 Y Y W , 0 Z Z W .
X = W X T r , Y = W Y T r , Z = W Z T r ,
λ j = a + j Δ λ , with j = 0 , 1 , , n , Δ λ = ( b a ) n .
k = i k = j W Y ( λ k ) [ Y 0 Δ Y , Y 0 + Δ Y ] , with 0 < i < j < n .
k = 0 k = i W Y ( λ k ) + k = j k = n W Y ( λ k ) [ Y 0 Δ Y , Y 0 + Δ Y ] , with 0 i < j n .
p = α p 1 + β p 2 , with α 0 , β 0 , and α + β = 1
X L = min { W X T r } ,
subject to W Y T r = 97.436 and 0 r 1 .
Z i - min = min { W Z T r } ,
subject to W Y T r = 97.436 , W X T r = X i ,
and 0 r 1 .
Z i - max = max { W Z T r } ,
subject to W Y T r = 97.436 , W X T r = X i ,
and 0 r 1 .
Δ X = X U X L n .

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