Abstract

This work continues previous research by the same authors [J. Opt. Soc. Am. A 23, 2077 (2006) ], where empirical small–medium color differences were represented by an ellipsoidal equation ΔEGP in the Uniform Color System of the Optical Society of America. Now logarithmic compressions on chroma and lightness are introduced to produce a new space with Euclidean color-difference formulas ΔEE. The CIEDE2000, ΔEGP, and ΔEE formulas are found statistically equivalent in the prediction of many available empirical datasets. However, ΔEE is the simplest formula providing relationships with visual processing. These analyses hold true for CIE 1964 Supplementary Standard Observer and D65 illuminant.

© 2008 Optical Society of America

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References

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  1. CIE, Improvement to Industrial Color-Difference Evaluation, CIE Publ. 142 (CIE Central Bureau, 2001).
  2. M. R. Luo, G. Cui, and B. Rigg, “The development of CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
    [CrossRef]
  3. R. Huertas, M. Melgosa, and C. Oleari, “Performance of a color-difference formula based on OSA-UCS space using small-medium color differences,” J. Opt. Soc. Am. A 23, 2077-2084 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
  5. D. L. MacAdam, “Colorimetric data for samples of OSA uniform color scales,” J. Opt. Soc. Am. 68, 121-130 (1978).
    [CrossRef]
  6. C. Oleari, “Color opponencies in the system of the uniform color scales of the Optical Society of America,” J. Opt. Soc. Am. A 21, 677-682 (2004).
    [CrossRef]
  7. C. Oleari, “Hypotheses for chromatic opponency functions and their performance on classical psychophysical data,” Color Res. Appl. 30, 31-41 (2005).
    [CrossRef]
  8. M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11, 25-42 (1986).
    [CrossRef]
  9. C. Oleari, M. Melgosa, and R. Huertas, “Euclidean color-difference formula in chroma compressed OSA-UCS space,” in Proceedings of the 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV 2006) (IEEE Computer Society, 2006), pp. 294-297.
  10. 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]
  11. S. S. Guan and M. R. Luo, “Investigation of parametric effects using small colour-differences,” J. Opt. Soc. Am. A 24, 331-343 (1999).
  12. G. Cui, M. R. Luo, B. Rigg, G. Rösler, and K. Witt, “Uniform colour spaces based on the DIN99 colour difference formula,” Color Res. Appl. 27, 282-290 (2002).
    [CrossRef]
  13. K. Thomsen, “A Euclidean color space in high agreement with the CIE94 color difference formula,” Color Res. Appl. 25, 64-65 (2000).
    [CrossRef]
  14. E. Rohner and D. C. Rich, “Eine angenähert gleichförmige Farbabstandsformel für industrielle Farbtoleranzen von Köorperfarben,” Die Farbe 42, 207-220 (1996).
  15. J. H. Nobbs, “A lightness, chroma and hue splitting approach to CIEDE2000 colour differences,” Adv. Colour Sci. and Techno. 5, 46-53 (2002).
  16. P. Urban, M. R. Rosen, and R. S. Berns, “Embedding non-Euclidean color spaces into Euclidean color spaces with minimal isometric disagreement,” J. Opt. Soc. Am. A 24, 1516-1528 (2007).
    [CrossRef]
  17. R. S. Berns and Y. Zue, “Optimizing color-difference equations and uniform color spaces for industrial tolerancing,” in Proceedings of AIC 2007--Color Science for Industry, Y.E.Guanrong and X.U.Haisong, eds. (AIC, 2007), pp. 24-28.
  18. D. H. Kim and J. H. Nobbs, “New weightings functions for the weighted CIELAB color difference formula,” in Proceedings of AIC Colour 97 (AIC, 1997), Vol. 1, pp. 446-449.
  19. R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color tolerances using probit analysis,” Color Res. Appl. 16, 297-316 (1991).
    [CrossRef]
  20. K. Witt, “Geometric relations between scales of small colour differences,” Color Res. Appl. 24, 78-92 (1999).
    [CrossRef]
  21. C. C. Semmelroth, “Prediction of lightness and brightness on different backgrounds,” J. Opt. Soc. Am. 60, 1685-1689 (1970).
    [CrossRef] [PubMed]
  22. M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulas using the standardized residual sum of squares index,” J. Opt. Soc. Am. A 25, 1828-1834 (2008).
    [CrossRef]
  23. C. Oleari, “Comparison between color-space scales, uniform color-scales atlases and color-difference formulae,” Color Res. Appl. 26, 351-361 (2001).
    [CrossRef]
  24. S. S. Guan and M. R. Luo, “A colour-difference formula for assessing large colour-differences,” Color Res. Appl. 24, 344-355 (1999).
    [CrossRef]
  25. R. G. Kuehni, “Color difference formulas: an unsatisfactory state of affairs,” Color Res. Appl. 33, 324-326 (2008).
    [CrossRef]
  26. M. Melgosa, R. Huertas, and P. A. García, “Performance of CIEDE2000 color difference models for the RIT-DuPont dataset,” in Proceedings of AIC 2007--Color Science for Industry, Y.E.Guanrong and X.U.Haisong, eds. (AIC, 2007), pp. 293-295.

2008 (2)

2007 (2)

2006 (1)

2005 (1)

C. Oleari, “Hypotheses for chromatic opponency functions and their performance on classical psychophysical data,” Color Res. Appl. 30, 31-41 (2005).
[CrossRef]

2004 (1)

2002 (2)

J. H. Nobbs, “A lightness, chroma and hue splitting approach to CIEDE2000 colour differences,” Adv. Colour Sci. and Techno. 5, 46-53 (2002).

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

2001 (2)

M. R. Luo, G. Cui, and B. Rigg, “The development of CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

C. Oleari, “Comparison between color-space scales, uniform color-scales atlases and color-difference formulae,” Color Res. Appl. 26, 351-361 (2001).
[CrossRef]

2000 (1)

K. Thomsen, “A Euclidean color space in high agreement with the CIE94 color difference formula,” Color Res. Appl. 25, 64-65 (2000).
[CrossRef]

1999 (3)

S. S. Guan and M. R. Luo, “Investigation of parametric effects using small colour-differences,” J. Opt. Soc. Am. A 24, 331-343 (1999).

S. S. Guan and M. R. Luo, “A colour-difference formula for assessing large colour-differences,” Color Res. Appl. 24, 344-355 (1999).
[CrossRef]

K. Witt, “Geometric relations between scales of small colour differences,” Color Res. Appl. 24, 78-92 (1999).
[CrossRef]

1996 (1)

E. Rohner and D. C. Rich, “Eine angenähert gleichförmige Farbabstandsformel für industrielle Farbtoleranzen von Köorperfarben,” Die Farbe 42, 207-220 (1996).

1991 (1)

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color tolerances using probit analysis,” Color Res. Appl. 16, 297-316 (1991).
[CrossRef]

1986 (1)

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11, 25-42 (1986).
[CrossRef]

1978 (1)

1974 (1)

1970 (1)

Alman, D. H.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color tolerances using probit analysis,” Color Res. Appl. 16, 297-316 (1991).
[CrossRef]

Balonon-Rosen, M. R.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color tolerances using probit analysis,” Color Res. Appl. 16, 297-316 (1991).
[CrossRef]

Berns, R. S.

M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulas using the standardized residual sum of squares index,” J. Opt. Soc. Am. A 25, 1828-1834 (2008).
[CrossRef]

P. Urban, M. R. Rosen, and R. S. Berns, “Embedding non-Euclidean color spaces into Euclidean color spaces with minimal isometric disagreement,” J. Opt. Soc. Am. A 24, 1516-1528 (2007).
[CrossRef]

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color tolerances using probit analysis,” Color Res. Appl. 16, 297-316 (1991).
[CrossRef]

R. S. Berns and Y. Zue, “Optimizing color-difference equations and uniform color spaces for industrial tolerancing,” in Proceedings of AIC 2007--Color Science for Industry, Y.E.Guanrong and X.U.Haisong, eds. (AIC, 2007), pp. 24-28.

Cui, G.

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]

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

M. R. Luo, G. Cui, and B. Rigg, “The development of CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
[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]

M. Melgosa, R. Huertas, and P. A. García, “Performance of CIEDE2000 color difference models for the RIT-DuPont dataset,” in Proceedings of AIC 2007--Color Science for Industry, Y.E.Guanrong and X.U.Haisong, eds. (AIC, 2007), pp. 293-295.

Guan, S. S.

S. S. Guan and M. R. Luo, “A colour-difference formula for assessing large colour-differences,” Color Res. Appl. 24, 344-355 (1999).
[CrossRef]

S. S. Guan and M. R. Luo, “Investigation of parametric effects using small colour-differences,” J. Opt. Soc. Am. A 24, 331-343 (1999).

Huertas, R.

M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulas using the standardized residual sum of squares index,” J. Opt. Soc. Am. A 25, 1828-1834 (2008).
[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]

R. Huertas, M. Melgosa, and C. Oleari, “Performance of a color-difference formula based on OSA-UCS space using small-medium color differences,” J. Opt. Soc. Am. A 23, 2077-2084 (2006).
[CrossRef]

M. Melgosa, R. Huertas, and P. A. García, “Performance of CIEDE2000 color difference models for the RIT-DuPont dataset,” in Proceedings of AIC 2007--Color Science for Industry, Y.E.Guanrong and X.U.Haisong, eds. (AIC, 2007), pp. 293-295.

C. Oleari, M. Melgosa, and R. Huertas, “Euclidean color-difference formula in chroma compressed OSA-UCS space,” in Proceedings of the 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV 2006) (IEEE Computer Society, 2006), pp. 294-297.

Kim, D. H.

D. H. Kim and J. H. Nobbs, “New weightings functions for the weighted CIELAB color difference formula,” in Proceedings of AIC Colour 97 (AIC, 1997), Vol. 1, pp. 446-449.

Kuehni, R. G.

R. G. Kuehni, “Color difference formulas: an unsatisfactory state of affairs,” Color Res. Appl. 33, 324-326 (2008).
[CrossRef]

Luo, M. R.

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

M. R. Luo, G. Cui, and B. Rigg, “The development of CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

S. S. Guan and M. R. Luo, “A colour-difference formula for assessing large colour-differences,” Color Res. Appl. 24, 344-355 (1999).
[CrossRef]

S. S. Guan and M. R. Luo, “Investigation of parametric effects using small colour-differences,” J. Opt. Soc. Am. A 24, 331-343 (1999).

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11, 25-42 (1986).
[CrossRef]

MacAdam, D. L.

Melgosa, M.

M. Melgosa, R. Huertas, and R. S. Berns, “Performance of recent advanced color-difference formulas using the standardized residual sum of squares index,” J. Opt. Soc. Am. A 25, 1828-1834 (2008).
[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]

R. Huertas, M. Melgosa, and C. Oleari, “Performance of a color-difference formula based on OSA-UCS space using small-medium color differences,” J. Opt. Soc. Am. A 23, 2077-2084 (2006).
[CrossRef]

C. Oleari, M. Melgosa, and R. Huertas, “Euclidean color-difference formula in chroma compressed OSA-UCS space,” in Proceedings of the 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV 2006) (IEEE Computer Society, 2006), pp. 294-297.

M. Melgosa, R. Huertas, and P. A. García, “Performance of CIEDE2000 color difference models for the RIT-DuPont dataset,” in Proceedings of AIC 2007--Color Science for Industry, Y.E.Guanrong and X.U.Haisong, eds. (AIC, 2007), pp. 293-295.

Nobbs, J. H.

J. H. Nobbs, “A lightness, chroma and hue splitting approach to CIEDE2000 colour differences,” Adv. Colour Sci. and Techno. 5, 46-53 (2002).

D. H. Kim and J. H. Nobbs, “New weightings functions for the weighted CIELAB color difference formula,” in Proceedings of AIC Colour 97 (AIC, 1997), Vol. 1, pp. 446-449.

Oleari, C.

R. Huertas, M. Melgosa, and C. Oleari, “Performance of a color-difference formula based on OSA-UCS space using small-medium color differences,” J. Opt. Soc. Am. A 23, 2077-2084 (2006).
[CrossRef]

C. Oleari, “Hypotheses for chromatic opponency functions and their performance on classical psychophysical data,” Color Res. Appl. 30, 31-41 (2005).
[CrossRef]

C. Oleari, “Color opponencies in the system of the uniform color scales of the Optical Society of America,” J. Opt. Soc. Am. A 21, 677-682 (2004).
[CrossRef]

C. Oleari, “Comparison between color-space scales, uniform color-scales atlases and color-difference formulae,” Color Res. Appl. 26, 351-361 (2001).
[CrossRef]

C. Oleari, M. Melgosa, and R. Huertas, “Euclidean color-difference formula in chroma compressed OSA-UCS space,” in Proceedings of the 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV 2006) (IEEE Computer Society, 2006), pp. 294-297.

Reniff, L.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color tolerances using probit analysis,” Color Res. Appl. 16, 297-316 (1991).
[CrossRef]

Rich, D. C.

E. Rohner and D. C. Rich, “Eine angenähert gleichförmige Farbabstandsformel für industrielle Farbtoleranzen von Köorperfarben,” Die Farbe 42, 207-220 (1996).

Rigg, B.

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

M. R. Luo, G. Cui, and B. Rigg, “The development of CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11, 25-42 (1986).
[CrossRef]

Rohner, E.

E. Rohner and D. C. Rich, “Eine angenähert gleichförmige Farbabstandsformel für industrielle Farbtoleranzen von Köorperfarben,” Die Farbe 42, 207-220 (1996).

Rosen, M. R.

Rösler, G.

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

Semmelroth, C. C.

Snyder, G. D.

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color tolerances using probit analysis,” Color Res. Appl. 16, 297-316 (1991).
[CrossRef]

Thomsen, K.

K. Thomsen, “A Euclidean color space in high agreement with the CIE94 color difference formula,” Color Res. Appl. 25, 64-65 (2000).
[CrossRef]

Urban, P.

Witt, K.

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

K. Witt, “Geometric relations between scales of small colour differences,” Color Res. Appl. 24, 78-92 (1999).
[CrossRef]

Zue, Y.

R. S. Berns and Y. Zue, “Optimizing color-difference equations and uniform color spaces for industrial tolerancing,” in Proceedings of AIC 2007--Color Science for Industry, Y.E.Guanrong and X.U.Haisong, eds. (AIC, 2007), pp. 24-28.

Adv. Colour Sci. and Techno. (1)

J. H. Nobbs, “A lightness, chroma and hue splitting approach to CIEDE2000 colour differences,” Adv. Colour Sci. and Techno. 5, 46-53 (2002).

Color Res. Appl. (10)

R. S. Berns, D. H. Alman, L. Reniff, G. D. Snyder, and M. R. Balonon-Rosen, “Visual determination of suprathreshold color tolerances using probit analysis,” Color Res. Appl. 16, 297-316 (1991).
[CrossRef]

K. Witt, “Geometric relations between scales of small colour differences,” Color Res. Appl. 24, 78-92 (1999).
[CrossRef]

C. Oleari, “Comparison between color-space scales, uniform color-scales atlases and color-difference formulae,” Color Res. Appl. 26, 351-361 (2001).
[CrossRef]

S. S. Guan and M. R. Luo, “A colour-difference formula for assessing large colour-differences,” Color Res. Appl. 24, 344-355 (1999).
[CrossRef]

R. G. Kuehni, “Color difference formulas: an unsatisfactory state of affairs,” Color Res. Appl. 33, 324-326 (2008).
[CrossRef]

M. R. Luo, G. Cui, and B. Rigg, “The development of CIE 2000 colour-difference formula: CIEDE2000,” Color Res. Appl. 26, 340-350 (2001).
[CrossRef]

C. Oleari, “Hypotheses for chromatic opponency functions and their performance on classical psychophysical data,” Color Res. Appl. 30, 31-41 (2005).
[CrossRef]

M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colors,” Color Res. Appl. 11, 25-42 (1986).
[CrossRef]

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

K. Thomsen, “A Euclidean color space in high agreement with the CIE94 color difference formula,” Color Res. Appl. 25, 64-65 (2000).
[CrossRef]

Die Farbe (1)

E. Rohner and D. C. Rich, “Eine angenähert gleichförmige Farbabstandsformel für industrielle Farbtoleranzen von Köorperfarben,” Die Farbe 42, 207-220 (1996).

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (6)

Other (5)

CIE, Improvement to Industrial Color-Difference Evaluation, CIE Publ. 142 (CIE Central Bureau, 2001).

C. Oleari, M. Melgosa, and R. Huertas, “Euclidean color-difference formula in chroma compressed OSA-UCS space,” in Proceedings of the 3rd European Conference on Color in Graphics, Imaging and Vision (CGIV 2006) (IEEE Computer Society, 2006), pp. 294-297.

M. Melgosa, R. Huertas, and P. A. García, “Performance of CIEDE2000 color difference models for the RIT-DuPont dataset,” in Proceedings of AIC 2007--Color Science for Industry, Y.E.Guanrong and X.U.Haisong, eds. (AIC, 2007), pp. 293-295.

R. S. Berns and Y. Zue, “Optimizing color-difference equations and uniform color spaces for industrial tolerancing,” in Proceedings of AIC 2007--Color Science for Industry, Y.E.Guanrong and X.U.Haisong, eds. (AIC, 2007), pp. 24-28.

D. H. Kim and J. H. Nobbs, “New weightings functions for the weighted CIELAB color difference formula,” in Proceedings of AIC Colour 97 (AIC, 1997), Vol. 1, pp. 446-449.

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Figures (4)

Fig. 1
Fig. 1

Figure equal to Fig. 3 of the previous paper [3], showing the (J, G) plane of the OSA-UCS space with the BFD (Bradford University) ellipses [8] (thick line) and the ellipses representing the color-difference formula Δ E G P (thin line). The ellipse parameters are a H = 1.154 , b H = 0.018 , a C = 1.121 , and b C = 0.051 , while a L and b L are assumed to have no effect because the ellipses are given at constant lightness; the values of the parameters are the same as in the previous paper up to a rounding [3] and are equal to those given in Table 1, although obtained in two different but equivalent ways, by minimizing RMS × PF 3 (RMS, root mean square) in [3] and by minimizing only the RMS in this work.

Fig. 2
Fig. 2

Representation of an ellipse-like line, centered in C OSA , transformed by chroma log compression into a circle-like line centered in C E .

Fig. 3
Fig. 3

Empirical short semiaxes (◻) of the whole BFD set of ellipses [8] as functions of the chroma C OSA of the center of the ellipse and the lines represented by the two sides of relation (12). These two lines represent in an equally good way the empirical values of the short semiaxes, as shown by the RMS values between the empirical data and the points of these lines: 0.379 for the left side of relation (12) (thin straight line) and 0.374 for the right side (thick line).

Fig. 4
Fig. 4

The ( J E , G E ) plane of the chroma log-compressed space, obtained from the OSA-UCS space, with empirical BFD ellipses [8] (thick line), corresponding equal-radius circles (thin lines), and net of the cylindrical coordinates of the OSA-UCS space at constant lightness. The values of the transformation parameters are a C = 1.055 and b C = 0.058 , as given in Table 1.

Tables (8)

Tables Icon

Table 1 STRESS of Four Different Color-Difference Formulas on the Empirical Basis of the Constant Luminance BFD Ellipses a

Tables Icon

Table 2 F-Test among All the Color-Difference Formulas Considered, Δ E G P , Δ E E , CIEDE2000, and DIN99d a

Tables Icon

Table 3 Equation Parameters ( a L , b L , a C , b C , a H , b H ) , RMS, and STRESS Values for Δ E G P and for the Two Δ E E Formulas, Computed for Each One of the Datasets Constituting the COM Datasets, Using Their Own Empirical Background Luminance Y b (Second Column)

Tables Icon

Table 4 Equation Parameters ( a L , b L , a C , b C , a H , b H ) , RMS, and STRESS Values for Δ E G P and for the Two Δ E E Formulas, Computed for the Two COM Datasets, Using the Background Luminance Y b = 30 , as in the OSA-UCS Space

Tables Icon

Table 5 STRESS Values of All the Color-Difference Formulas Considered, Δ E G P , both Δ E E ’s, CIEDE2000, and DIN99d, Related to All the Different Datasets Considered a

Tables Icon

Table 6 Comparison between Δ E G P and Δ E E ’s Formulas Based on F-Test of the STRESS (Table 5) and on the Empirical Data Constituted by BFD Ellipses and by Individual and COM Datasets a

Tables Icon

Table 7 Comparison between Δ E 00 and All the Other Considered Formulas ( Δ E G P , both Δ E E ’s and DIN99d) Based on F-test of the STRESS (Table 5) and the Empirical Data Constituted by BFD Ellipses and by Individual and COM Datasets a

Tables Icon

Table 8 Number of Independent Color Pairs N (in Brackets is the Number of Nonindependent Color Pairs Obtained by Weighting Factors and Employed in the Computation) and Critical Values [ F C , F C 1 ] of the Two-Tailed F-Distribution at a 5% Significance Level for Each One of the Individual Datasets Constituting the COM Datasets and for the W-COM and unW-COM Datasets a

Equations (40)

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

( Δ E GP ) 2 = ( Δ ( 10 L OSA ) S L ) 2 + ( Δ ( 10 C OSA ) S C ) 2 + ( Δ ( 10 H OSA ) S H ) 2 ,
C OSA = G 2 + J 2 ,
( Δ H OSA ) 2 = ( Δ E 0 ) 2 ( Δ L OSA ) 2 ( Δ C OSA ) 2
( Δ E 0 ) 2 = ( Δ L OSA ) 2 + ( Δ J ) 2 + ( Δ G ) 2 ,
S L = a L + b L ( 10 L ¯ OSA ) = 2.499 + 0.007 ( 10 L ¯ OSA ) ,
S C = a C + b C ( 10 C ¯ OSA ) = 1.235 + 0.058 ( 10 C ¯ OSA ) ,
S H = a H + b H ( 10 C ¯ OSA ) = 1.392 + 0.017 ( 10 C ¯ OSA )
Δ ( 10 C OSA ) S C = Δ ( 10 C OSA ) a C + b C ( 10 C OSA ) .
Δ C E = Δ ( 10 C OSA ) a C + b C ( 10 C OSA ) ,
C E ( 1 b C ) ln [ 1 + b C a C ( 10 C OSA ) ] ;
G E = C E cos ( h ) ,
J E = C E sin ( h ) ,
h = arctan ( J G ) .
O C E C E A = O C O S A C O S A B , i.e. , C O S A B = C E A × O C O S A O C E .
a H + b H ( 10 C OSA ) b C ( 10 C OSA ) ln ( 1 + b C a C ( 10 C OSA ) ) .
( Δ E E ) 2 ( Δ G E ) 2 + ( Δ J E ) 2 ( Δ ( 10 H OSA ) S H ) 2 + ( Δ ( 10 C OSA ) S C ) 2 .
Δ ( 10 L OSA ) S L = Δ ( 10 L OSA ) a L + b L ( 10 L OSA ) .
L E ( 1 b L ) ln [ 1 + b L a L ( 10 L OSA ) ]
Δ L E = Δ ( 10 L OSA ) S L = Δ ( 10 L OSA ) a L + b L ( 10 L OSA ) .
L E 10 L OSA a L
Δ ( 10 L OSA ) S L Δ L E = Δ ( 10 L OSA ) a L .
Δ E E = ( Δ L E ) 2 + ( Δ G E ) 2 + ( Δ J E ) 2 ,
Δ E E = ( Δ L E ) 2 + ( Δ G E ) 2 + ( Δ J E ) 2 ,
L E = ( 1 b L ) ln [ 1 + b L a L ( 10 L OSA ) ]
with a L = 2.890 , b L = 0.015 ,
G E = C E cos ( h ) ,
J E = C E sin ( h ) ,
h = arctan ( J G ) ,
C E = ( 1 b C ) ln [ 1 + b C a C ( 10 C OSA ) ]
with a C = 1.256 , b C = 0.050 ,
C OSA = G 2 + J 2 .
X 10 , n = 94.81 ; Y 10 , n = 100.00 ; Z 10 , n = 107.33 ,
T c p 6500 K for BFD - D 65 ,
X 10 , n = 94.65 ; Y 10 , n = 100.00 ; Z 10 , n = 103.97 ,
T c p 6300 K for BFD - M ,
X 10 , n = 98.07 ; Y 10 , n = 100.00 ; Z 10 , n = 118.23 ,
T c p 6800 K for BFD - C .
RMS = i ( Δ E i Δ V i ) 2 N ,
STRESS = 100 i ( Δ E i F 1 Δ V i ) 2 i ( F 1 Δ V i ) 2 with F 1 = i ( Δ E i ) 2 i Δ E i Δ V i .
F A B ( STRESS A STRESS B ) 2 ,

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