Abstract

The performances of uniform color spaces and color-difference formulae for predicting threshold color differences were investigated based on visual assessments of 893 pairs of printed color patches under a D65 source. The average ΔEab,10* of the pairs was 1.1 units. A threshold psychophysical experiment was repeated three times by a panel of 16 observers with normal color vision. The experimental data were used to evaluate nine color-difference formulae and uniform color spaces using the standardized residual sum of squares (STRESS) measure. The results indicated that all formulae and spaces performed very similarly to each other, and outperformed CIELAB for threshold color differences. The chromaticity-discrimination ellipses were used to compare with previous results from small color differences [Color Res. Appl. (2011), doi:10.1002/col.20689], and they agreed with each other, except for the purple color center.

© 2012 Optical Society of America

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    [CrossRef]
  29. M. R. Luo and B. Rigg, “Chromaticity-discrimination ellipses for surface colours,” Color Res. Appl. 11, 25–42 (1986).
    [CrossRef]
  30. M. Melgosa, E. Hita, A. J. Poza, D. H. Alman, and R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (1)

2009 (2)

S. Morillas, L. Gómez-Robledo, R. Huertas, and M. Melgosa, “Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula,” J. Mod. Opt. 56, 1447–1456 (2009).
[CrossRef]

C. Oleari, M. Melgosa, and R. Huertas, “Euclidean colour-difference formula for small-medium color differences in log-compressed OSA-UCS space,” J. Opt. Soc. Am. A 26, 121–133 (2009).
[CrossRef]

2008 (1)

2007 (2)

2006 (2)

R. Huertas, M. Melgosa, and E. Hita, “Influence of random-dot textures on perception of suprathreshold color differences,” J. Opt. Soc. Am. A 23, 2067–2076 (2006).
[CrossRef]

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[CrossRef]

2003 (1)

E. D. Montag and D. C. Wilber, “A comparison of constant stimuli and gray-scale methods of color difference scaling,” Color Res. Appl. 28, 36–44 (2003).
[CrossRef]

2002 (1)

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]

2001 (2)

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

G. Cui, M. R. Luo, B. Rigg, and W. Li, “Colour-difference evaluation using CRT colours. Part II: parametric effects,” Color Res. Appl. 26, 403–412 (2001).
[CrossRef]

1997 (1)

M. Melgosa, E. Hita, A. J. Poza, D. H. Alman, and R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[CrossRef]

1995 (1)

K. Witt, “CIE guidelines for coordinated future work on industrial colour-difference evaluation,” Color Res. Appl. 20, 399–403 (1995).
[CrossRef]

1986 (1)

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

1984 (1)

F. J. J. Clarke, R. McDonald, and B. Rigg, “Modification to the JPC79 colour-difference formula,” J. Soc. Dyers Colour. 100, 128–132 (1984).
[CrossRef]

1981 (1)

C. Alder, “A Monte Carlo method for the validation of discrimination ellipse data,” J. Soc. Dyers Colour. 97, 514–517 (1981).
[CrossRef]

1980 (1)

R. McDonald, “Industrial pass/fail colour matching. Part I—preparation of visual colour matching data,” J. Soc. Dyers Colour. 96, 372–376 (1980).
[CrossRef]

1977 (1)

A. R. Robertson, “The CIE1976 colour-difference formulae,” Color Res. Appl. 2, 7–11 (1977).

1974 (1)

1972 (2)

E. Coates, S. Day, J. R. Provost, and B. Rigg, “The measurement and assessment of colour differences for industrial use—the accuracy of colour-difference equations,” J. Soc. Dyers Colour. 88, 69–75 (1972).
[CrossRef]

E. Coates, S. Day, J. R. Provost, and B. Rigg, “The measurement and assessment of colour differences for industrial use III. Method of scaling visual assessments,” J. Soc. Dyers Colour. 88, 186–190 (1972).
[CrossRef]

1970 (1)

K. McLaren, “Color passing—visual or instrumental?” J. Soc. Dyers Colour. 86, 389–392 (1970).
[CrossRef]

Alder, C.

C. Alder, “A Monte Carlo method for the validation of discrimination ellipse data,” J. Soc. Dyers Colour. 97, 514–517 (1981).
[CrossRef]

Alman, D. H.

M. Melgosa, E. Hita, A. J. Poza, D. H. Alman, and R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[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]

M. Melgosa, E. Hita, A. J. Poza, D. H. Alman, and R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[CrossRef]

Clarke, F. J. J.

F. J. J. Clarke, R. McDonald, and B. Rigg, “Modification to the JPC79 colour-difference formula,” J. Soc. Dyers Colour. 100, 128–132 (1984).
[CrossRef]

Coates, E.

E. Coates, S. Day, J. R. Provost, and B. Rigg, “The measurement and assessment of colour differences for industrial use—the accuracy of colour-difference equations,” J. Soc. Dyers Colour. 88, 69–75 (1972).
[CrossRef]

E. Coates, S. Day, J. R. Provost, and B. Rigg, “The measurement and assessment of colour differences for industrial use III. Method of scaling visual assessments,” J. Soc. Dyers Colour. 88, 186–190 (1972).
[CrossRef]

Cui, G.

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

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[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]

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

G. Cui, M. R. Luo, B. Rigg, and W. Li, “Colour-difference evaluation using CRT colours. Part II: parametric effects,” Color Res. Appl. 26, 403–412 (2001).
[CrossRef]

M. R. Luo, C. Minchew, P. Kenyon, and G. Cui, “Verification of CIEDE2000 using industrial data,” in Proceedings of Interim Meeting of the International Colour Association (AIC 2004 Colour and Paints) (AIC, 2004), pp. 97–102.

M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and colour-difference formulae using printed samples,” Color Res. Appl., article first published online 15 September 2011, doi:10.1002/col.20689 .
[CrossRef]

G. Cui, M. R. Luo, and B. Rigg, “Colour difference evaluation under illuminant A,” in Proceedings of the 10th Congress of the International Colour Association (AIC Colour 05), pp. 575–578.

R. Huertas, A. Trémeau, M. Melgosa, L. Gómez-Robledo, G. Cui, and M. R. Luo, “Checking Recent colour-difference formulas with a dataset of metallic samples and just noticeable colour-difference assessments,” in Proceedings of the 5th European Conference on Colour in Graphics, Imaging, and Vision (CGIV, 2010), pp. 504–509.

Day, S.

E. Coates, S. Day, J. R. Provost, and B. Rigg, “The measurement and assessment of colour differences for industrial use III. Method of scaling visual assessments,” J. Soc. Dyers Colour. 88, 186–190 (1972).
[CrossRef]

E. Coates, S. Day, J. R. Provost, and B. Rigg, “The measurement and assessment of colour differences for industrial use—the accuracy of colour-difference equations,” J. Soc. Dyers Colour. 88, 69–75 (1972).
[CrossRef]

Dekker, N.

García, P. A.

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

M. Melgosa, R. Huertas, and P. A. García, “Analysis of color-differences with different magnitudes using the visual data employed at CIEDE2000 development,” in Proceedings of Interim Meeting of the International Colour Association (AIC2008), pp. 279–280.

Gómez-Robledo, L.

S. Morillas, L. Gómez-Robledo, R. Huertas, and M. Melgosa, “Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula,” J. Mod. Opt. 56, 1447–1456 (2009).
[CrossRef]

R. Huertas, A. Trémeau, M. Melgosa, L. Gómez-Robledo, G. Cui, and M. R. Luo, “Checking Recent colour-difference formulas with a dataset of metallic samples and just noticeable colour-difference assessments,” in Proceedings of the 5th European Conference on Colour in Graphics, Imaging, and Vision (CGIV, 2010), pp. 504–509.

Hita, E.

R. Huertas, M. Melgosa, and E. Hita, “Influence of random-dot textures on perception of suprathreshold color differences,” J. Opt. Soc. Am. A 23, 2067–2076 (2006).
[CrossRef]

M. Melgosa, E. Hita, A. J. Poza, D. H. Alman, and R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[CrossRef]

Huang, M.

M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and colour-difference formulae using printed samples,” Color Res. Appl., article first published online 15 September 2011, doi:10.1002/col.20689 .
[CrossRef]

Huertas, R.

C. Oleari, M. Melgosa, and R. Huertas, “Euclidean colour-difference formula for small-medium color differences in log-compressed OSA-UCS space,” J. Opt. Soc. Am. A 26, 121–133 (2009).
[CrossRef]

S. Morillas, L. Gómez-Robledo, R. Huertas, and M. Melgosa, “Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula,” J. Mod. Opt. 56, 1447–1456 (2009).
[CrossRef]

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 difference,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[CrossRef]

R. Huertas, M. Melgosa, and E. Hita, “Influence of random-dot textures on perception of suprathreshold color differences,” J. Opt. Soc. Am. A 23, 2067–2076 (2006).
[CrossRef]

R. Huertas, A. Trémeau, M. Melgosa, L. Gómez-Robledo, G. Cui, and M. R. Luo, “Checking Recent colour-difference formulas with a dataset of metallic samples and just noticeable colour-difference assessments,” in Proceedings of the 5th European Conference on Colour in Graphics, Imaging, and Vision (CGIV, 2010), pp. 504–509.

M. Melgosa, R. Huertas, and P. A. García, “Analysis of color-differences with different magnitudes using the visual data employed at CIEDE2000 development,” in Proceedings of Interim Meeting of the International Colour Association (AIC2008), pp. 279–280.

Kenyon, P.

M. R. Luo, C. Minchew, P. Kenyon, and G. Cui, “Verification of CIEDE2000 using industrial data,” in Proceedings of Interim Meeting of the International Colour Association (AIC 2004 Colour and Paints) (AIC, 2004), pp. 97–102.

Kirchner, E.

Kittelmann, P.

P. Kittelmann, “Visuelle Beurteilung von kleinen und großen Farbunterschieden und Beschreibung mit Farbabstandsformeln,” Ph.D. thesis (Berlin University of Technology, 2010), http://opus.kobv.de/tuberlin/volltexte/2010/2634/.

Li, C.

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[CrossRef]

Li, W.

G. Cui, M. R. Luo, B. Rigg, and W. Li, “Colour-difference evaluation using CRT colours. Part II: parametric effects,” Color Res. Appl. 26, 403–412 (2001).
[CrossRef]

Liu, H.

M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and colour-difference formulae using printed samples,” Color Res. Appl., article first published online 15 September 2011, doi:10.1002/col.20689 .
[CrossRef]

Luo, M. R.

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[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]

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

G. Cui, M. R. Luo, B. Rigg, and W. Li, “Colour-difference evaluation using CRT colours. Part II: parametric effects,” Color Res. Appl. 26, 403–412 (2001).
[CrossRef]

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

M. Huang, H. Liu, G. Cui, and M. R. Luo, “Testing uniform colour spaces and colour-difference formulae using printed samples,” Color Res. Appl., article first published online 15 September 2011, doi:10.1002/col.20689 .
[CrossRef]

R. Huertas, A. Trémeau, M. Melgosa, L. Gómez-Robledo, G. Cui, and M. R. Luo, “Checking Recent colour-difference formulas with a dataset of metallic samples and just noticeable colour-difference assessments,” in Proceedings of the 5th European Conference on Colour in Graphics, Imaging, and Vision (CGIV, 2010), pp. 504–509.

G. Cui, M. R. Luo, and B. Rigg, “Colour difference evaluation under illuminant A,” in Proceedings of the 10th Congress of the International Colour Association (AIC Colour 05), pp. 575–578.

M. R. Luo, C. Minchew, P. Kenyon, and G. Cui, “Verification of CIEDE2000 using industrial data,” in Proceedings of Interim Meeting of the International Colour Association (AIC 2004 Colour and Paints) (AIC, 2004), pp. 97–102.

MacAdam, D. L.

McDonald, R.

F. J. J. Clarke, R. McDonald, and B. Rigg, “Modification to the JPC79 colour-difference formula,” J. Soc. Dyers Colour. 100, 128–132 (1984).
[CrossRef]

R. McDonald, “Industrial pass/fail colour matching. Part I—preparation of visual colour matching data,” J. Soc. Dyers Colour. 96, 372–376 (1980).
[CrossRef]

McLaren, K.

K. McLaren, “Color passing—visual or instrumental?” J. Soc. Dyers Colour. 86, 389–392 (1970).
[CrossRef]

Melgosa, M.

S. Morillas, L. Gómez-Robledo, R. Huertas, and M. Melgosa, “Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula,” J. Mod. Opt. 56, 1447–1456 (2009).
[CrossRef]

C. Oleari, M. Melgosa, and R. Huertas, “Euclidean colour-difference formula for small-medium color differences in log-compressed OSA-UCS space,” J. Opt. Soc. Am. A 26, 121–133 (2009).
[CrossRef]

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 difference,” J. Opt. Soc. Am. A 24, 1823–1829 (2007).
[CrossRef]

M. Melgosa, “Request for existing experimental datasets on color differences,” Color Res. Appl. 32, 159 (2007).
[CrossRef]

R. Huertas, M. Melgosa, and E. Hita, “Influence of random-dot textures on perception of suprathreshold color differences,” J. Opt. Soc. Am. A 23, 2067–2076 (2006).
[CrossRef]

M. Melgosa, E. Hita, A. J. Poza, D. H. Alman, and R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[CrossRef]

M. Melgosa, R. Huertas, and P. A. García, “Analysis of color-differences with different magnitudes using the visual data employed at CIEDE2000 development,” in Proceedings of Interim Meeting of the International Colour Association (AIC2008), pp. 279–280.

R. Huertas, A. Trémeau, M. Melgosa, L. Gómez-Robledo, G. Cui, and M. R. Luo, “Checking Recent colour-difference formulas with a dataset of metallic samples and just noticeable colour-difference assessments,” in Proceedings of the 5th European Conference on Colour in Graphics, Imaging, and Vision (CGIV, 2010), pp. 504–509.

Minchew, C.

M. R. Luo, C. Minchew, P. Kenyon, and G. Cui, “Verification of CIEDE2000 using industrial data,” in Proceedings of Interim Meeting of the International Colour Association (AIC 2004 Colour and Paints) (AIC, 2004), pp. 97–102.

Montag, E. D.

E. D. Montag and D. C. Wilber, “A comparison of constant stimuli and gray-scale methods of color difference scaling,” Color Res. Appl. 28, 36–44 (2003).
[CrossRef]

Morillas, S.

S. Morillas, L. Gómez-Robledo, R. Huertas, and M. Melgosa, “Fuzzy analysis for detection of inconsistent data in experimental datasets employed at the development of the CIEDE2000 colour-difference formula,” J. Mod. Opt. 56, 1447–1456 (2009).
[CrossRef]

Oleari, C.

Poza, A. J.

M. Melgosa, E. Hita, A. J. Poza, D. H. Alman, and R. S. Berns, “Suprathreshold color-difference ellipsoids for surface colors,” Color Res. Appl. 22, 148–155 (1997).
[CrossRef]

Provost, J. R.

E. Coates, S. Day, J. R. Provost, and B. Rigg, “The measurement and assessment of colour differences for industrial use—the accuracy of colour-difference equations,” J. Soc. Dyers Colour. 88, 69–75 (1972).
[CrossRef]

E. Coates, S. Day, J. R. Provost, and B. Rigg, “The measurement and assessment of colour differences for industrial use III. Method of scaling visual assessments,” J. Soc. Dyers Colour. 88, 186–190 (1972).
[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]

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

G. Cui, M. R. Luo, B. Rigg, and W. Li, “Colour-difference evaluation using CRT colours. Part II: parametric effects,” Color Res. Appl. 26, 403–412 (2001).
[CrossRef]

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

F. J. J. Clarke, R. McDonald, and B. Rigg, “Modification to the JPC79 colour-difference formula,” J. Soc. Dyers Colour. 100, 128–132 (1984).
[CrossRef]

E. Coates, S. Day, J. R. Provost, and B. Rigg, “The measurement and assessment of colour differences for industrial use III. Method of scaling visual assessments,” J. Soc. Dyers Colour. 88, 186–190 (1972).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Distributions of prepared color centers in CIELAB (a) a10*b10* plane and (b) Cab,10*L10* plane.

Fig. 2.
Fig. 2.

Distribution of CIELAB ΔEab,10* for the 893 pairs studied.

Fig. 3.
Fig. 3.

Distributions of color differences in CIELAB (a) Δa10*Δb10* and (b) ΔCab,10*ΔL10* for the yellow color center.

Fig. 4.
Fig. 4.

Relationship between the systematic error and slope (f) and intercept (b).

Fig. 5.
Fig. 5.

Correlation between visual assessment (z-score) and CIELAB ΔEab,10* value for the gray center.

Fig. 6.
Fig. 6.

CIELAB a10*b10* chromaticity ellipses from two different studies: the threshold color-difference ellipses fitted to data reported in the current paper, TCD (solid curve), and the SCD ellipses from data in a previous paper [28], SCD (dotted curve).

Fig. 7.
Fig. 7.

Chromaticity ellipses plotted in different uniform color spaces: (a) CAM02-SCD, (b) CAM02-UCS, (c) DIN99d, (d) OSA, and (e) OSA-Gp-Eu. The semiaxes of all these ellipses were enlarged three times, except for OSA space.

Tables (8)

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Table 1. Measured CIELAB Values for the 17 Color Centers Studied

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Table 2. Intra- and Inter-Variability of Each Observer in WD% Units

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Table 3. Performance of Different Color-Difference Formulae in Terms of STRESS

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Table 4. F-Test of the Color-Difference Formulae (FC=0.88, 1/FC=1.14)

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Table 5. Performance of Original and Optimized Color-Difference Formulae (FC=0.88, 1/FC=1.14)

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Table 6. Parameters of the Chromaticity Ellipses Fitted to the Experimental Results Reported in This Paper, for the 17 CIE Color Centers in the a10*b10* Plane

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Table 7. Comparing Ellipses Fitted to TCDs and SCDs for the 17 CIE Color Centers in Terms of STRESS Value

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Table 8. Comparison of Local and Global Uniformity of Our Experimental TCD Ellipses in Six Color Spaces

Equations (9)

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

STRESS=100(ΔVif1ΔEi)2ΔVi2withf1=ΔEiΔViΔEi2,
STRESS=100(ΔEif2ΔVi)2ΔEi2withf2=ΔEiΔViΔVi2,
STRESS=100(ΔEif3ΔVi)2f32ΔVi2withf3=1f1=ΔEi2ΔEiΔVi,
STRESS=100(ΔVif4ΔEi)2f42ΔEi2withf4=1f2=ΔVi2ΔEiΔVi,
STRESS=1001(ΔEiΔVi)2ΔEi2ΔVi2,
e=1001[ΔVi(fΔVi+b)]2ΔVi2(fΔVi+b)2.
VM=i=1N(ΔVifMΔEMi)2/(N1)M{A,B},
F=VAVB=(ΔVifAΔEAi)2(ΔVifBΔEBi)2=STRESSA2STRESSB2.
ΔE2=g11Δa10*2+2g12Δa10*Δb10*+g22Δb10*2+g33ΔL10*2,

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