Abstract

Threshold-discrimination ellipses were obtained by three normal observers, at five color centers, by the use of two experimental devices, which provided light–surface colors, and the same method and experimental conditions. The ellipses obtained for each center in both devices were quite similar when the sample distributions were appropriate and slightly smaller for object color than for aperture color. The ellipses predicted by three recent color-difference formulas based on the CIE uniform color space (CIELAB) were compared with those experimentally obtained by us as well as by other researchers who analyzed a greater number of color centers. The color-difference formula proposed by the CIE Technical Committee 1-29 [Color Res. Appl. 18, 137 (1993)] provides the best prediction of the semiaxis relationship for all the experimental datasets used, confirming their good performance in previous works [Appl. Opt. 33, 8069 (1993)], although the differences with respect to the experimental results are higher than those attributable to the interobserver variability.

© 1996 Optical Society of America

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  37. M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-discrimination thresholds from the CIE (x, y, Y) space to the CIE 1976 (L*, a*, b*),” Color Res. Appl. 19, 10–18 (1994).
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1994 (3)

K. Witt, “Modified CIELAB formula tested using a textile pass/fail data set,” Color Res. Appl. 19, 273–276 (1994).
[CrossRef]

M. Melgosa, J. J. Quesada, E. Hita, “Uniformity of some recent color metrics tested with an accurate color-difference tolerance dataset,” Appl. Opt. 33, 8069–8077 (1994).
[CrossRef] [PubMed]

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-discrimination thresholds from the CIE (x, y, Y) space to the CIE 1976 (L*, a*, b*),” Color Res. Appl. 19, 10–18 (1994).

1993 (1)

D. H. Alman, “CIE Technical Committee 1-29, Industrial color-difference evaluation progress report,” Color Res. Appl. 18, 137–139 (1993).
[CrossRef]

1992 (2)

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Some classical color differences calculated with new formulas,” J. Opt. Soc. Am. A 9, 1247–1253 (1992).
[CrossRef]

T. Indow, A. R. Robertson, M. von Grunau, G. H. Fielder, “Discrimination ellipsoids of aperture and simulated surface colors by matching and paired comparison,” Color Res. Appl. 17, 6–23 (1992).
[CrossRef]

1991 (1)

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

1990 (3)

M. Melgosa, E. Hita, L. Jiménez del Barco, J. Romero, “Comparative analysis of colour discrimination data obtained with aperture-colours and surface-colours,” J. Opt. 21, 223– 231 (1990).
[CrossRef]

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-difference formulae,” Opt. Pur. Apl. 23, 137–145 (1990).

R. G. Kuehni, “Industrial color-difference: progress and problems,” Color Res. Appl. 15, 261–265 (1990).
[CrossRef]

1988 (1)

1987 (2)

M. R. Luo, B. Rigg, “BFD(l:c) colour-difference formula. Part 1. Development of the formula,” J. Soc. Dyers Colour. 103, 86–94 (1987).
[CrossRef]

K. Witt, “Three-dimensional threshold of color-difference perceptibility in painted samples: variability of observers in four CIE color regions,” Color Res. Appl. 12, 128–134 (1987).
[CrossRef]

1986 (3)

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

M. Cheung, B. Rigg, “Colour-difference ellipsoids for five CIE colourcentres,” Color Res. Appl. 11, 185–195 (1986).
[CrossRef]

E. Hita, L. Jiménez del Barco, J. Romero, “Differential color thresholds from metameric matches: experimental results concerning failures of colorimetric additivity,” J. Opt. Soc. Am. A 3, 1203–1209 (1986).
[CrossRef] [PubMed]

1985 (1)

D. L. MacAdam, “Metric coefficients for CIE color-difference formulas,” Color Res. Appl. 10, 45–49 (1985).
[CrossRef]

1984 (1)

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

1983 (1)

K. Witt, G. Döring, “Parametric variations in a threshold color-difference ellipsoid for green painted samples,” Color Res. Appl. 8, 153–163 (1983).
[CrossRef]

1982 (3)

R. McDonald, “A review of the relationship between visual and instrumental assessment of colour difference, part 1,” J. Oil Colour Chem. Assoc. 65, 43–53 (1982);“A review of the relationship between visual and instrumental assessment of color difference, part 2,” J. Oil Colour Chem. Assoc. 65, 93–106 (1982).

C. Alder, K. P. Chaing, T. F. Chong, E. Coates, A. A. Khalili, B. Rigg, “Uniform chromaticity scales—new experimental data,” J. Soc. Dyers Colour. 98, 14–20 (1982).
[CrossRef]

E. Hita, J. Romero, L. Jiménez del Barco, R. Martínez, “Temporal aspects of color discrimination,” J. Opt. Soc. Am. 72, 578–582 (1982).
[CrossRef] [PubMed]

1978 (1)

A. R. Robertson, “CIE guidelines for coordinated research on colour-difference evaluation,” Color Res. Appl. 3, 149–151 (1978).

1971 (1)

1959 (1)

1957 (1)

1952 (1)

W. H. Kruskal, W. A. Wallis, “Use of ranks in one-criterion variance analysis,” J. Am. Stat. Assoc. 47, 583–621 (1952).
[CrossRef]

1949 (1)

1942 (1)

Alder, C.

C. Alder, K. P. Chaing, T. F. Chong, E. Coates, A. A. Khalili, B. Rigg, “Uniform chromaticity scales—new experimental data,” J. Soc. Dyers Colour. 98, 14–20 (1982).
[CrossRef]

Alman, D. H.

D. H. Alman, “CIE Technical Committee 1-29, Industrial color-difference evaluation progress report,” Color Res. Appl. 18, 137–139 (1993).
[CrossRef]

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

Alman, D.H.

“Industrialcolour-difference evaluation,” CIE Pub. 116D.H. Alman, chairman (CIE Central Bureau, Vienna, 1995).

Balonon-Rosen, M. R.

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

Berns, R. S.

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

Brown, W. R. J.

Chaing, K. P.

C. Alder, K. P. Chaing, T. F. Chong, E. Coates, A. A. Khalili, B. Rigg, “Uniform chromaticity scales—new experimental data,” J. Soc. Dyers Colour. 98, 14–20 (1982).
[CrossRef]

Cheung, M.

M. Cheung, B. Rigg, “Colour-difference ellipsoids for five CIE colourcentres,” Color Res. Appl. 11, 185–195 (1986).
[CrossRef]

Chong, T. F.

C. Alder, K. P. Chaing, T. F. Chong, E. Coates, A. A. Khalili, B. Rigg, “Uniform chromaticity scales—new experimental data,” J. Soc. Dyers Colour. 98, 14–20 (1982).
[CrossRef]

Clarke, F. J. J.

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

Coates, E.

C. Alder, K. P. Chaing, T. F. Chong, E. Coates, A. A. Khalili, B. Rigg, “Uniform chromaticity scales—new experimental data,” J. Soc. Dyers Colour. 98, 14–20 (1982).
[CrossRef]

Cruz, A.

A. Cruz, “Proyecto, construcción y puesta a punto de un colorímetro de estímulose spectrales. Determinación de las funciones de mezcla de colores para observadores espanoles,” Ph.D. dissertation (Universidad de Madrid, Madrid, 1962).
[PubMed]

Döring, G.

K. Witt, G. Döring, “Parametric variations in a threshold color-difference ellipsoid for green painted samples,” Color Res. Appl. 8, 153–163 (1983).
[CrossRef]

Fielder, G. H.

T. Indow, A. R. Robertson, M. von Grunau, G. H. Fielder, “Discrimination ellipsoids of aperture and simulated surface colors by matching and paired comparison,” Color Res. Appl. 17, 6–23 (1992).
[CrossRef]

Fielder, G. M.

García-Beltrán, A.

M. Melgosa, M. M. Pérez, J. A. Martínez, A. García-Beltrán, “Coeficientes métricos asociados a las fórmulas de diferencia de color CMC(l:c) y BFD(l:c),” in Proceedings of the Second Congreso Nacional de Color (Sociedad Espanola de Optica, Madrid, Spain, 1991), pp. 166–171.

Hita, E.

M. Melgosa, J. J. Quesada, E. Hita, “Uniformity of some recent color metrics tested with an accurate color-difference tolerance dataset,” Appl. Opt. 33, 8069–8077 (1994).
[CrossRef] [PubMed]

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-discrimination thresholds from the CIE (x, y, Y) space to the CIE 1976 (L*, a*, b*),” Color Res. Appl. 19, 10–18 (1994).

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Some classical color differences calculated with new formulas,” J. Opt. Soc. Am. A 9, 1247–1253 (1992).
[CrossRef]

M. Melgosa, E. Hita, L. Jiménez del Barco, J. Romero, “Comparative analysis of colour discrimination data obtained with aperture-colours and surface-colours,” J. Opt. 21, 223– 231 (1990).
[CrossRef]

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-difference formulae,” Opt. Pur. Apl. 23, 137–145 (1990).

L. Jiménez del Barco, E. Hita, J. Romero, J. Vida, “Color-prediction discrepancies and differential chromaticity thresholds with photopigment bleaching,” J. Opt. Soc. Am. A 5, 432–437 (1988).
[CrossRef] [PubMed]

E. Hita, L. Jiménez del Barco, J. Romero, “Differential color thresholds from metameric matches: experimental results concerning failures of colorimetric additivity,” J. Opt. Soc. Am. A 3, 1203–1209 (1986).
[CrossRef] [PubMed]

E. Hita, J. Romero, L. Jiménez del Barco, R. Martínez, “Temporal aspects of color discrimination,” J. Opt. Soc. Am. 72, 578–582 (1982).
[CrossRef] [PubMed]

M. Melgosa, M. M. Pérez, L. Jiménez del Barco, E. Hita, “A test of TC1-29 color-difference formula using some classical datasets (preliminary report),” in Proceedings of the European Optical Society Annual Meeting (EOSAM 93), (Universidad de Zaragoza, Zaragoza, Spain1993), Vol. 3, pp. 37–38.

Indow, T.

T. Indow, A. R. Robertson, M. von Grunau, G. H. Fielder, “Discrimination ellipsoids of aperture and simulated surface colors by matching and paired comparison,” Color Res. Appl. 17, 6–23 (1992).
[CrossRef]

Jiménez del Barco, L.

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-discrimination thresholds from the CIE (x, y, Y) space to the CIE 1976 (L*, a*, b*),” Color Res. Appl. 19, 10–18 (1994).

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Some classical color differences calculated with new formulas,” J. Opt. Soc. Am. A 9, 1247–1253 (1992).
[CrossRef]

M. Melgosa, E. Hita, L. Jiménez del Barco, J. Romero, “Comparative analysis of colour discrimination data obtained with aperture-colours and surface-colours,” J. Opt. 21, 223– 231 (1990).
[CrossRef]

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-difference formulae,” Opt. Pur. Apl. 23, 137–145 (1990).

L. Jiménez del Barco, E. Hita, J. Romero, J. Vida, “Color-prediction discrepancies and differential chromaticity thresholds with photopigment bleaching,” J. Opt. Soc. Am. A 5, 432–437 (1988).
[CrossRef] [PubMed]

E. Hita, L. Jiménez del Barco, J. Romero, “Differential color thresholds from metameric matches: experimental results concerning failures of colorimetric additivity,” J. Opt. Soc. Am. A 3, 1203–1209 (1986).
[CrossRef] [PubMed]

E. Hita, J. Romero, L. Jiménez del Barco, R. Martínez, “Temporal aspects of color discrimination,” J. Opt. Soc. Am. 72, 578–582 (1982).
[CrossRef] [PubMed]

M. Melgosa, M. M. Pérez, L. Jiménez del Barco, E. Hita, “A test of TC1-29 color-difference formula using some classical datasets (preliminary report),” in Proceedings of the European Optical Society Annual Meeting (EOSAM 93), (Universidad de Zaragoza, Zaragoza, Spain1993), Vol. 3, pp. 37–38.

Khalili, A. A.

C. Alder, K. P. Chaing, T. F. Chong, E. Coates, A. A. Khalili, B. Rigg, “Uniform chromaticity scales—new experimental data,” J. Soc. Dyers Colour. 98, 14–20 (1982).
[CrossRef]

Kruskal, W. H.

W. H. Kruskal, W. A. Wallis, “Use of ranks in one-criterion variance analysis,” J. Am. Stat. Assoc. 47, 583–621 (1952).
[CrossRef]

Kuehni, R. G.

R. G. Kuehni, “Industrial color-difference: progress and problems,” Color Res. Appl. 15, 261–265 (1990).
[CrossRef]

Luo, M. R.

M. R. Luo, B. Rigg, “BFD(l:c) colour-difference formula. Part 1. Development of the formula,” J. Soc. Dyers Colour. 103, 86–94 (1987).
[CrossRef]

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

MacAdam, D. L.

MacAdam, D.L.

D.L. MacAdam, Color Measurement, Vol. 27 of the Springer Series on Optical Sciences (Springer-Verlag, Berlin, 1981), Chap. 8.

Martínez, J. A.

M. Melgosa, M. M. Pérez, J. A. Martínez, A. García-Beltrán, “Coeficientes métricos asociados a las fórmulas de diferencia de color CMC(l:c) y BFD(l:c),” in Proceedings of the Second Congreso Nacional de Color (Sociedad Espanola de Optica, Madrid, Spain, 1991), pp. 166–171.

Martínez, R.

McDonald, R.

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

R. McDonald, “A review of the relationship between visual and instrumental assessment of colour difference, part 1,” J. Oil Colour Chem. Assoc. 65, 43–53 (1982);“A review of the relationship between visual and instrumental assessment of color difference, part 2,” J. Oil Colour Chem. Assoc. 65, 93–106 (1982).

Melgosa, M.

M. Melgosa, J. J. Quesada, E. Hita, “Uniformity of some recent color metrics tested with an accurate color-difference tolerance dataset,” Appl. Opt. 33, 8069–8077 (1994).
[CrossRef] [PubMed]

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-discrimination thresholds from the CIE (x, y, Y) space to the CIE 1976 (L*, a*, b*),” Color Res. Appl. 19, 10–18 (1994).

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Some classical color differences calculated with new formulas,” J. Opt. Soc. Am. A 9, 1247–1253 (1992).
[CrossRef]

M. Melgosa, E. Hita, L. Jiménez del Barco, J. Romero, “Comparative analysis of colour discrimination data obtained with aperture-colours and surface-colours,” J. Opt. 21, 223– 231 (1990).
[CrossRef]

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-difference formulae,” Opt. Pur. Apl. 23, 137–145 (1990).

M. Melgosa, M. M. Pérez, J. A. Martínez, A. García-Beltrán, “Coeficientes métricos asociados a las fórmulas de diferencia de color CMC(l:c) y BFD(l:c),” in Proceedings of the Second Congreso Nacional de Color (Sociedad Espanola de Optica, Madrid, Spain, 1991), pp. 166–171.

M. Melgosa, M. M. Pérez, L. Jiménez del Barco, E. Hita, “A test of TC1-29 color-difference formula using some classical datasets (preliminary report),” in Proceedings of the European Optical Society Annual Meeting (EOSAM 93), (Universidad de Zaragoza, Zaragoza, Spain1993), Vol. 3, pp. 37–38.

Pérez, M. M.

M. Melgosa, M. M. Pérez, L. Jiménez del Barco, E. Hita, “A test of TC1-29 color-difference formula using some classical datasets (preliminary report),” in Proceedings of the European Optical Society Annual Meeting (EOSAM 93), (Universidad de Zaragoza, Zaragoza, Spain1993), Vol. 3, pp. 37–38.

M. Melgosa, M. M. Pérez, J. A. Martínez, A. García-Beltrán, “Coeficientes métricos asociados a las fórmulas de diferencia de color CMC(l:c) y BFD(l:c),” in Proceedings of the Second Congreso Nacional de Color (Sociedad Espanola de Optica, Madrid, Spain, 1991), pp. 166–171.

M. M. Pérez, “Determinación experimental de umbrales de discriminación cromática bajo distintos modos de presentación: adecuación a recientes fórmulas de diferencia de color,” Ph.D. dissertation (Universidad de Granada, Granada, 1994).

Quesada, J. J.

Reniff, L.

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

Rigg, B.

M. R. Luo, B. Rigg, “BFD(l:c) colour-difference formula. Part 1. Development of the formula,” J. Soc. Dyers Colour. 103, 86–94 (1987).
[CrossRef]

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

M. Cheung, B. Rigg, “Colour-difference ellipsoids for five CIE colourcentres,” Color Res. Appl. 11, 185–195 (1986).
[CrossRef]

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

C. Alder, K. P. Chaing, T. F. Chong, E. Coates, A. A. Khalili, B. Rigg, “Uniform chromaticity scales—new experimental data,” J. Soc. Dyers Colour. 98, 14–20 (1982).
[CrossRef]

Robertson, A. R.

T. Indow, A. R. Robertson, M. von Grunau, G. H. Fielder, “Discrimination ellipsoids of aperture and simulated surface colors by matching and paired comparison,” Color Res. Appl. 17, 6–23 (1992).
[CrossRef]

A. R. Robertson, “CIE guidelines for coordinated research on colour-difference evaluation,” Color Res. Appl. 3, 149–151 (1978).

Romero, J.

Sachs, L.

L. Sachs, Applied Statistics, Springer Series on Statistics (Springer-Verlag, New York, 1982).
[CrossRef]

Snyder, G. D.

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

Stiles, W.S.

G. Wyszecki, W.S. Stiles, Color Science, 2nd ed. (Wiley, New York, 1982), Tables 2 (5.4.1), I (5.4.2), II (5.4.2), and I (5.4.3).

Vida, J.

von Grunau, M.

T. Indow, A. R. Robertson, M. von Grunau, G. H. Fielder, “Discrimination ellipsoids of aperture and simulated surface colors by matching and paired comparison,” Color Res. Appl. 17, 6–23 (1992).
[CrossRef]

Wallis, W. A.

W. H. Kruskal, W. A. Wallis, “Use of ranks in one-criterion variance analysis,” J. Am. Stat. Assoc. 47, 583–621 (1952).
[CrossRef]

Witt, K.

K. Witt, “Modified CIELAB formula tested using a textile pass/fail data set,” Color Res. Appl. 19, 273–276 (1994).
[CrossRef]

K. Witt, “Three-dimensional threshold of color-difference perceptibility in painted samples: variability of observers in four CIE color regions,” Color Res. Appl. 12, 128–134 (1987).
[CrossRef]

K. Witt, G. Döring, “Parametric variations in a threshold color-difference ellipsoid for green painted samples,” Color Res. Appl. 8, 153–163 (1983).
[CrossRef]

“Parametric effects in colour-difference evaluation,” CIE Pub. 101, K. Witt, chairman (CIE Central Bureau, Vienna, 1993).

Wyszecki, G.

G. Wyszecki, G. M. Fielder, “New color matching ellipses,” J. Opt. Soc. Am. 61, 1135–1152 (1971).
[CrossRef] [PubMed]

G. Wyszecki, “Propagation of errors in colorimetric transformations,” J. Opt. Soc. Am. 49, 389–393 (1959).
[CrossRef]

G. Wyszecki, “Current developments in Colorimetry,” in Proceedings of AIC Colour'73 (American Institute of Chemists, Bethesda, Md., 1973), pp. 25–51.

G. Wyszecki, W.S. Stiles, Color Science, 2nd ed. (Wiley, New York, 1982), Tables 2 (5.4.1), I (5.4.2), II (5.4.2), and I (5.4.3).

Appl. Opt. (1)

Color Res. Appl. (12)

D. H. Alman, “CIE Technical Committee 1-29, Industrial color-difference evaluation progress report,” Color Res. Appl. 18, 137–139 (1993).
[CrossRef]

A. R. Robertson, “CIE guidelines for coordinated research on colour-difference evaluation,” Color Res. Appl. 3, 149–151 (1978).

M. Cheung, B. Rigg, “Colour-difference ellipsoids for five CIE colourcentres,” Color Res. Appl. 11, 185–195 (1986).
[CrossRef]

K. Witt, G. Döring, “Parametric variations in a threshold color-difference ellipsoid for green painted samples,” Color Res. Appl. 8, 153–163 (1983).
[CrossRef]

K. Witt, “Three-dimensional threshold of color-difference perceptibility in painted samples: variability of observers in four CIE color regions,” Color Res. Appl. 12, 128–134 (1987).
[CrossRef]

K. Witt, “Modified CIELAB formula tested using a textile pass/fail data set,” Color Res. Appl. 19, 273–276 (1994).
[CrossRef]

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

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

T. Indow, A. R. Robertson, M. von Grunau, G. H. Fielder, “Discrimination ellipsoids of aperture and simulated surface colors by matching and paired comparison,” Color Res. Appl. 17, 6–23 (1992).
[CrossRef]

R. G. Kuehni, “Industrial color-difference: progress and problems,” Color Res. Appl. 15, 261–265 (1990).
[CrossRef]

D. L. MacAdam, “Metric coefficients for CIE color-difference formulas,” Color Res. Appl. 10, 45–49 (1985).
[CrossRef]

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-discrimination thresholds from the CIE (x, y, Y) space to the CIE 1976 (L*, a*, b*),” Color Res. Appl. 19, 10–18 (1994).

J. Am. Stat. Assoc. (1)

W. H. Kruskal, W. A. Wallis, “Use of ranks in one-criterion variance analysis,” J. Am. Stat. Assoc. 47, 583–621 (1952).
[CrossRef]

J. Oil Colour Chem. Assoc. (1)

R. McDonald, “A review of the relationship between visual and instrumental assessment of colour difference, part 1,” J. Oil Colour Chem. Assoc. 65, 43–53 (1982);“A review of the relationship between visual and instrumental assessment of color difference, part 2,” J. Oil Colour Chem. Assoc. 65, 93–106 (1982).

J. Opt. (1)

M. Melgosa, E. Hita, L. Jiménez del Barco, J. Romero, “Comparative analysis of colour discrimination data obtained with aperture-colours and surface-colours,” J. Opt. 21, 223– 231 (1990).
[CrossRef]

J. Opt. Soc. Am. (6)

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

J. Soc. Dyers Colour. (3)

C. Alder, K. P. Chaing, T. F. Chong, E. Coates, A. A. Khalili, B. Rigg, “Uniform chromaticity scales—new experimental data,” J. Soc. Dyers Colour. 98, 14–20 (1982).
[CrossRef]

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

M. R. Luo, B. Rigg, “BFD(l:c) colour-difference formula. Part 1. Development of the formula,” J. Soc. Dyers Colour. 103, 86–94 (1987).
[CrossRef]

Opt. Pur. Apl. (1)

M. Melgosa, E. Hita, J. Romero, L. Jiménez del Barco, “Color-difference formulae,” Opt. Pur. Apl. 23, 137–145 (1990).

Other (12)

PhotoResearch PR-704 SpectraScan Operating Manual, Division of Kollmorgen Instruments Corporation, 9330 De Soto Avenue, P.O. Box 2192, Chatsworth, Calif. 91313-2192.

“Colorimetry,” CIE Pub. 15.2, 2nd ed. (CIE Central Bureau, Vienna, 1986), Sect. 1.4

A. Cruz, “Proyecto, construcción y puesta a punto de un colorímetro de estímulose spectrales. Determinación de las funciones de mezcla de colores para observadores espanoles,” Ph.D. dissertation (Universidad de Madrid, Madrid, 1962).
[PubMed]

D.L. MacAdam, Color Measurement, Vol. 27 of the Springer Series on Optical Sciences (Springer-Verlag, Berlin, 1981), Chap. 8.

M. Melgosa, M. M. Pérez, J. A. Martínez, A. García-Beltrán, “Coeficientes métricos asociados a las fórmulas de diferencia de color CMC(l:c) y BFD(l:c),” in Proceedings of the Second Congreso Nacional de Color (Sociedad Espanola de Optica, Madrid, Spain, 1991), pp. 166–171.

L. Sachs, Applied Statistics, Springer Series on Statistics (Springer-Verlag, New York, 1982).
[CrossRef]

M. Melgosa, M. M. Pérez, L. Jiménez del Barco, E. Hita, “A test of TC1-29 color-difference formula using some classical datasets (preliminary report),” in Proceedings of the European Optical Society Annual Meeting (EOSAM 93), (Universidad de Zaragoza, Zaragoza, Spain1993), Vol. 3, pp. 37–38.

G. Wyszecki, W.S. Stiles, Color Science, 2nd ed. (Wiley, New York, 1982), Tables 2 (5.4.1), I (5.4.2), II (5.4.2), and I (5.4.3).

G. Wyszecki, “Current developments in Colorimetry,” in Proceedings of AIC Colour'73 (American Institute of Chemists, Bethesda, Md., 1973), pp. 25–51.

“Industrialcolour-difference evaluation,” CIE Pub. 116D.H. Alman, chairman (CIE Central Bureau, Vienna, 1995).

M. M. Pérez, “Determinación experimental de umbrales de discriminación cromática bajo distintos modos de presentación: adecuación a recientes fórmulas de diferencia de color,” Ph.D. dissertation (Universidad de Granada, Granada, 1994).

“Parametric effects in colour-difference evaluation,” CIE Pub. 101, K. Witt, chairman (CIE Central Bureau, Vienna, 1993).

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Figures (4)

Fig. 1
Fig. 1

Schematic view of the Wright visual colorimeter used. See text for notation used.

Fig. 2
Fig. 2

Comparison of the semiaxis relationships, orientations, and areas of the threshold ellipses obtained by observer MP in experiments 1 and 2.

Fig. 3
Fig. 3

Same as Fig. 2, but for experiments 3 and 4.

Fig. 4
Fig. 4

Same as Fig. 2, but for experiments 1 and 3.

Tables (6)

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Table 1 Experimental Ellipses in the CIE x, y Diagram for our Three Observers and the Four Experiments Performed

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Table 2 Mean Values x ̄ and Standard Deviations σ of the Differences between the Main Parameters of the x, y Ellipses Obtained by Observers FC and MP

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Table 3 Average Differences of the Results Predicted by Three Color-Difference Formulas and Our Experimental Results

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Table 4 Same as Table 3, but for Other Experimental Results Obtained with Aperture and Object Colors

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Table 5 Statistical Significance from the U-Test for the Differences between Predicted and Measured Semiaxis Relationships in Several Datasets

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Table 6 Same as Table 5 but for Predicted and Measured Areas

Equations (13)

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

Δ E CMC = [ ( Δ L * / l S 1 ) 2 + ( Δ C * / c S c ) 2 + ( Δ H * / S h ) 2 ] 1 / 2 ,
Δ E BFD = [ ( Δ L BFD / l ) 2 + ( Δ C * / c D c ) 2 + ( Δ H * / D h ) 2 + ( R t Δ C * Δ H * / D c D h ) 2 ] 1 / 2 ,
Δ E 94 * = [ ( Δ L * / K 1 T 1 ) 2 + ( Δ C * / K c T c ) 2 + ( Δ H * / K h T h ) 2 ] 1 / 2 .
Δ E = [ b 11 ( Δ a * ) 2 + b 22 ( Δ b * ) 2 + 2 b 12 ( Δ a * ) ( Δ b * ) + 2 b 13 ( Δ a * ) ( Δ L * ) + 2 b 23 ( Δ b * ) ( Δ L * ) + b 33 ( Δ L * ) 2 ] 1 / 2 ,
x ̄
x ̄
x ̄
x ̄
x ̄
b 11 = b 22 = b 33 = 1 , b 12 = b 13 = b 23 = 0.
b 11 = 1 C * 2 ( a * 2 S c 2 + b * 2 S c 2 ) , b 22 = 1 C * 2 ( b * 2 S c 2 + a * 2 S h 2 ) , b 12 = a * b * C * 2 ( 1 S c 2 - 1 S h 2 ) , b 33 = 1 l 2 S 1 2 , b 13 = b 23 = 0 .
b 11 = 1 C * 2 ( a * 2 D c 2 + b * 2 D h 2 - R t a * b * C * D c D h ) , b 22 = 1 C * 2 ( b * 2 D c 2 + a * 2 D h 2 + R t a * b * C * D c D h ) , b 12 = 1 C * 2 [ a * b * ( 1 D c 2 - 1 D h 2 ) + R t ( a * 2 - b * 2 ) 2 C * D c D h ] , b 33 = ( { 0.613 Y 0 [ ( L * + 16 ) / 116 ] 2 } / { 1.5 + Y 0 [ ( L * + 16 ) / 116 ] 3 } ) 2 , b 13 = b 23 = 0 .
b 11 = 1 C * 2 ( a * 2 T c 2 + b * 2 T h 2 ) , b 22 = 1 C * 2 ( b * 2 T c 2 + a * 2 T h 2 ) , b 12 = a * b * C * 2 ( 1 T c 2 - 1 T h 2 ) , b 33 = 1 K 1 2 T 1 2 , b 13 = b 23 = 0 .

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