Abstract

A set of five color difference formulas, cdf-G*, one for each of five regions of the CIE1931 chromatic diagram, is proposed and compared with the CIELUV, CIELAB, and LABNHU formulas. The cdf-G* formulas fit more closely several sets of color difference data. They are useful for color difference applications.

© 1989 Optical Society of America

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References

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  1. M. R. Pointer, “A Comparison of the CIE 1976 Color Spaces,” Color Res. Appl. 6, 108–118 (1981).
    [CrossRef]
  2. E. Hita, J. Romero, L. Jimenez del Barco, A. Carrillo, “Uniform Color Spaces. A Comparative Analysis for Color Discrimination Data,” Die Farbe 31, (4–6), 229–242 (1983–84).
  3. R. G. Kuehni, “Advances in Color-Difference Formulas,” Color Res. Appl. 7, 19–23 (1982).
    [CrossRef]
  4. D. L. MacAdam, “Metric Coefficients for CIE Color-Difference Formulas,” Color Res. Appl. 10, 45–49 (1985).
    [CrossRef]
  5. K. Richter, “Cube-Root Color Spaces and Chromatic Adaptation,” Color Res. Appl. 5, 25–43 (1980).
    [CrossRef]
  6. K. D. Chickering, “Optimization of the MacAdam-Modified 1965 Friele Color-Difference Formula,” J. Opt. Soc. Am. 57, 537–541 (1967).
    [CrossRef] [PubMed]
  7. D. L. MacAdam, “Specification of Small Chromaticity Differences in Daylight,” J. Opt. Soc. Am. 33, 18–26 (1943).
    [CrossRef]
  8. D. L. MacAdam, “Visual Sensitivities to Color Differences in Daylight,” J. Opt. Soc. Am. 32, 247–274 (1942).
    [CrossRef]
  9. W. R. J. Brown, D. L. MacAdam, “Visual Sensitivities to Combined Chromaticity and Luminance Differences,” J. Opt. Soc. Am. 39, 808–834 (1949).
    [CrossRef] [PubMed]
  10. G. Wyszecki, G. M. Fielder, “New Color-Matching Ellipses,” J. Opt. Soc. Am. 61, 1135–1152 (1971).
    [CrossRef] [PubMed]
  11. A. R. Robertson, “CIE Guidelines for Coordinated Research on Color-Difference Evaluation,” Color Res. Appl. 3, 149–151 (1978).

1985 (1)

D. L. MacAdam, “Metric Coefficients for CIE Color-Difference Formulas,” Color Res. Appl. 10, 45–49 (1985).
[CrossRef]

1982 (1)

R. G. Kuehni, “Advances in Color-Difference Formulas,” Color Res. Appl. 7, 19–23 (1982).
[CrossRef]

1981 (1)

M. R. Pointer, “A Comparison of the CIE 1976 Color Spaces,” Color Res. Appl. 6, 108–118 (1981).
[CrossRef]

1980 (1)

K. Richter, “Cube-Root Color Spaces and Chromatic Adaptation,” Color Res. Appl. 5, 25–43 (1980).
[CrossRef]

1978 (1)

A. R. Robertson, “CIE Guidelines for Coordinated Research on Color-Difference Evaluation,” Color Res. Appl. 3, 149–151 (1978).

1971 (1)

1967 (1)

1949 (1)

1943 (1)

1942 (1)

Brown, W. R. J.

Carrillo, A.

E. Hita, J. Romero, L. Jimenez del Barco, A. Carrillo, “Uniform Color Spaces. A Comparative Analysis for Color Discrimination Data,” Die Farbe 31, (4–6), 229–242 (1983–84).

Chickering, K. D.

Fielder, G. M.

Hita, E.

E. Hita, J. Romero, L. Jimenez del Barco, A. Carrillo, “Uniform Color Spaces. A Comparative Analysis for Color Discrimination Data,” Die Farbe 31, (4–6), 229–242 (1983–84).

Jimenez del Barco, L.

E. Hita, J. Romero, L. Jimenez del Barco, A. Carrillo, “Uniform Color Spaces. A Comparative Analysis for Color Discrimination Data,” Die Farbe 31, (4–6), 229–242 (1983–84).

Kuehni, R. G.

R. G. Kuehni, “Advances in Color-Difference Formulas,” Color Res. Appl. 7, 19–23 (1982).
[CrossRef]

MacAdam, D. L.

Pointer, M. R.

M. R. Pointer, “A Comparison of the CIE 1976 Color Spaces,” Color Res. Appl. 6, 108–118 (1981).
[CrossRef]

Richter, K.

K. Richter, “Cube-Root Color Spaces and Chromatic Adaptation,” Color Res. Appl. 5, 25–43 (1980).
[CrossRef]

Robertson, A. R.

A. R. Robertson, “CIE Guidelines for Coordinated Research on Color-Difference Evaluation,” Color Res. Appl. 3, 149–151 (1978).

Romero, J.

E. Hita, J. Romero, L. Jimenez del Barco, A. Carrillo, “Uniform Color Spaces. A Comparative Analysis for Color Discrimination Data,” Die Farbe 31, (4–6), 229–242 (1983–84).

Wyszecki, G.

Color Res. Appl. (5)

R. G. Kuehni, “Advances in Color-Difference Formulas,” Color Res. Appl. 7, 19–23 (1982).
[CrossRef]

D. L. MacAdam, “Metric Coefficients for CIE Color-Difference Formulas,” Color Res. Appl. 10, 45–49 (1985).
[CrossRef]

K. Richter, “Cube-Root Color Spaces and Chromatic Adaptation,” Color Res. Appl. 5, 25–43 (1980).
[CrossRef]

A. R. Robertson, “CIE Guidelines for Coordinated Research on Color-Difference Evaluation,” Color Res. Appl. 3, 149–151 (1978).

M. R. Pointer, “A Comparison of the CIE 1976 Color Spaces,” Color Res. Appl. 6, 108–118 (1981).
[CrossRef]

Die Farbe (1)

E. Hita, J. Romero, L. Jimenez del Barco, A. Carrillo, “Uniform Color Spaces. A Comparative Analysis for Color Discrimination Data,” Die Farbe 31, (4–6), 229–242 (1983–84).

J. Opt. Soc. Am. (5)

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Figures (10)

Fig. 1
Fig. 1

CIE1931 chromatic diagram divided into the five regions studied: (1) x = 0.315,y = 0.215; (2) x = 0.222,y = 0.302; (3) x = 0.390,y = 0.445; (4) x = 0.490,y = 0.385; (5) x = 0.310,y = 0.150; (6) x = 0.230,y = 0.205; (7) x = 0.125,y = 0.275; (8) x = 0.300,y = 0.400; (9) x = 0.420,y = 0.500; (10) x = 0.450,y = 0.450; (11) x = 0.550,y = 0.380; (12) x = 0.400,y = 0.325.

Fig. 2
Fig. 2

Agreement of the orientations of discrimination ellipses of MacAdam8 with those obtained by use of the indicated formulas.

Fig. 3
Fig. 3

Agreement of the semiaxes ratios of discrimination ellipses of MacAdam8 with those obtained by use of the indicated formulas.

Fig. 4
Fig. 4

Agreement of the areas of discrimination ellipses of MacAdam8 with those obtained by use of the indicated formulas.

Fig. 5
Fig. 5

Agreement of the orientations of discrimination ellipses of Brown and MacAdam9 with those obtained by use of the indicated formulas.

Fig. 6
Fig. 6

Agreement of the semiaxes ratios of discrimination ellipses of Brown and MacAdam9 with those obtained by use of the indicated formulas.

Fig. 7
Fig. 7

Agreement of the areas of discrimination ellipses of Brown and MacAdam9 with those obtained by use of the indicated formulas.

Fig. 8
Fig. 8

Agreement of the orientations of discrimination ellipses of Wyszecki and Fielder10 with those obtained by use of the indicated formulas.

Fig. 9
Fig. 9

Agreement of the semiaxes ratios of discrimination ellipses of Wyszecki and Fielder10 with those obtained by use of the indicated formulas.

Fig. 10
Fig. 10

Agreement of the areas of discrimination ellipses of Wyszecki and Fielder10 with those obtained by use of the indicated formulas.

Tables (3)

Tables Icon

Table I Name Given to Each Formula and Number of Points for Each Regression in the Different Regions of the Chromatic Diagram

Tables Icon

Table II Evaluations of Agreements Between Sets of Discrimination Ellipses and the Different Formulas Analyzed; e 1 2 1 / 2; Mean Square Deviation; d 1 2 1 / 2; Mean Absolute Deviation

Tables Icon

Table III Evaluations of Agreements Between Discrimination Ellipses of MacAdam7 and Those Obtained by the Formulas in the Different Regions Analyzed; e 1 2 1 / 2: Mean Square Deviation. d 1 2 1 / 2: Mean Absolute Deviation

Equations (23)

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g 11 = ( 1047.244 + 34.186 239.130 x y 1967.544 y x + y + 182.493 y x 0.873 x 2 ) 10 4 , 2 g 12 = ( 923.375 1218.056 x 1213.075 x x + y 154.531 y x ) 10 4 , g 22 = [ 802.643 + ( 1835.061 4362.785 x ) y + 5361.953 x 2 + 162.750 x + y + 4.998 y 0.050 y 2 0.422 x 2 ] 10 4 ;
g 11 = ( 79.466 307.984 x + 854.974 x 2 72.313 x y 28.652 x + y 0.648 y x + 4.812 y 2 ) 10 4 , 2 g 12 = ( 16.253 332.176 x + 25.745 x + y + 135.978 x y + 260.266 x y x + y 2.813 x y x y ) 10 4 , g 22 = ( 6.165 + 221.473 x 2 21.788 y x + 11.781 69.955 x x + y + 0.431 x y 0.456 y x 0.006 x 2 + 0.963 y 2 + 2 y 2 ) 10 4 ;
g 11 = ( 231.988 162.962 x 2 34.238 y 13.758 x y ) 10 4 , 2 g 12 = ( 83.127 + 37.493 x + 30.989 y x ) 10 4 , g 22 = ( 27.246 + 49.241 x y ) 10 4 ;
g 11 = ( 126.473 9.132 x y 91.671 + 61.655 y x + 34.631 x 2 ) 10 4 , 2 g 12 = ( 213.375 + 748.080 y 2 946.554 x y 70.755 x + y 12.625 x y 19.740 x 2 ) 10 4 , g 22 = ( 111.684 + 109.355 x 2 108.599 x y 15.181 x y + 2.515 x y 91.057 y x ) 10 4 ;
g 11 = ( 23.146 + 10.532 y 2 ) 10 4 , 2 g 12 = ( 358.385 + 40.111 x 2 222.251 x 14.701 y 2 ) 10 4 , g 22 = ( 2.931 173.461 x 2 + 35.684 y 5.108 x 2 ) 10 4 .
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