Relative significance of the terms in the CIEDE2000 and CIE94 color-difference formulas

Manuel Melgosa, Rafael Huertas, and Roy S. Berns

Manuel Melgosa,^{1} Rafael Huertas,^{1} and Roy S. Berns^{2}

^{1}Departamento de Óptica, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

^{2}Munsell Color Science Laboratory, Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology 54 Lomb Memorial Drive, Rochester, New York 14623-5604 USA

Manuel Melgosa, Rafael Huertas, and Roy S. Berns, "Relative significance of the terms in the CIEDE2000 and CIE94 color-difference formulas," J. Opt. Soc. Am. A 21, 2269-2275 (2004)

CIELAB-based color-difference formulas are used to improve the prediction of visually perceived color differences through the introduction of various corrections to CIELAB. In our study we analyze the relative importance of these corrections. From the combined dataset employed for the development of CIEDE2000, we found that the improvement of CIE94 over CIELAB was considerably greater than that of CIEDE2000 over CIE94. Chroma-difference correction was the most important correction in both CIE94 and CIEDE2000. With an arbitrary value of 100 assigned to this correction, the score of the hue-difference correction in CIE94 was 21, and the scores of the four remaining corrections in CIEDE2000 were as follows: hue difference, 29; rotation term, 8; lightness difference, 8; and gray correction, 6. At 95% confidence level each of the corrections introduced in CIEDE2000 or CIE94 was statistically significant for the whole combined dataset, in agreement with the results reported by CIE TC 1-47 and 1-29. For the combined dataset, the differences between CMC and CIEDE2000 were found to be statistically significant at 95% confidence level, but the differences between CMC and CIE94 were not. From subsets of the combined dataset it was concluded that further analyses of the lightness-difference and gray corrections proposed by CIEDE2000 would be desirable, using new experimental data.

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Number of Color Pairs and Relative Weights (See Text) in the Geographical and Zonal Subsets Constituting the COM Dataset^{
a
}

Geographical Subsets

COM

Zonal Subsets

Lightness

Chroma

Hue

Blue

Gray

BFD-P

2776 (1)

195 (1)

579 (1)

445 (1)

570 (1)

419 (1)

Leeds

307 (9)

109 (2)

69 (8)

25 (18)

83 (7)

112 (4)

RIT-DuPont

156 (18)

20 (10)

19 (30)

16 (28)

32 (18)

23 (18)

Witt

418 (7)

28 (7)

134 (4)

74 (6)

94 (6)

85 (5)

Total

11273

809

2237

1787

2291

1706

The relative weights for each of the four geographical subsets, in both the COM dataset and the zonal subsets, are shown in parentheses. The last row shows the total number of color pairs used in our computations, obtained by addition of the number of color pairs in each geographical subset multiplied by its corresponding weight.

Table 2

PF/3 Values for the COM Dataset (Weighted^{
a
}
and Unweighted) and Each of the Four Geographical Subsets, Obtained by Using Different Color-Difference Formulas^{
b
}

Color-Difference Formulas

COM (Weighted)

Geographical Subsets

COM (Unweighted)

BFD-P

Leeds

RIT-DuPont

Witt

CIEDE2000

33.7

38.1

23.2

23.4

39.0

37.4

CIEDE2000-Lightness

35.4

40.4

31.2

23.1

35.5

39.4

CIEDE2000-Chroma

56.3

56.3

44.6

35.7

70.9

57.2

CIEDE2000-Hue

40.3

44.5

28.3

26.7

44.1

44.0

CIEDE2000-Rot.Term

35.4

39.0

23.7

20.6

44.8

38.7

CIEDE2000-Gray

35.1

39.9

25.6

21.3

40.5

39.1

CIE94

38.3

43.0

33.4

20.1

42.3

42.3

CIE94-Chroma

58.1

59.3

47.7

31.7

73.9

60.0

CIE94-Hue

42.5

47.4

34.5

22.4

47.3

46.8

CIELAB

56.1

56.3

47.2

30.6

70.9

57.3

CMC

37.9

39.8

27.5

28.3

46.8

39.8

See Table 1
for applied weights.
The formulas used were CIEDE2000 and CIE94, with their corresponding modified versions (see text), CIELAB, and CMC. Results for the last three CIE-recommended formulas are shown in bold.

Table 3

PF/3 Values for the COM Dataset and Each of Its Five Zonal Subsets, Obtained by Using Different Color-Difference Formulas^{
a
}

Color-Difference Formulas

COM (Weighted)

Zonal Subsets

Lightness

Chroma

Hue

Blue

Gray

CIEDE2000

33.7

40.3

32.1

31.9

36.8

33.3

CIEDE2000-Lightness

35.4

40.7

CIEDE2000-Chroma

56.3

49.5

CIEDE2000-Hue

40.3

36.8

CIEDE2000-Rot.Term

35.4

40.4

CIEDE2000-Gray

35.1

35.1

CIE94

38.3

40.7

33.7

35.2

40.8

41.1

CIE94-Chroma

58.1

53.6

CIE94-Hue

42.5

42.3

CIELAB

56.1

41.3

54.0

43.1

55.7

40.4

CMC

37.9

44.1

33.6

37.5

38.7

38.6

The formulas used were CIEDE2000 and CIE94 with their modified versions (see text) in their respective specific subsets (values for the other subsets have been omitted because they are considered irrelevant), CIELAB, and CMC. Results for the three last CIE-recommended formulas are shown in bold.

Table 4

Average Values of Parameter ${V}_{\mathit{AB},i}$
for CIEDE2000 and CIE94 Complete and Modified Formulas, Obtained by Using the COM Dataset and the Corresponding Zonal Subsets^{
a
}

For each modified formula, only the color pairs in the relevant zonal subset are considered. The statistical significance of each modified formula is given by p
values from the Mann–Whitney19
nonparametric test. The weights shown in Table 1
have been considered.
0.276, 0.221, 0.206, 0.228 and 0.245 for Lightness, Chroma, Hue, Blue, and Gray zonal subsets, respectively.
0.234 and 0.221 for Chroma and Hue zonal subsets, respectively.

Tables (4)

Table 1

Number of Color Pairs and Relative Weights (See Text) in the Geographical and Zonal Subsets Constituting the COM Dataset^{
a
}

Geographical Subsets

COM

Zonal Subsets

Lightness

Chroma

Hue

Blue

Gray

BFD-P

2776 (1)

195 (1)

579 (1)

445 (1)

570 (1)

419 (1)

Leeds

307 (9)

109 (2)

69 (8)

25 (18)

83 (7)

112 (4)

RIT-DuPont

156 (18)

20 (10)

19 (30)

16 (28)

32 (18)

23 (18)

Witt

418 (7)

28 (7)

134 (4)

74 (6)

94 (6)

85 (5)

Total

11273

809

2237

1787

2291

1706

The relative weights for each of the four geographical subsets, in both the COM dataset and the zonal subsets, are shown in parentheses. The last row shows the total number of color pairs used in our computations, obtained by addition of the number of color pairs in each geographical subset multiplied by its corresponding weight.

Table 2

PF/3 Values for the COM Dataset (Weighted^{
a
}
and Unweighted) and Each of the Four Geographical Subsets, Obtained by Using Different Color-Difference Formulas^{
b
}

Color-Difference Formulas

COM (Weighted)

Geographical Subsets

COM (Unweighted)

BFD-P

Leeds

RIT-DuPont

Witt

CIEDE2000

33.7

38.1

23.2

23.4

39.0

37.4

CIEDE2000-Lightness

35.4

40.4

31.2

23.1

35.5

39.4

CIEDE2000-Chroma

56.3

56.3

44.6

35.7

70.9

57.2

CIEDE2000-Hue

40.3

44.5

28.3

26.7

44.1

44.0

CIEDE2000-Rot.Term

35.4

39.0

23.7

20.6

44.8

38.7

CIEDE2000-Gray

35.1

39.9

25.6

21.3

40.5

39.1

CIE94

38.3

43.0

33.4

20.1

42.3

42.3

CIE94-Chroma

58.1

59.3

47.7

31.7

73.9

60.0

CIE94-Hue

42.5

47.4

34.5

22.4

47.3

46.8

CIELAB

56.1

56.3

47.2

30.6

70.9

57.3

CMC

37.9

39.8

27.5

28.3

46.8

39.8

See Table 1
for applied weights.
The formulas used were CIEDE2000 and CIE94, with their corresponding modified versions (see text), CIELAB, and CMC. Results for the last three CIE-recommended formulas are shown in bold.

Table 3

PF/3 Values for the COM Dataset and Each of Its Five Zonal Subsets, Obtained by Using Different Color-Difference Formulas^{
a
}

Color-Difference Formulas

COM (Weighted)

Zonal Subsets

Lightness

Chroma

Hue

Blue

Gray

CIEDE2000

33.7

40.3

32.1

31.9

36.8

33.3

CIEDE2000-Lightness

35.4

40.7

CIEDE2000-Chroma

56.3

49.5

CIEDE2000-Hue

40.3

36.8

CIEDE2000-Rot.Term

35.4

40.4

CIEDE2000-Gray

35.1

35.1

CIE94

38.3

40.7

33.7

35.2

40.8

41.1

CIE94-Chroma

58.1

53.6

CIE94-Hue

42.5

42.3

CIELAB

56.1

41.3

54.0

43.1

55.7

40.4

CMC

37.9

44.1

33.6

37.5

38.7

38.6

The formulas used were CIEDE2000 and CIE94 with their modified versions (see text) in their respective specific subsets (values for the other subsets have been omitted because they are considered irrelevant), CIELAB, and CMC. Results for the three last CIE-recommended formulas are shown in bold.

Table 4

Average Values of Parameter ${V}_{\mathit{AB},i}$
for CIEDE2000 and CIE94 Complete and Modified Formulas, Obtained by Using the COM Dataset and the Corresponding Zonal Subsets^{
a
}

For each modified formula, only the color pairs in the relevant zonal subset are considered. The statistical significance of each modified formula is given by p
values from the Mann–Whitney19
nonparametric test. The weights shown in Table 1
have been considered.
0.276, 0.221, 0.206, 0.228 and 0.245 for Lightness, Chroma, Hue, Blue, and Gray zonal subsets, respectively.
0.234 and 0.221 for Chroma and Hue zonal subsets, respectively.