Rafael Huertas, Manuel Melgosa, and Claudio 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)

An investigation of the color metrics and the complexity of the CIEDE2000 formula shows that CIELAB space is inadequate to represent small–medium color differences. The OSA-UCS (Uniform Color Space) Committee has shown that no space with uniform scale for large color differences exists. Therefore the practical way for color-difference specification is a color-difference formula in a nonuniform space. First, the BFD (Bradford University) ellipses are considered in the OSA-UCS space, and their very high regularity suggests a new and very simple color-difference formula at constant luminance. Then the COM (combined) data set used for the development of the CIEDE2000 formula is considered in the OSA-UCS space, and the color-difference formula is extended to sample pairs with a different luminance factor. The value of the performance factor $\mathit{PF}/3$ for the proposed OSA-UCS-based formula shows that the formula performs like the more complex CIEDE2000 formula for small–medium color differences.

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${S}_{C}$ and ${S}_{H}$ Weights and Corresponding Linear Correlation Indices r Obtained by Linear Fits of the Long and Short Semiaxes of the Ellipses and Obtained by Minimizing the $\mathit{PF}/3$ Index as Functions of the Chroma ${C}_{\mathit{OSA},s}$ of the Color Standard s (the Center of the Ellipse)^{
a
}

Factor 10 is due to the unit of measure of ${C}_{\mathit{OSA},s}$ equal to 10 jnd. The minimization of the $\mathit{PF}/3$ index and the $\mathit{PF}/3$^{
13
}
related to the three sets of ellipses BFD, BFD-P, and BFD-A are evaluated on 100 points per ellipse.

Table 2

Number of Color Pairs Corresponding to the Filtered Data Sets Used for the Computation of the Weighting Functions ${S}_{L},\phantom{\rule{0.3em}{0ex}}{S}_{C}$, and ${S}_{H}$ (Table 3, Left Side)^{
a
}

$\Delta {E}_{0}$ is the Euclidean distance in OSA-UCS space. The factors in parentheses must be applied in order to give approximately the same weight to the four data sets when they are put together to constitute the COM1 data sets, used for the computation of the weighting functions in COM data sets.

Table 3

Weighting Functions ${S}_{L},\phantom{\rule{0.3em}{0ex}}{S}_{C}$, and ${S}_{H}$ Obtained by Two Different Techniques and Computed for Different Subsets as Functions of the Average Lightness ${\overline{L}}_{\mathit{OSA}}$ and Average Chroma ${\overline{C}}_{\mathit{OSA}}$^{
a
}

For the first technique, linear correlation indices r are given. Values of the $\mathit{PF}/3$^{
13
}
computed for the corresponding different color-difference formulas related to different data sets (BFD-P,
^{
8
}
Leeds,
^{
10
}
RIT–DuPont,
^{
11
}
and Witt
^{
12
}
) constituting the COM data set.

Table 4

Values of the $\mathit{PF}/3$^{
a
} Computed for Different Color-Difference Formulas and Related to the Three Sets of Ellipses BFD, BFD-P, and BFD-A (Evaluated on 100 Points per Ellipse) and Different Data Sets (BFD-P,^{
b
} Leeds,^{
c
} RIT–DuPont,^{
d
} and Witt^{
e
}) Constituting the COM Data Set^{
f
}

Data Set

Number of Color Pairs

$\mathit{PF}/3$^{
a
}

CIELAB’76

CIEDE2000

$10\times \Delta {E}_{0}$

$\Delta {E}_{\mathit{GP}}$

BFD-P ellipses

8000

54.9

22.2

50.6

22.7

BFD-A ellipses

5200

49.1

22.0

50.1

21.9

BFD ellipses

13,200

52.7

22.1

50.9

22.5

BFD-P^{
b
}

2776

56.3

37.3

53.2

38.1

Leeds^{
c
}

307

47.2

22.0

50.9

30.0

RIT–DuPont^{
d
}

156

30.6

19.3

29.5

21.7

Witt^{
e
}

418

70.9

38.7

63.1

41.7

COM
^{
2, 9
}

11,273 (1:9:18:7)

56.1

32.6

53.0

35.6

Ref. 13.
Ref. 8.
Leeds, Ref. 10.
RIT–DuPont, Ref. 11.
Witt, Ref. 12.
In the column of the “Number of Color Pairs” a set of four numbers is reported in parentheses, representing the relative weights to be applied to the color pairs of the subsets BFD-P, Leeds, RIT–DuPont, and Witt, to ensure that all of them have nearly the same weight in the $\mathit{PF}/3$ computation. The $\mathit{PF}/3$ index is evaluated with weights proposed by Eqs. (2)–(4).

Tables (4)

Table 1

${S}_{C}$ and ${S}_{H}$ Weights and Corresponding Linear Correlation Indices r Obtained by Linear Fits of the Long and Short Semiaxes of the Ellipses and Obtained by Minimizing the $\mathit{PF}/3$ Index as Functions of the Chroma ${C}_{\mathit{OSA},s}$ of the Color Standard s (the Center of the Ellipse)^{
a
}

Factor 10 is due to the unit of measure of ${C}_{\mathit{OSA},s}$ equal to 10 jnd. The minimization of the $\mathit{PF}/3$ index and the $\mathit{PF}/3$^{
13
}
related to the three sets of ellipses BFD, BFD-P, and BFD-A are evaluated on 100 points per ellipse.

Table 2

Number of Color Pairs Corresponding to the Filtered Data Sets Used for the Computation of the Weighting Functions ${S}_{L},\phantom{\rule{0.3em}{0ex}}{S}_{C}$, and ${S}_{H}$ (Table 3, Left Side)^{
a
}

$\Delta {E}_{0}$ is the Euclidean distance in OSA-UCS space. The factors in parentheses must be applied in order to give approximately the same weight to the four data sets when they are put together to constitute the COM1 data sets, used for the computation of the weighting functions in COM data sets.

Table 3

Weighting Functions ${S}_{L},\phantom{\rule{0.3em}{0ex}}{S}_{C}$, and ${S}_{H}$ Obtained by Two Different Techniques and Computed for Different Subsets as Functions of the Average Lightness ${\overline{L}}_{\mathit{OSA}}$ and Average Chroma ${\overline{C}}_{\mathit{OSA}}$^{
a
}

For the first technique, linear correlation indices r are given. Values of the $\mathit{PF}/3$^{
13
}
computed for the corresponding different color-difference formulas related to different data sets (BFD-P,
^{
8
}
Leeds,
^{
10
}
RIT–DuPont,
^{
11
}
and Witt
^{
12
}
) constituting the COM data set.

Table 4

Values of the $\mathit{PF}/3$^{
a
} Computed for Different Color-Difference Formulas and Related to the Three Sets of Ellipses BFD, BFD-P, and BFD-A (Evaluated on 100 Points per Ellipse) and Different Data Sets (BFD-P,^{
b
} Leeds,^{
c
} RIT–DuPont,^{
d
} and Witt^{
e
}) Constituting the COM Data Set^{
f
}

Data Set

Number of Color Pairs

$\mathit{PF}/3$^{
a
}

CIELAB’76

CIEDE2000

$10\times \Delta {E}_{0}$

$\Delta {E}_{\mathit{GP}}$

BFD-P ellipses

8000

54.9

22.2

50.6

22.7

BFD-A ellipses

5200

49.1

22.0

50.1

21.9

BFD ellipses

13,200

52.7

22.1

50.9

22.5

BFD-P^{
b
}

2776

56.3

37.3

53.2

38.1

Leeds^{
c
}

307

47.2

22.0

50.9

30.0

RIT–DuPont^{
d
}

156

30.6

19.3

29.5

21.7

Witt^{
e
}

418

70.9

38.7

63.1

41.7

COM
^{
2, 9
}

11,273 (1:9:18:7)

56.1

32.6

53.0

35.6

Ref. 13.
Ref. 8.
Leeds, Ref. 10.
RIT–DuPont, Ref. 11.
Witt, Ref. 12.
In the column of the “Number of Color Pairs” a set of four numbers is reported in parentheses, representing the relative weights to be applied to the color pairs of the subsets BFD-P, Leeds, RIT–DuPont, and Witt, to ensure that all of them have nearly the same weight in the $\mathit{PF}/3$ computation. The $\mathit{PF}/3$ index is evaluated with weights proposed by Eqs. (2)–(4).