Color-difference formula for evaluating color pairs with no separation: &#x0394;E<sub>NS</sub>

Fereshteh Mirjalili; Ming Ronnier Luo; Guihua Cui; Jan Morovic

doi:10.1364/JOSAA.36.000789

Journal of the Optical Society of America A
Vol. 36,
Issue 5,
pp. 789-799
(2019)
•https://doi.org/10.1364/JOSAA.36.000789

Color-difference formula for evaluating color pairs with no separation: ΔE_NS

Fereshteh Mirjalili, Ming Ronnier Luo, Guihua Cui, and Jan Morovic

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Fereshteh Mirjalili, Ming Ronnier Luo, Guihua Cui, and Jan Morovic, "Color-difference formula for evaluating color pairs with no separation: ΔE_NS," J. Opt. Soc. Am. A 36, 789-799 (2019)

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Abstract

All color-difference formulas are developed to evaluate color differences for pairs of stimuli with hairline separation. In printing applications, however, color differences are frequently judged between a pair of samples with no separation (NS) because they are printed adjacently on the same piece of paper. A new formula, $Δ E_{NS}$ , has been developed for pairs of stimuli with NS. An experiment was conducted to investigate the effect of different color-difference magnitudes using sample pairs with NS. 1012 printed pairs with NS were prepared around 11 CIE recommended color centers. The pairs, representing four color-difference magnitudes of 1, 2, 4, and 8 CIELAB units were visually evaluated by a panel of 19 observers using the gray-scale method. Comparison of the present data based on pairs with NS, and previously generated data using pairs with hairline separation, showed a clear separation effect. A new color-difference equation for the NS viewing condition ( $Δ E_{NS}$ ) is proposed by modifying the CIEDE2000 formula. The separation effect can be well described by the new formula. For a sample pair with NS, when the CIEDE2000 color difference is less than 9.1, a larger color difference leads to a larger lightness difference, but has no effect on the chromatic difference. When the CIEDE2000 color difference is greater than 9.1, the effect is the opposite. The new formula is recommended for future research to evaluate its performance in appropriate applications.

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	Color Center	$L^{*}$	$a^{*}$	$b^{*}$	$C_{a b}^{*}$	$h_{a b}$
1	Gray	61.1	−3.2	3.2	4.5	135
2	Red	41.0	33.2	25.5	41.9	38
3	High-chroma orange	60.3	33.0	64.3	72.2	63
4	Yellow	84.1	−6.7	50.4	50.9	98
5	High-chroma yellow green	63.2	−29.3	44.1	53.0	124
6	Green	56.2	−32.5	4.9	32.8	172
7	High-chroma green	56.0	−45.7	5.7	46.1	173
8	Blue-green	50.6	−18.7	−6.9	19.9	200
9	Blue	37.0	−1.3	−27.9	28.0	267
10	High-chroma purple	45.4	18.9	−25.0	31.4	307
11	Black	29.8	−3.1	2.3	3.8	143

Gray-Scale Number (GS)	$L^{*}$	$a^{*}$	$b^{*}$	$Δ L^{*}$	$Δ E_{a b}^{*}$
1	41.50	0.05	1.70	0.00	0.00
2	41.20	0.12	1.49	0.29	0.38
3	41.09	−0.01	1.34	0.40	0.55
4	42.17	0.13	1.42	0.68	0.75
5	43.07	0.09	1.76	1.58	1.58
6	45.14	0.09	1.67	3.65	3.65
7	48.81	0.04	1.39	7.32	7.32
8	56.00	−0.50	1.17	14.51	14.53
Standard	41.49	0.04	1.71

Color Center	$L^{} a^{}$	$L^{} b^{}$	$a^{} b^{}$	$Δ E_{M}$				Overall STRESS
Color Center	$L^{} a^{}$	$L^{} b^{}$	$a^{} b^{}$	1	2	4	8	Overall STRESS
Gray	17	19	24	29	22	20	19	22
Red	24	24	33	35	30	30	27	30
High-chroma orange	23	23	34	33	30	27	26	29
Yellow	23	26	39	44	35	27	24	29
High-chroma yellow green	25	25	36	41	31	28	24	28
Green	25	25	37	39	32	29	24	29
High-chroma green	19	22	30	30	26	26	21	25
Blue-green	28	29	36	46	33	29	27	31
Blue	32	30	35	56	39	28	27	30
High-chroma purple	22	25	38	35	29	26	25	28
Black	24	24	33	36	29	27	24	27
Mean	24	25	34	39	30	27	24	28

Color Difference Formula	$a$	$b$	$c$	$d$
CIELAB	0.05	0.22	0.72	0.95
CIEDE2000	0.08	0.27	0.70	0.91
CIE94	0.08	0.34	0.73	0.94
CAM02-UCS	0.07	0.28	0.72	0.93
CAM16-UCS	0.07	0.27	0.73	0.93

Reference White			Pair 1				Pair 2
$X_{n}$	$Y_{n}$	$Z_{n}$		$X$	$Y$	$Z$		$X$	$Y$	$Z$
95.78	100.00	104.61	$S_{1}$	8.90	9.53	23.10	$S_{2}$	58.26	64.26	24.83
			$P_{1}$	9.21	9.72	23.38	$P_{2}$	59.10	64.76	25.50

	$L^{*}$	$a^{*}$	$b^{*}$	$C^{*}$	$Δ E_{00}$	$D_{L}$	$Δ E_{NS}$
$S_{1}$	36.99	−1.92	−29.53	29.59	0.95	0.35	1.25
$P_{1}$	37.34	−0.82	−29.42	29.43
$S_{2}$	84.1	−7.82	48.76	49.38	0.61	0.32	0.80
$P_{2}$	84.36	−6.91	48.10	48.59

	$L^{*}$	$a^{*}$	$b^{*}$	$C^{*}$	$Δ E_{00}$	$D_{L}$	$Δ E_{NS}$
$S_{1}$	36.99	−1.92	−29.53	29.59	0.95	0.35	1.25
$P_{1}$	37.34	−0.82	−29.42	29.43
$S_{2}$	84.1	−7.82	48.76	49.38	0.61	0.32	0.80
$P_{2}$	84.36	−6.91	48.10	48.59

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Journal of the Optical Society of America A