Some classical color differences calculated with new formulas

M. Melgosa; E. Hita; J. Romero; L. Jiménez del Barco

doi:10.1364/JOSAA.9.001247

Journal of the Optical Society of America A
Vol. 9,
Issue 8,
pp. 1247-1254
(1992)
•https://doi.org/10.1364/JOSAA.9.001247

Some classical color differences calculated with new formulas

M. Melgosa, E. Hita, J. Romero, and L. Jiménez del Barco

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M. Melgosa, E. Hita, J. Romero, and L. Jiménez del Barco, "Some classical color differences calculated with new formulas," J. Opt. Soc. Am. A 9, 1247-1254 (1992)

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Abstract

An evaluation of chromatic and color-threshold differences was carried out by using the CMC(l:c) and the BFD(l:c) color-difference formulas [ J. Soc. Dyers Colour. 100, 128 ( 1984); J. Soc. Dyers Colour. 103, 86 ( 1987)] from experimental threshold results obtained with visual colorimeters [ J. Opt. Soc. Am. 32, 247 ( 1942); J. Opt. Soc. Am. 39, 808 ( 1949); J. Opt. Soc. Am. 47, 137 ( 1957); J. Opt. Soc. Am. 61, 1135 ( 1971)]. The good results previously reported on the use of these two new formulas with surface colors are also found for the chromatic differences calculated, especially with the BFD(1:1) formula. In the case of color differences BFD(0.6:1) improves the results achieved with BFD(1:1) and gives results similar to those of CMC(1:1). The claim of CMC(l:c) and BFD(l:c) as sometimes superior alternatives to the currently recommended CIE formulas CIELUV and CIELAB can be supported by the present results.

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Study	Value	CIELUV	CIELAB	CMC(1:1)	BFD(1:1)
MacAdam11;1942	〈ΔE〉	0.857	0.728	0.339	0.415
Observe: PGN	σ1%	20.73	24.94	25.89	33.60
No. of ellipses:24	σ2%	26.08	34.47	32.21	27.70
Brown, MacAdam12; 1949	〈ΔE〉	0.701	0.570	0.311	0.392
Observe: WRJB	σ1%	26.29	22.37	33.15	35.20
No. of ellipses: 34	σ2%	23.88	23.93	23.06	17.24
Observer: DLM	〈ΔE〉	0.690	0.545	0.291	0.370
	σ1%	33.76	26.80	25.77	27.41
No. of ellipses:33	σ2%	24.15	18.40	19.48	17.73
Wyszecki, Fielder14; 1971	〈ΔE〉	1.338	1.042	0.691	0.888
Observer: GF	σ1%	33.88	32.02	24.50	20.13
No. of ellipses: 28	σ2%	26.55	24.31	16.97	15.80
Observer: AR	〈ΔE〉	1.264	0.996	0.681	0.877
	σ1%	28.92	26.35	24.97	23.17
No. of ellipses: 28	σ2%	18.81	21.06	20.60	18.78
Observer: GW	〈ΔE〉	1.437	1.122	0.741	0.942
	σ1%	40.23	35.83	27.95	20.03
No. of ellipses: 28	σ2%	26.86	26.93	20.16	18.76
Brown13; 1957	〈ΔE〉	1.028	0.897	0.449	0.552
Observe: unweighted	σ1%	31.09	30.75	28.35	32.09
No. of ellipses: 21	σ2%	28.47	27.55	24.83	22.09
Observer: weighted	〈ΔE〉	0.810	0.714	0.360	0.444
	σ1%	22.03	28.14	21.64	35.07
No. of ellipses: 21	σ2%	27.20	26.59	21.55	19.03
Luo, Rigg20; 1986	〈ΔE〉	1.213	1.142	0.799	1.053
Observer:—	σ1%	37.59	38.55	18.35	17.40
No. of ellipses: 131	σ2%	28.35	25.13	16.18	13.60

Study	Value	CIELUV	CIELAB	CMC(1:1)	BFD(1:1)
MacAdam11; 1942	ΔE	0.872	0.890	0.313	0.317
x = 0.160, y = 0.057	σ2%	59.15	67.52	59.92	53.50
Brown, MacAdam12; 1949 (WRJB)	ΔE	0.677	0.609	0.353	0.370
x = 0.171, y = 0.189	σ2%	55.48	60.96	64.87	57.00
Brown13; 1957 (unweighted)	AE	1.263	1.189	0.439	0.481
x = 0.209, y = 0.137	σ2%	54.34	64.09	56.34	50.82
Wyszecki, Fielder14; 1971 (GW)	ΔE	1.478	1.599	0.661	0.827
x = 0.3425, y = 0.5280	σ2%	35.43	52.29	43.56	35.16
Luo, Rigg20; 1986	ΔE	2.096	2.028	1.157	1.180
x = 0.6218, y = 0.3343	σ2%	55.11	45.46	35.50	28.31
x = 0.1755, y = 0.1316	ΔE	1.738	1.951	0.876	0.883
	σ2%	61.69	63.51	53.08	40.39

Study	Value	CIELUV	CIELAB	CMC(1:1)	BFD(1:1)
Brown, MacAdam12;1949	〈ΔE〉	0.536	0.447	0.284	0.355
Observer: WRJB	σ1%	39.87	25.05	26.27	28.87
No. of ellipsoids:34	σ2%	42.06	36.08	32.31	35.53
Observer: DLM	〈ΔE〉	0.549	0.448	0.285	0.355
	σ1%	46.53	30.68	24.74	25.09
No. of ellipsoids:33	σ2%	39.99	33.00	29.23	32.44
Wyszecki, Fielder14; 1971	〈ΔE〉	1.178	0.953	0.732	0.912
Observer: GF	σ1%	34.45	28.98	20.80	19.23
No. of ellipsoids:28	σ2%	39.15	33.14	30.91	32.53
Observer: AR	〈ΔE〉	1.097	0.892	0.708	0.876
	σ1%	26.40	22.95	15.56	14.63
No. of ellipsoids: 28	σ2%	33.46	26.66	25.00	26.52
Observer: GW	〈ΔE〉	1.248	1.001	0.759	0.941
	σ1%	40.95	33.66	22.84	17.06
No. of ellipsoids: 28	σ2%	40.91	34.32	31.48	33.19
Brown13; 1957	〈ΔE〉	1.103	0.926	0.562	0.665
Observer: unweighted	σ1%	27.27	25.22	27.70	28.69
No. of ellipsoids: 21	σ2%	36.38	32.95	28.42	27.96
Observer: weighted	〈ΔE〉	0.788	0.671	0.396	0.474
	σ1%	20.95	24.73	24.97	26.97
No. of ellipsoids: 21	σ2%	35.72	31.86	26.42	26.57
Cheung, Rigg21; 1986	〈ΔE〉	2.236	1.788	1.360	1.650
Observers: 20	σ1%	22.06	19.31	13.23	8.45
No. of ellipsoids: 5	σ2%	36.59	31.58	31.95	32.36
Witt22; 1990	〈ΔE〉	0.501	0.378	0.272	0.358
Observers:22–24	σ1%	27.50	23.18	9.49	9.49
No. of ellipsoids: 5	σ2%	45.69	39.30	39.09	42.57

Study	Value	CMC(0.6:1)	BFD(0.6:1)
Brown, MacAdam12; 1949	〈ΔE〉	0.325	0.392
Observer: WRJB	σ1%	22.29	25.37
No. of ellipsoids: 34	σ2%	29.21	31.22
Observer: DLM	〈ΔE〉	0.330	0.396
	σ1%	23.42	23.91
No. of ellipsoids: 33	σ2%	27.34	28.91
Wyszecki, Fielder14; 1971	〈ΔE〉	0.872	1.052
Observer: GF	σ1%	19.04	18.46
No. of ellipsoids: 28	σ2%	30.00	29.61
Observer: AR	〈ΔE〉	0.876	1.046
	σ1%	14.12	12.89
No. of ellipsoids: 28	σ2%	27.24	25.87
Observer: GW	〈ΔE〉	0.904	1.085
	σ1%	20.86	16.69
No. of ellipsoids: 28	σ2%	30.20	29.75
Brown13; 1957	〈ΔE〉	0.732	0.841
Observer: unweighted	σ1%	30.52	30.43
No. of ellipsoids: 21	σ2%	33.18	31.10
Observer: weighted	〈ΔE〉	0.489	0.570
	σ1%	21.95	23.25
No. of ellipsoids: 21	σ2%	28.50	26.81
Cheung, Rigg21; 1986	〈ΔE〉	1.741	2.016
Observers: 20	σ1%	12.54	9.04
No. of ellipsoids: 5	σ2%	34.00	31.47
Witt22; 1990	〈ΔE〉	0.309	0.389
Observers: 22–24	σ1%	11.38	6.83
No. of ellipsoids: 5	σ2%	35.16	38.02

Samples	Value	CIELUV	CIELAB	CMC(1:1)	BFD(1:1)
Fixed: value = 5	〈ΔE〉	12.008	10.242	4.341	5.457
Variable: chroma	σ2%	30.20	20.51	35.46	41.83
No. of pairs: 350
Fixed: value = 5	〈ΔE〉	11.689	8.446	4.749	5.874
Variable: hue	σ2%	62.77	64.64	50.73	38.44
No. of pairs: 365
Fixed: hue 5.0 R	〈ΔE〉	12.171	10.855	10.918	10.756
Variable: value	σ2%	30.08	13.92	32.20	24.36
No. of pairs: 53
Fixed: hue 10.0 Y	〈ΔE〉	11.765	10.080	8.802	8.807
Variable: value	σ2%	12.69	2.52	27.26	23.37
No. of pairs: 40
Fixed: hue 5.0 BG	〈ΔE〉	11.814	10.349	9.988	9.983
Variable: value	σ2%	16.58	3.58	28.46	21.58
No. of pairs: 61
Fixed: hue 10.0 PB	〈ΔE〉	16.912	11.043	12.483	11.615
Variable: value	σ2%	48.11	8.98	27.95	16.51
No. of pairs: 78

Abstract

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Tables (5)

Equations (19)

Journal of the Optical Society of America A