Color difference formulas tested by use with chromatic discrimination data and new formulas

Javier Romero; Jose A. Garcia; Luis Jiménez del Barco; Enrique Hita

doi:10.1364/AO.28.004697

Applied Optics
Vol. 28,
Issue 21,
pp. 4697-4702
(1989)
•https://doi.org/10.1364/AO.28.004697

Color difference formulas tested by use with chromatic discrimination data and new formulas

Javier Romero, Jose A. Garcia, Luis Jiménez del Barco, and Enrique Hita

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Javier Romero, Jose A. Garcia, Luis Jiménez del Barco, and Enrique Hita, "Color difference formulas tested by use with chromatic discrimination data and new formulas," Appl. Opt. 28, 4697-4702 (1989)

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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.

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Regions	Formulas	Points
Blue	cdf-Gb	74
Green	cdf-Gg	258
Orange	cdf-Go	28
Red	cdf-Gr	118
Achromatic	cdf-Ga	62

		cdf-G*	CIELUV	CIELAB	LABNHU
MacAdam (1943)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.130	0.290	0.489	0.379
MacAdam (1943)	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.086	0.235	0.362	0.313
MacAdam (1942)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.180	0.359	0.491	0.491
MacAdam (1942)	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.132	0.276	0.391	0.382
Brown and MacAdam (1949)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.295	0.393	0.404	0.385
Ob: WRB	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.232	0.327	0.304	0.299
Wyszecki and Fielder (1971)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.411	0.539	0.507	0.440
Ob: GW	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.335	0.391	0.396	0.355

Regions			CIELUV	CIELAB	LABNHU
(Points)
		cdf-Gb
Blue (20)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.202	0.499	0.747	0.790
Blue (20)	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.134	0.378	0.501	0.521
		cdf-Gg
Green (28)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.185	0.327	0.562	0.402
Green (28)	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.112	0.276	0.424	0.335
		cdf-Go
Orange (20)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.015	0.157	0.460	0.229
Orange (20)	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.011	0.130	0.367	0.200
		cdf-Gr
Red (22)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.077	0.293	0.548	0.545
Red (22)	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.049	0.227	0.376	0.342
		cdf-Ga
Achromatic (16)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.111	0.287	0.321	0.312
Achromatic (16)	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.095	0.216	0.267	0.247

Regions	Formulas	Points
Blue	cdf-Gb	74
Green	cdf-Gg	258
Orange	cdf-Go	28
Red	cdf-Gr	118
Achromatic	cdf-Ga	62

		cdf-G*	CIELUV	CIELAB	LABNHU
MacAdam (1943)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.130	0.290	0.489	0.379
MacAdam (1943)	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.086	0.235	0.362	0.313
MacAdam (1942)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.180	0.359	0.491	0.491
MacAdam (1942)	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.132	0.276	0.391	0.382
Brown and MacAdam (1949)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.295	0.393	0.404	0.385
Ob: WRB	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.232	0.327	0.304	0.299
Wyszecki and Fielder (1971)	${〈 e_{1}^{2} 〉}^{1 / 2}$	0.411	0.539	0.507	0.440
Ob: GW	${〈 d_{1}^{2} 〉}^{1 / 2}$	0.335	0.391	0.396	0.355

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Equations (23)

Applied Optics