Ratio Comparisons of Color Differences

Y. Sugiyama; Hilton Wright

doi:10.1364/JOSA.54.000075

Journal of the Optical Society of America
Vol. 54,
Issue 1,
pp. 75-78
(1964)
•https://doi.org/10.1364/JOSA.54.000075

Ratio Comparisons of Color Differences

Y. Sugiyama and Hilton Wright

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Y. Sugiyama and Hilton Wright, "Ratio Comparisons of Color Differences," J. Opt. Soc. Am. 54, 75-78 (1964)

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Abstract

A group of 14 observers made ratio comparisons among a number of color differences consisting of Munsell color samples. The same color differences had been judged previously in another experiment by the method of paired comparisons. The results of the two experiments were found to be equivalent, indicating that both methods of judgment—the ratio method and the paired comparison method—can be used with good reliability for the scaling of color differences.

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Color pair i	Paired comparison experiment 0.347 ( ${\hat{α}}_{i}$ +2.98)	Ratio comparison experiment ${\hat{t}}_{i}$
1	1.35	1.44
2	1.08	1.01
3	0.98	0.92
4	1.27	1.23
5	0.58	0.63
6	0.96	0.98

Pair combination	${\bar{R}}_{i j}$	$\frac{{\hat{t}}_{i}}{{\hat{t}}_{j}}$	$\frac{{\hat{α}}_{i} + η}{{\hat{α}}_{j} + η}$
(1,2)	1.42	1.42	1.25
(1,3)	1.50	1.56	1.38
(1,4)	1.22	1.17	1.06
(1,5)	2.26	2.28	2.33
(1,6)	1.52	1.47	1.41
(2,3)	1.14	1.10	1.10
(2,4)	0.82	0.82	0.85
(2,5)	1.48	1.60	1.86
(2,6)	1.10	1.03	1.13
(3,4)	0.75	0.75	0.77
(3,5)	1.43	1.46	1.68
(3,6)	0.98	0.94	1.02
(4,5)	1.92	1.95	2.19
(4,6)	1.16	1.25	1.32
(5,6)	0.58	0.64	0.60

Color pair i	Paired comparison experiment 0.347 ( ${\hat{α}}_{i}$ +2.98)	Ratio comparison experiment ${\hat{t}}_{i}$
1	1.35	1.44
2	1.08	1.01
3	0.98	0.92
4	1.27	1.23
5	0.58	0.63
6	0.96	0.98

Pair combination	${\bar{R}}_{i j}$	$\frac{{\hat{t}}_{i}}{{\hat{t}}_{j}}$	$\frac{{\hat{α}}_{i} + η}{{\hat{α}}_{j} + η}$
(1,2)	1.42	1.42	1.25
(1,3)	1.50	1.56	1.38
(1,4)	1.22	1.17	1.06
(1,5)	2.26	2.28	2.33
(1,6)	1.52	1.47	1.41
(2,3)	1.14	1.10	1.10
(2,4)	0.82	0.82	0.85
(2,5)	1.48	1.60	1.86
(2,6)	1.10	1.03	1.13
(3,4)	0.75	0.75	0.77
(3,5)	1.43	1.46	1.68
(3,6)	0.98	0.94	1.02
(4,5)	1.92	1.95	2.19
(4,6)	1.16	1.25	1.32
(5,6)	0.58	0.64	0.60

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Journal of the Optical Society of America