Utility of Color-Difference Formulas for Match-Acceptability
Decisions

S. M. Jaeckel

doi:10.1364/AO.12.001299

Applied Optics
Vol. 12,
Issue 6,
pp. 1299-1316
(1973)
•https://doi.org/10.1364/AO.12.001299

Utility of Color-Difference Formulas for Match-Acceptability Decisions

S. M. Jaeckel

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
S. M. Jaeckel, "Utility of Color-Difference Formulas for Match-Acceptability Decisions," Appl. Opt. 12, 1299-1316 (1973)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

Pass–fail decisions for three groups of textile patterns around twelve color centers were correlated statistically with color differences, from filter–colorimeter measurements, according to twenty formulas. Almost completely acceptable or unacceptable patterns were omitted, leaving 854 involving over 37,000 decisions. A more balanced selection of 589 patterns involved nearly 28,000 decisions. Adams Chromatic Value type formulas, especially the Morton and the Glasser Cube Root versions, performed significantly better both than most others and than assessors too severe or too lenient and no worse than assessors of correct severity. Problems are discussed.

Full Article | PDF Article

More Like This

Color Difference Formulas and Visual Acceptability

D. Strocka
Appl. Opt. 10(6) 1308-1313 (1971)

Improved Color-Difference Formula, with Applications to the Perceptibility and Acceptability of Fadings

I. H. Godlove
J. Opt. Soc. Am. 41(11) 760-772 (1951)

The Size of Acceptable Color Differences

Hugh R. Davidson and Elaine Friede
J. Opt. Soc. Am. 43(7) 581-589 (1953)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (9)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (18)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (3)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

HATRA-200					Industrial

Sets	Color	a	b	c	Sets	Color	a	b	c
(1)–(4)	blue^b	79	13	76	000–200	pink	89	50	72
(5)–(7)	red^b	59	12	51	300–500	pale blue	69	48	59
(8)–(10)	yellow	60	6	58	600	aqua^c	44	38	42
					700 & 900	fuchsia	65	59	65
					900	navy	42	14	38

Total		198	31	185		Total	309	209	276

Third, HATRA-560 group							Selected HATRA plain-knit group

Sets	Color	a	b	c	c Plain	c Ripple	Sets	c	c₁	c₂	c₃	c₄
(11)–(16)	blue	120	79	91	47	44	(3,4,11,12,15)	84	25	12	27	20
(17)–(22)	red	120	66	91	46	45	(6,7,17,18,21)	82	19	11	23	29
(23)–(24)	yellow	40	24	34	34	—	(10,23,24)	53	22	5	7	19
(25)–(32)	green	160	89	125	86	39	(25)–(29)	86	25	22	23	16
(33)–(38)	brown	120	67	94	50	44	(33)–(35)	50	16	12	14	8

Total		560	325	435	263	172		355	107	62	94	92

Color	x	y	%Y	Color	x	y	%Y

HATRA-185 patterns				Industrial-234 patterns cont. (& aqua)
blue	0.2024	0.2065	19.07	pale blue sp^a	0.2732	0.2873	59.71
red	0.4270	0.2429	18.23	pale blue sr^a	0.2677	0.2849	59.42
yellow	0.4204	0.4515	67.42	pale blue M^a	0.2746	0.2907	64.79

Industrial-234 patterns				aqua sp^a	0.2660	0.3046	60.92

pink sp^a	0.3475	0.3029	63.89	light fuchsia sp^a	0.4588	0.2523	22.26
pink sr^a	0.3494	0.3023	61.90	deep fuchsia sp^a	0.5218	0.2454	12.15
pink M^a	0.3405	0.2992	64.84	navy sp^a	0.2310	0.2027	2.13

HATRA-435 plain-knit				HATRA-435 ripple

blue	0.2128	0.1989	19.26	blue	0.2115	0.1943	15.89
half-strength blue	0.2274	0.2246	27.53	half-strength blue	0.2235	0.2155	23.95
red	0.4349	0.2448	18.32	red	0.4487	0.2446	16.46
half-strength red	0.3998	0.2501	25.09	half-strength red	0.4160	0.2476	21.64
yellow	0.4084	0.4672	70.57
green	0.2805	0.3960	22.84	green	0.2820	0.3940	19.91
brown	0.3758	0.3146	13.92	brown	0.3807	0.3095	11.39

HATRA-185							Industrial-234 and Aqua

Set	Hue	Direction of change	%A	10⁴Δx	10⁴Δy	10²ΔY	Set	Hue	Structure^a	%A	10⁴Δx	10⁴Δy	10²ΔY
(1)	blue	stronger	38	−36	−58	−106	000	pink	sp	6	−11	+44	+150
(2)	blue	weaker	59	+8	+10	+120	100	pink	sr	8	−80	−31	+94
(3)	blue	redder	6	+40	−10	−68	200	pink	M	52	+41	+16	−288
(4)	blue	yellower	6	+36	+91	+5	300	pale blue	sp	13	+38	+69	−105
(5)	red	weaker	38	−73	+10	+153	400	pale blue	sr	6	+95	+59	+88
(6)	red	bluer	6	−137	−30	−103	500	pale blue	M	6	+67	+62	+18
(7)	red	yellower	6	+42	+42	+9	600	aqua	sp	10	+74	+24	−445
(8)	yellow	weaker	67	−17	−9	+103	700	light fuchsia	sp	10	−144	−41	+245
(9)	yellow	bluer	63	+5	+26	+107	800	deep fuchsia	sp	10	−79	−56	+118
(10)	yellow	redder	7	+35	−31	−205	900	navy	sp	8	+75	+144	−9

Code	Reference	Code	Reference
Adams (1942) Spaces3		MacAdam (1943) Ellipsoids9
ACV	Nickerson & Stultz (1944)4	IR	Ingle & Rudick (1953)10
Ze2	Saunderson & Milner (1946)6	DF	Davidson & Friede (1953)1
Ze5	Saunderson & Milner (1946)6	DF	Davidson & Friede (1953)1
		DH	Davidson & Hanlon (1955)11
Cube-root versions		SG	Simon & Goodwin (1957)12
$G^{\frac{1}{3}} 1$	Glasser el al. (1958)6	BB	Berger & Brockes (1962)13
$G^{\frac{1}{3}} 2$	Reilly modified (1963)7	FMC	Chickering (1967)14
$M^{\frac{1}{3}}$	Morton (1969)8	Fkk	Wyszecki (1968)16
Others, Mainly Linear CIE Transformations
JH	Hunter (1942)16	C64	Wyszecki (1963)20
SH	Scofield (1943)17	Md	Mudd & Woods (1970)21
HGf	Hunter (1958)18	CDR	Coates, Day, & Rigg (1969)22
HGY	ASTM (1968)19

Formula	ΔL	Δa	Δb
ACV	9.66ΔVy	42(ΔVx − ΔVy)	16.8(ΔVy − ΔVz)
$M^{\frac{1}{3}}$	$\frac{7.988 Δ Y}{{Y_{0}}^{\frac{2}{3}}}$	$34.717 (\frac{Δ X}{{X_{0}}^{\frac{2}{3}}} - \frac{Δ Y}{{Y_{0}}^{\frac{2}{3}}})$	$13.885 (\frac{Δ Y}{{Y_{0}}^{\frac{2}{3}}} - \frac{Δ Z}{{Z_{0}}^{\frac{2}{3}}})$
$G^{\frac{1}{3}} 1$	$25.29 Δ (Y^{\frac{1}{3}})$	$106 {Δ [{(1.02 X)}^{\frac{1}{3}}] - Δ (Y^{\frac{1}{3}})}$	$42.34 {Δ (Y^{\frac{1}{3}}) - Δ [{(\frac{Z}{1.18})}^{\frac{1}{3}}]}$
$G^{\frac{1}{3}} 2$	$25.29 Δ (G^{* \frac{1}{3}})$	$106 {Δ (R^{* \frac{1}{3}}) - Δ G^{* \frac{1}{3}}}$	$42.34 [Δ (G^{* \frac{1}{3}}) - Δ (B^{* \frac{1}{3}})]$
HGY	$10 Δ (Y^{\frac{1}{2}})$	$17.5 Δ (\frac{1.02 X - Y}{Y^{\frac{1}{2}}})$	$7 Δ (\frac{Y - 0.847 Z}{Y^{\frac{1}{2}}})$
$G^{\frac{1}{3}} 2$ : R* = 1.1084X + 0.0852Y − 0.1454Z
G* = −0.0010X + 1.0005Y + 0.0004Z
B* = −0.0062X + 0.00394Y + 0.8192Z

Group	% Levels:		5 or (4.5)	4 or (2.5)	2 or (1)	5×

						10⁻¹	10⁻²	10⁻³	10⁻⁴	10⁻⁶	10⁻⁸
	Ze2	sig.		( $G^{\frac{1}{3}} 2$ )						HGY	C64
	$M^{\frac{1}{3}}$	better			$G^{\frac{1}{3}} 2$	HGY, DH			JH		C64
HATRA-185	$G^{\frac{1}{3}} 1$	than		( $G^{\frac{1}{3}} 2$ )	(HGY)						C64
	ACV		( $G^{\frac{1}{3}} 2$ )		(HGY)	DH		JH			C64
	$G^{\frac{1}{3}} 2$										G64

	$M^{\frac{1}{3}}$	sig.				$G^{\frac{1}{3}} 1$ , Ze2	ACV, HGY $G^{\frac{1}{3}} 2$		C64
Ind.-234	$G^{\frac{1}{3}} 1$	better		Ze2		ACV, HGY $G^{\frac{1}{3}} 2$		C64
	Ze2	than					C64
	ACV					C64
	$G^{\frac{1}{3}} 2$					C64

	$M^{\frac{1}{3}}$	sig.	Ze2				ACV, $G^{\frac{1}{3}} 2$		HGY		C64
Combined-419	$G^{\frac{1}{3}} 1$	better				ACV	$G^{\frac{1}{3}} 2$	HGY			C64
	Ze2	than			( $G^{\frac{1}{3}} 2$ )			HGY			C64
	ACV		HGY								C64
	$G^{\frac{1}{3}} 2$										C64

					5×

% levels:		4	2	1	10⁻¹	10⁻²	10⁻³	10⁻⁴	10⁻⁵	10⁻⁶ or (⁻⁷)	10⁻⁸
CDR	sig.				JH, Fkk				$M^{\frac{1}{3}}, G^{\frac{1}{3}} 1$	ACV	Ze2-FMC
					$G^{\frac{1}{3}} 2$
JH	better			$M^{\frac{1}{3}}$	$G^{\frac{1}{3}} 1$	ACV				Ze2	HGf-FMC
Fkk	than		ACV			Ze2		HGf, HGY	Ze5		C64, FMC
$G^{\frac{1}{3}} 2$					$M^{\frac{1}{3}}$	$G^{\frac{1}{3}} 1$		ACV	FMC	(HGf)	Ze2, Ze5
											C64, HGY
$M^{\frac{1}{3}}$					ACV, FMC	Ze2	Ze5, C64	HGf	HGY
$G^{\frac{1}{3}} 1$						FMC	C64	ACV, Ze2	HGY
								HGf, Ze5
ACV					FMC	Ze2	Ze5, C64	HGf	HGY
Ze2		FMC		Ze5	C64		HGf			HGY

% levels		5 or (4.5)	4	3.5	3	2	1.5	1	0.5	0.05	0.0005
JH		Ze2					$G^{\frac{1}{3}} 2, G^{\frac{1}{3}} 1$	ACV, $M^{\frac{1}{3}} 1$ , C64	FMC	HGY
Fkk	sig.						$G^{\frac{1}{3}} 2, G^{\frac{1}{3}} 1$	$M^{\frac{1}{3}}$	C64, FMC	HGY
							ACV
CDR	better					HGY, FMC
Ze2	than				ACV	$M^{\frac{1}{3}}$ , FMC					HGY
$G^{\frac{1}{3}} 2$			FMC					HGY
$G^{\frac{1}{3}} 1$		(ACV)				HGY
ACV				HGY
$M^{\frac{1}{3}}$				HGY

	ΔE₅₀	ΔE₆₀	ΔE₇₀	Independent
Different	1.8	1.6	1.3	%A
assessor	2.0	1.7	1.4	%A
groups	2.5	2.1	1.8	%A
All	2.1	1.7	1.5	%A
assessors	1.8	1.3	0.8	ΔE

Group		185	234	435	D&F
Mean %A		70.8	41.2	45.9	50.5
	$G^{\frac{1}{3}} 1$	1.08	2.29	1.75	1.74
	$G^{\frac{1}{3}} 2$	1.08	2.32	1.77	1.77
Mean ΔE	$M^{\frac{1}{3}}$	1.08	2.34	1.71	1.74
	HGY	1.10	2.48	1.64	1.48
	ACV	1.11	2.40	1.70	1.67

	$G^{\frac{1}{3}} 1$	1.57	2.05	1.66	1.75
	$G^{\frac{1}{3}} 2$	1.55	2.09	1.65	1.78
ΔE₅₀	$M^{\frac{1}{3}}$	1.55	2.08	1.63	1.75
	HGY	1.61	2.20	1.56	1.49
	ACV	1.61	2.15	1.61	1.68

	$G^{\frac{1}{3}} 1$	1.10	1.50	1.23	1.35
ΔE₇₀	$G^{\frac{1}{3}} 2$	1.10	1.56	1.23	1.37
	$M^{\frac{1}{3}}$	1.09	1.49	1.20	1.35
	HGY	1.12	1.56	1.18	1.18
	ACV	1.13	1.60	1. 19	1.30

Formula	$M^{\frac{1}{3}} (- 0.62)$ ^a	$G^{\frac{1}{3}} 1 (- 0.62)$
Fkk(−0.66)	0.79	0.81
$G^{\frac{1}{2}} 2 (- 0.66)$	0.95	0.96

Formula	$M^{\frac{1}{3}} (- 0.62)$ ^a	$G^{\frac{1}{3}} 1 (- 0.62)$
Fkk(−0.66)	0.79	0.81
$G^{\frac{1}{2}} 2 (- 0.66)$	0.95	0.96

Abstract

Cited By

Figures (9)

Tables (18)

Equations (3)

Applied Optics