General method for deriving an XYZ tristimulus space exemplified by use of the Stiles–Burch<sub>1955</sub> 2° color matching data

Jan Henrik Wold; Arne Valberg

doi:10.1364/JOSAA.16.002845

Journal of the Optical Society of America A
Vol. 16,
Issue 12,
pp. 2845-2858
(1999)
•https://doi.org/10.1364/JOSAA.16.002845

General method for deriving an XYZ tristimulus space exemplified by use of the Stiles–Burch₁₉₅₅ 2° color matching data

Jan Henrik Wold and Arne Valberg

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Jan Henrik Wold and Arne Valberg, "General method for deriving an XYZ tristimulus space exemplified by use of the Stiles–Burch₁₉₅₅ 2° color matching data," J. Opt. Soc. Am. A 16, 2845-2858 (1999)

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Abstract

Using, as an example, the color matching functions of the $Stiles - {Burch}_{1955}$ 2° pilot group, we show how an XYZ representation of color space can be developed from a given set of color matching data. In doing this, we present a set of criteria that unequivocally defines the representation. The method outlined is general and can be applied to any set of color matching data, in particular those sets that are related to the physiological fundamentals.

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Stimulus	Chromaticity Coordinates
	XYZ Representation			RGB Representation
	$x^{'}$	$y^{'}$	$z^{'}$	$r^{'}$	$g^{'}$	$b^{'}$
$X^{'}$	1	0	0	1.286778	-0.289693	0.002915
$Y^{'}$	0	1	0	-1.726122	2.754146	-0.028024
$Z^{'}$	0	0	1	-0.758220	0.129175	1.629045
$R^{'}$	0.730100^a	0.269857^a	0.000043^a	1	0	0
$G^{'}$	0.275117^a	0.716046^a	0.008837^a	0	1	0
$B^{'}$	0.169856^a	0.017098^a	0.813046^a	0	0	1
E	0.33499^b	0.33618^b	0.32883^b	1/3	1/3	1/3

Stimulus	Chromaticity Coordinates
	$\hat{R} \hat{G} \hat{B}$ Representation			RGB Representation			XYZ Representation
	${\hat{r}}^{\cdot}$	${\hat{g}}^{\cdot}$	${\hat{b}}^{\cdot}$	$r^{\cdot}$	$g^{\cdot}$	$b^{\cdot}$	$x^{\cdot}$	$y^{\cdot}$	$z^{\cdot}$
${\hat{R}}^{\cdot}$	1	0	0	0.987276	0.013898	-0.001174	0.711098	0.288731	0.000171
${\hat{G}}^{\cdot}$	0	1	0	-0.641980	1.603785	0.038195	0.140704	0.820029	0.039267
${\hat{B}}^{\cdot}$	0	0	1	-0.016470	0.009406	1.007064	0.164841	0.023416	0.811743
$R^{\cdot}$	1.008820^a	-0.009413^a	0.000593^a	1	0	0	0.719976	0.278331	0.001693
$G^{\cdot}$	0.379787^a	0.628741^a	-0.008528^a	0	1	0	0.280003	0.709951	0.010046
$B^{\cdot}$	0.032081^a	-0.016113^a	0.984032^a	0	0	1	0.168864	0.019861	0.811275
$X^{\cdot}$	1.219337	-0.223789	0.004452	1.307675	-0.309671	0.001996	1	0	0
$Y^{\cdot}$	-0.577170	1.609561	-0.032391	-1.827264	2.857460	-0.030196	0	1	0
$Z^{\cdot}$	-73.430328	8.968607	65.461721	-0.792535	0.136905	1.655630	0	0	1
E	0.579468^b	0.265210^b	0.155322^b	1/3	1/3	1/3	1/3	1/3	1/3

Stimulus	Chromaticity Coordinates
	XYZ Representation			RGB Representation
	$x^{'}$	$y^{'}$	$z^{'}$	$r^{'}$	$g^{'}$	$b^{'}$
$X^{'}$	1	0	0	1.286778	-0.289693	0.002915
$Y^{'}$	0	1	0	-1.726122	2.754146	-0.028024
$Z^{'}$	0	0	1	-0.758220	0.129175	1.629045
$R^{'}$	0.730100^a	0.269857^a	0.000043^a	1	0	0
$G^{'}$	0.275117^a	0.716046^a	0.008837^a	0	1	0
$B^{'}$	0.169856^a	0.017098^a	0.813046^a	0	0	1
E	0.33499^b	0.33618^b	0.32883^b	1/3	1/3	1/3

Stimulus	Chromaticity Coordinates
	$\hat{R} \hat{G} \hat{B}$ Representation			RGB Representation			XYZ Representation
	${\hat{r}}^{\cdot}$	${\hat{g}}^{\cdot}$	${\hat{b}}^{\cdot}$	$r^{\cdot}$	$g^{\cdot}$	$b^{\cdot}$	$x^{\cdot}$	$y^{\cdot}$	$z^{\cdot}$
${\hat{R}}^{\cdot}$	1	0	0	0.987276	0.013898	-0.001174	0.711098	0.288731	0.000171
${\hat{G}}^{\cdot}$	0	1	0	-0.641980	1.603785	0.038195	0.140704	0.820029	0.039267
${\hat{B}}^{\cdot}$	0	0	1	-0.016470	0.009406	1.007064	0.164841	0.023416	0.811743
$R^{\cdot}$	1.008820^a	-0.009413^a	0.000593^a	1	0	0	0.719976	0.278331	0.001693
$G^{\cdot}$	0.379787^a	0.628741^a	-0.008528^a	0	1	0	0.280003	0.709951	0.010046
$B^{\cdot}$	0.032081^a	-0.016113^a	0.984032^a	0	0	1	0.168864	0.019861	0.811275
$X^{\cdot}$	1.219337	-0.223789	0.004452	1.307675	-0.309671	0.001996	1	0	0
$Y^{\cdot}$	-0.577170	1.609561	-0.032391	-1.827264	2.857460	-0.030196	0	1	0
$Z^{\cdot}$	-73.430328	8.968607	65.461721	-0.792535	0.136905	1.655630	0	0	1
E	0.579468^b	0.265210^b	0.155322^b	1/3	1/3	1/3	1/3	1/3	1/3

Abstract

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Equations (48)

Journal of the Optical Society of America A