Kromatika koordinati depende de longeso CIEXYZ , CIE XYZ o CIE1931 en kolorimetrio esas un ek kolor-spaci kreita en 1931 ed es konsiderata kom por altra kolor-spaci (ex. CIELUV e CIELab ). Lua skopo esis perceptar diferi pri kolori da homal okulo, e deskriptar to kom tri-dimensionala (x, y, z – kromatika koordinati).
Nomo dil kolor-modelo devenas de nomo Internacionala Komisiono pri Lumizo (France Commission Internationale de l’Eclairage ), e faktori "X", "Y" e "Z" es kreita precipue por homala okuli (fotorecevili ).
La kolor-modelo CIELUV , qua anke kreesis da la komisiono, es strikte relatat a kolor-spaco CIEXYZ.
Kolor-parametri CIE 1976 L*u*v* recevesis de CIE XYZ per sequa equacioni (
(
u
′
,
v
′
)
:
{\displaystyle (u',v'){:}}
L
∗
=
116
(
Y
/
Y
n
)
1
/
3
−
16
,
{\displaystyle L^{*}=116(Y/Y_{n})^{1/3}-16,}
u
∗
=
13
L
∗
(
u
′
−
u
n
′
)
,
{\displaystyle u^{*}=13L^{*}(u'-u_{n}'),}
v
∗
=
13
L
∗
(
v
′
−
v
n
′
)
.
{\displaystyle v^{*}=13L^{*}(v'-v_{n}').}
Faktori
u
n
′
,
{\displaystyle u_{n}',}
v
n
′
{\displaystyle v_{n}'}
Y
n
{\displaystyle Y_{n}}
blanko di lum -fonto. Por tipala mezur-geometrio di observanto 2° e lumizo C, ke to es:
u
n
′
=
0,200
9
{\displaystyle u_{n}'=0{,}2009}
v
n
′
=
0,461
0
,
{\displaystyle v_{n}'=0{,}4610,}
e por blanka lumo en temperaturo 6500 K
Y
n
=
0,331
00.
{\displaystyle Y_{n}=0{,}33100.}
Equacioni por
u
′
{\displaystyle u'}
v
′
{\displaystyle v'}
u
′
=
4
X
/
(
X
+
15
Y
+
3
Z
)
=
4
x
/
(
−
2
x
+
12
y
+
3
)
,
{\displaystyle u'=4X/(X+15Y+3Z)=4x/(-2x+12y+3),}
v
′
=
9
Y
/
(
X
+
15
Y
+
3
Z
)
=
9
y
/
(
−
2
x
+
12
y
+
3
)
.
{\displaystyle v'=9Y/(X+15Y+3Z)=9y/(-2x+12y+3).}
En transformado inversa uzesis dependaji
(
u
′
,
v
′
)
{\displaystyle (u',v')}
(
x
,
y
)
{\displaystyle (x,y)}
x
=
27
u
′
/
(
18
u
′
−
48
v
′
+
36
)
,
{\displaystyle x=27u'/(18u'-48v'+36),}
y
=
12
v
′
/
(
18
u
′
−
48
v
′
+
36
)
.
{\displaystyle y=12v'/(18u'-48v'+36).}
Transformo CIELUV a XYZ deskriptata es per:
u
′
=
u
∗
/
(
13
L
∗
)
+
u
n
,
{\displaystyle u'=u^{*}/(13L^{*})+u_{n},}
v
′
=
v
∗
/
(
13
L
∗
)
+
v
n
,
{\displaystyle v'=v^{*}/(13L^{*})+v_{n},}
Y
=
Y
n
(
(
L
∗
+
16
)
/
116
)
3
,
{\displaystyle Y=Y_{n}((L^{*}+16)/116)^{3},}
X
=
−
9
Y
u
′
/
(
(
u
′
−
4
)
v
′
−
u
′
v
′
)
,
{\displaystyle X=-9Yu'/((u'-4)v'-u'v'),}
Z
=
(
9
Y
−
15
v
′
Y
−
v
′
X
)
/
3
v
′
.
{\displaystyle Z=(9Y-15v'Y-v'X)/3v'.}
La CIELab es nune maxim populara metodo di deskripto koloro ed ank es precize relat a CIEXYZ.
La transformado es segun sequa equacioni :
L
*
=
116
f
(
Y
/
Y
n
)
−
16
{\displaystyle L{\textrm {*}}=116f({Y}/{Y_{\textrm {n}}})-16}
a
*
=
500
(
f
(
X
/
X
n
)
−
f
(
Y
/
Y
n
)
)
{\displaystyle a{\textrm {*}}=500\left(f({X}/{X_{\textrm {n}}})-f({Y}/{Y_{\textrm {n}}})\right)}
b
*
=
200
(
f
(
Y
/
Y
n
)
−
f
(
Z
/
Z
n
)
)
{\displaystyle b{\textrm {*}}=200\left(f({Y}/{Y_{\textrm {n}}})-f({Z}/{Z_{\textrm {n}}})\right)}
ube:
f
(
χ
)
=
χ
1
/
3
{\displaystyle f(\chi )=\chi ^{1/3}}
χ
>
(
6
/
29
)
3
{\displaystyle \chi >(6/29)^{3}}
f
(
χ
)
=
(
841
/
108
)
χ
+
4
/
29
{\displaystyle f(\chi )=(841/108)\chi +4/29}
χ
⩽
(
6
/
29
)
3
{\displaystyle \chi \leqslant (6/29)^{3}}
X
,
Y
,
Z
{\displaystyle X,Y,Z}
X
n
,
Y
n
,
Z
n
{\displaystyle X_{\textrm {n}},Y_{\textrm {n}},Z_{\textrm {n}}}
blanko segun determinita lumizanto.
