Graphics Reference
In-Depth Information
The CIE color system is remarkably useful; it's so standard that colorimeters mea-
sure
X
,
Y
, and
Z
values of light, for instance. In the CIE system, each color
has
XYZ
-coordinates; it's tempting to measure the “distance” between two col-
ors
C
1
=
X
1
X
+
Y
1
Y
+
Z
1
Z
and
C
2
=
X
2
X
+
Y
2
Y
+
Z
2
Z
by computing the
Euclidean distance between the triples
(
X
1
,
Y
1
,
Z
1
)
and
(
X
2
,
Y
2
,
Z
2
)
. Unfortunately,
this does
not
correspond to the
perceived
color distance: If
C
1
and
C
2
have the
same Euclidean distance as
C
3
and
C
4
, the perceived distance between them may
be very different.
Fortunately, one can transform the
XYZ
-coordinates,
nonlinearly,
to get new
coordinates in which the Euclidean distance
does
correspond to perceptual dis-
tance. The 1960 CIE
Luv
color coordinates were developed to meet this need,
but they were superseded by the 1976 CIE
L
∗
u
∗
v
∗
uniform color space.
Letting
X
w
,
Y
w
, and
Z
w
denote the
XYZ
-coordinates of the color to be used as white, the
L
∗
u
∗
v
∗
coordinates of a color with
XYZ
-coordinates
(
X
,
Y
,
Z
)
are defined by the
formula for
L
∗
given in Equation 28.10, and
4
X
X
+
15
Y
+
3
Z
,
u
=
(28.30)
9
Y
X
+
15
Y
+
3
Z
,
v
=
(28.31)
4
X
w
X
w
+
15
Y
w
+
3
Z
w
,
u
w
=
(28.32)
9
Y
w
X
w
+
15
Y
w
+
3
Z
w
,
v
w
=
(28.33)
u
∗
=
13
L
∗
(
u
−
u
w
)
, and
(28.34)
v
∗
=
13
L
∗
(
v
−
v
w
)
.
(28.35)
The CIE has also defined
L
∗
a
∗
b
∗
color coordinates (sometimes called “Lab”
color) by
a
∗
=
500
(
X
Y
w
)
3
and
X
w
)
3
/
−
(
Y
/
(28.36)
b
∗
=
500
(
Y
Z
w
)
3
,
X
w
)
3
/
−
(
Z
/
(28.37)
where
X
w
,
Y
w
, and
Z
w
denote the
XYZ
-coordinates of the white point. Both
L
∗
u
∗
v
∗
and
L
∗
a
∗
b
∗
can be used to measure “distance” in color space, and both
see frequent use in computer graphics, although
L
∗
a
∗
b
∗
seems to be more widely
used in the description of displayed colors.
The CIE diagram we've shown is based on the 1931 tabulation of colors, in which
samples subtended a 2
◦
field of view on the retina. There's also a 1964 tabulation
for a 10
◦
field of view, emphasizing larger areas of constant color. For much of
computer graphics, the narrower field of view is more relevant.
The mapping from the space of all spectra (which is infinite-dimensional) to
the space of response triples (which is three-dimensional) is more or less linear
