Image Processing Reference

In-Depth Information

Fig. 3.9
The RGB color

cube. Each dot corresponds to

a particular pixel value.

Multiple dots on the same

lineallhavethesamecolor,

but different levels of

illumination

Fig. 3.10
(
a
) The triangle

where all color vectors pass

through. The value of a point

on the triangle is defined

using normalized RGB

coordinates. (
b
)The

chromaticity plane

3.2.3 The Normalized RGB Color Representation

If we have the following three RGB pixel values
(
0
,
50
,
0
)
,
(
0
,
100
,
0
)
, and

(
0
,
223
,
0
)
in the RGB color cube, we can see that they all lie on the same vec-

tor, namely the one spanned by
(
0
,
0
,
0
)
and
(
0
,
255
,
0
)
. We say that all values are a

shade of green and go even further and say that they all have the same color (green),

but different levels of illumination. This also applies to the rest of the color cube.

For example, the points
(
40
,
20
,
50
)
,
(
100
,
50
,
125
)
and
(
200
,
100
,
250
)
all lie on

the same vector and therefore have the same color, but just different illumination

levels. This is illustrated in Fig.
3.9
.

If we generalize this idea of different points on the same line having the same

color, then we can see that all possible lines pass through the triangle defined by

the points
(
1
,
0
,
0
)
,
(
0
,
1
,
0
)
and
(
0
,
0
,
1
)
, see Fig.
3.10
(a). The actual point
(r,g,b)

where a line intersects the triangle is found as
2
:

R

R
+
G
+
B
,

G

R
+
G
+
B
,

B

R
+
G
+
B

(r,g,b)
=

(3.5)

These values are named
normalized RGB
and denoted
(r,g,b)
. In Table
3.3
the

rgb values of some RGB values are shown. Note that each value is in the interval

[

0
,
1

]

and that
r

+

g

+

b

=

1. This means that if we know two of the normalized

2
Note that the formula is undefined for
(R,G,B)
=
(
0
,
0
,
0
)
. We therefore make the following

definition:
(r,g,b)
≡
(
0
,
0
,
0
)
when
(R,G,B)
=
(
0
,
0
,
0
)
.