Image Processing Reference
In-Depth Information
F
Conversion Between RGB and YUV/YC
b
C
r
In this appendix the conversions from the RGB color space to the YUV/YC
b
C
r
(and
similar) color spaces, and reverse, are derived. That is, we seek a conversion from
[
]
[
Y,X
1
,X
2
]
[
Y,X
1
,X
2
]
[
]
.
In Sect. 3.3.3 it was stated that the luminance,
Y
, contains intensity information
while
X
1
and
X
2
code the color information as
weighted difference signals
with
respect to
Y
. That is:
R,G,B
to
, and one from
to
R,G,B
=
W
R
·
+
W
G
·
+
W
B
·
∈[
]
Y
R
G
BY
0
,
255
(F.1)
W
X
1
X
1
=
W
B
·
(B
−
Y)
X
1
∈[−
W
X
1
·
255
,W
X
1
·
255
]
(F.2)
1
−
W
X
2
X
2
=
W
R
·
−
X
2
∈[−
W
X
2
·
255
,W
X
2
·
]
(R
Y)
255
(F.3)
1
−
F.1
The Output of a Colorless Signal
=
=
When a colorless signal is present, i.e.,
R
G
B
,wehave
B
−
Y
B
−
W
R
·
R
−
W
G
·
G
−
W
B
·
B
X
1
=
W
X
1
·
W
B
=
W
X
1
·
⇒
1
−
1
−
W
B
B
−
W
R
·
B
−
W
G
·
B
−
W
B
·
B
X
1
=
W
X
1
·
⇔
1
−
W
B
B(
1
−
W
R
−
W
G
−
W
B
)
X
1
=
W
X
1
·
=
0
(F.4)
1
−
W
B
R
−
Y
R
−
W
R
·
R
−
W
G
·
G
−
W
B
·
B
X
2
=
W
X
2
·
−
W
R
=
W
X
2
·
⇒
1
1
−
W
R
R
−
W
R
·
R
−
W
G
·
R
−
W
B
·
R
X
2
=
W
X
2
·
⇔
1
−
W
R
R(
1
−
W
R
−
W
G
−
W
B
)
1
X
2
=
W
X
2
·
=
0
(F.5)
−
W
R
since
W
R
+
W
G
+
W
B
=
1.
