Image Processing Reference
In-Depth Information
ting them. Knowledge of human perception was taken into account when defining
the weights used for the conversion, see Sect.
3.2.2
:
Y
=
W
R
·
R
+
W
G
·
G
+
W
B
·
BY
∈[
0
,
255
]
(3.24)
where
W
R
+
1.
As the color screen technology matured, a need for transmitting color signals
arose. Two requirements were set up when defining how to transmit color sig-
nals: 1) The signal should be compatible with the already existing signals used for
monochrome screens and 2) the decoding on the receiver side should be as sim-
ple as possible. From this it followed that the color information was transmitted as
weighted difference signals
with respect to
Y
:
W
G
+
W
B
=
W
X
1
X
1
=
W
B
·
(B
−
Y)
X
1
∈[−
W
X
1
·
255
,W
X
1
·
255
]
(3.25)
1
−
W
X
2
X
2
=
W
R
·
(R
−
Y)
X
2
∈[−
W
X
2
·
255
,W
X
2
·
255
]
(3.26)
1
−
where
W
X
1
and
W
X
2
are weight factors,
W
R
and
W
B
are from Eq.
3.24
, and
X
1
and
X
2
encode the blue and red information, respectively. The green information
can then be inferred from
Y
,
X
1
and
X
2
. Note that when no color is present, i.e.
R
=
G
=
B
,wehave
X
1
=
0 and
X
2
=
0, see Appendix F. This means that
X
1
and
X
2
need not be send.
So, by transmitting
(Y, X
1
,X
2
)
a monochrome receiver can simply show
Y
,
while a color receiver can decode
(R,G,B)
and show a color signal using the fol-
lowing equations, see Appendix F for details:
1
W
R
W
X
2
−
R
=
Y
+
X
2
·
(3.27)
W
B
·
(
1
−
W
B
)
W
R
·
(
1
−
W
R
)
G
=
Y
−
X
1
·
−
X
2
·
(3.28)
W
X
1
·
W
X
2
·
W
G
W
G
1
−
W
B
W
X
1
B
=
Y
+
X
1
·
(3.29)
Note that since all the weights are known in advance the conversion becomes rather
simple.
One of the most well known color spaces using this principle is the YUV color
space. The YUV color space is for example used in most European TV transmission
standards. YUV uses the weights:
W
R
=
0
.
299,
W
G
=
0
.
587,
W
B
=
0
.
114,
W
X
1
=
0
.
436, and
W
X
2
=
0
.
615, and has the conversion listed below, see Appendix F for
details. In Table
3.3
the YUV values of some RGB values are shown.
⎡
⎤
⎡
⎤
⎡
⎤
Y
U
V
0
.
299
0
.
587
0
.
114
R
G
B
Y
∈[
0
,
255
]
⎣
⎦
=
⎣
⎦
·
⎣
⎦
−
0
.
147
−
0
.
289
0
.
436
U
∈[−
111
,
111
]
(3.30)
−
−
0
.
615
0
.
515
0
.
100
V
∈[−
157
,
157
]
