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

]