Image Processing Reference
In-Depth Information
X 2 = W X 2 · R + W X 2 · W G
1
· G + W X 2 · W B
1
· B
(F.9)
W R
W R
Inserting we get the following conversion from RGB to YUV:
Y
U
V
0 . 299
0 . 587
0 . 114
R
G
B
Y
∈[
0 , 255
]
=
·
0 . 147
0 . 289
0 . 436
U
∈[−
111 , 111
]
∈[−
]
0 . 615
0 . 515
0 . 100
V
157 , 157
(F.10)
The conversion from YUV to RGB is found by rearranging Eqs. F.1 , F.2 , and F.3
and inserting the weight factors as above. The equations for R and B follow trivially
by rearranging Eqs. F.2 and F.3 , respectively:
1
W R
W X 2
R
=
Y
+
X 2 ·
(F.11)
1
W B
W X 1
B
=
Y
+
X 1 ·
(F.12)
The equation for G is derived by inserting Eqs. F.11 and F.12 into F.1 and rearrang-
ing:
Y
Y
1
W R
W X 2
1
W B
W X 1
Y
=
W R ·
+
X 2 ·
+
W G ·
G
+
W B ·
+
X 1 ·
1
W B
W X 1
1
W R
W X 2
X 1 ·
W B ·
X 2 ·
W R ·
Y
·
( 1
W R
W B )
G
=
W G
W G
W G
W B · ( 1
W B )
W X 1 · W G
W R · ( 1
W R )
W X 2 · W G
G = Y X 1 ·
X 2 ·
(F.13)
Inserting the weights for YUV yields the following conversion from YUV to RGB:
R
G
B
1 . 000
0 . 000
1 . 140
Y
U
V
R
∈[
0 , 255
]
=
·
1 . 000
0 . 395
0 . 581
G
∈[
0 , 255
]
(F.14)
1 . 000
2 . 032
0 . 000
B
∈[
0 , 255
]
F.4
YC b C r
The conversion from RGB to YC b C r is found by inserting the following weights
into Eqs. F.1 , F.8 , and F.9 : W R =
0 . 299, W G =
0 . 587, W B =
0 . 114, W X 1 =
0 . 5, and
W X 2 =
0 . 5
Y
C b
C r
0 . 299
0 . 587
0 . 114
R
G
B
0
128
128
Y
∈[
0 , 255
]
=
·
+
0 . 169
0 . 331
0 . 500
C b ∈[
0 , 255
]
0 . 500
0 . 419
0 . 081
C r ∈[
0 , 255
]
(F.15)
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