DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 25.2 P BP R
components for SDTV
Eq 25.2
Eq 25.3
+0.5
R
Yl
-0.5 0
G
-0.5
P R axis
accompanying luma component. For Rec. 601 luma, the
equations are these:
05 .
PB= ⎛ 601
B'−Y'⎞ 1− 0. 114 ⎝ ⎠
1
= ⎛ 601
B'− Y'⎞ 1. 772 ⎝ ⎠
. ⎛ 601
≈ 0 564 B'−Y'⎞ ⎝ ⎠
05 .
PR= ⎛ 601
R'−Y'⎞ 1− 0. 299 ⎝ ⎠
1
= ⎛ 601
R'− Y'⎞ 1. 402 ⎝ ⎠
≈ 0. 713⎛
601
R'−Y'⎞ ⎝ ⎠
These scale factors are chosen to limit the excursion of
each color difference component to the range -0.5 to
+0.5 with respect to unity luma excursion: 0.114 in the
first expression above is the luma coefficient of blue,
and 0.299 in the second is for red. Figure 25.2 above
shows a plot of the [P B , P R ] plane.
Expressed in matrix form, the B’-Y’ and R’-Y’ rows of
Equation 25.1 are scaled by 0.5 ⁄0.886 and 0.5 ⁄0.701.
To encode from R’G’B’ where reference black is zero
and reference white is unity:
The first row of Equation 25.3 comprises the luma coefficients;
these sum to unity. The second and third rows
each sum to zero, a necessity for color difference
components. The two entries of 0.5 reflect the reference
excursions of P B and P R, at the blue and red prima-
304 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES
Cy
Mg
B
+0.5
P B axis
⎡601
Y'⎤⎡0.
299 0. 587 0. 114 ⎤ ⎡R'⎤
⎢ ⎥ ⎢
⎥ ⎢ ⎥
⎢ PB
⎥ = ⎢−0.
168736 −0.
331264 0. 5 ⎥ • ⎢G'⎥
⎢ ⎥
P ⎢
R 0. 5 0. 418688 0. 081312 B'
⎣⎢
⎦⎥
⎣
− − ⎥ ⎢ ⎥
⎦ ⎣ ⎦