DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Eq 26.5
Eq 26.6
Eq 26.7
To form 709Y’C B C R from [Y’, B’-Y’, R’-Y’] components in
the range [0…+1], use these equations:
709 709
219Y’
= 16 + ( 219⋅
Y’ )
112 709
CB= 128+
B’−Y’ 0. 9278
112 709
CR= 128+
R’−Y’ 0. 7874
( )
( )
To obtain 709 Y’C BC R from R’G’B’ ranging 0 to 1, scale
the rows of the matrix in Equation 26.3 by the factors
[219, 224, 224], corresponding to the excursions of
each of the components:
⎡709
219Y’
⎤ ⎡ 16 ⎤ ⎡ 46. 559 156. 629 15. 812⎤
⎡R’
⎤
⎢ ⎥ ⎢ ⎥ ⎢
⎥ ⎢ ⎥
⎢ CB
⎥ =
⎢
128
⎥
+
⎢
−25. 664 −86.
336 112
⎥
•
⎢
G’
⎥
⎢
C
⎥
R 128 112 101. 730 10. 270 B’
⎣⎢
⎦⎥
⎣
⎢
⎦
⎥
⎣
⎢ − − ⎦
⎥
⎣
⎢
⎦
⎥
Summing the first row of the matrix yields 219, the
luma excursion from black to white. The two entries of
112 reflect the positive C B C R extrema at blue and red.
To recover R’G’B’ in the range [0…+1] from 709Y’C B C R ,
use the inverse of Equation 26.6:
⎡R’
⎤ ⎡
⎤
⎛ ⎡709
0. 00456621 0 0. 00703036 Y’
⎤ ⎡ ⎤
⎞
⎢ ⎥ ⎢
⎥ ⎢219
16
⎜ ⎥ ⎢ ⎥⎟
⎢
G’
⎥
=
⎢
0. 00456621 −0. 00083627 −0.
00208984
⎥
• ⎜ ⎢ CB
⎥ −
⎢
128
⎥⎟
⎣
⎢B’
⎦
⎥
⎣
⎢0.
00456621 0. 00828393 0 ⎦
⎥ ⎜ ⎢
C
⎥
⎣⎢
⎦⎥
⎣
⎢128
⎦
⎥⎟
⎝ R ⎠
The 709 Y’C BC R components are integers in 8 bits; reconstructed
R’G’B’ is scaled to the range [0…+1].
Figure 24.2 (on page 285) illustrated that when R’G’B’
components are transformed to luma and color differences,
the unit R’G’B’ cube occupies only a small fraction
of the volume of the enclosing cube. In digital
video, only about 1 ⁄4 of Y’C BC R codewords correspond
to R’G’B’ values between zero and unity. Certain signalprocessing
operations (such as filtering) may produce
Y’C BC R codewords that lie outside the RGB-legal cube.
These codewords cause no difficulty in the Y’C BC R
domain, but potentially present a problem when
decoded to R’G’B’. Generally, R’G’B’ values are clipped
between 0 and 1.
CHAPTER 26 COMPONENT VIDEO COLOR CODING FOR HDTV 317