DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 25.3 CBCR components
for SDTV are shown
in their mathematical form.
The range outside
[-112 … +112] is available
for undershoot and overshoot.
At an 8-bit inter-
+112
R
face, an offset of +128 is
added to each color differ-
Yl
ence component. -112 0
The numerical values used in this
equation, and in those to follow,
are based on the Rec. 601 luma
coefficients. The coefficients for
HDTV are, unfortunately, different.
See Rec. 601 luma, on page 291.
G
-112
C R axis
For signal-processing arithmetic operations such as gain
adjustment, Y’, C B , and C R must be zero for black: The
interface offsets must be removed. For 8-bit luma arithmetic,
it is convenient to place reference black at
code 0 and reference white at code 219. Color difference
signals are most conveniently handled in two’s
complement form, scaled so that reference color difference
signals (at pure yellow, cyan, red, and blue) are
±112. Figure 25.3 above shows the C BC R color difference
plane scaled in this manner, without offsets.
As far as I am concerned, the offsets should be treated
as an interface feature. Most descriptions of Y’C B C R ,
though – including SMPTE and ITU standards – take the
Y’C B C R notation to include the offset. In the equations
to follow, I include the offset terms in gray. If your goal
is to compute abstract, mathematical quantities suitable
for signal processing, omit the offsets. If you are
concerned with the interface, include them.
These equations form Rec. 601 Y’CBCR components
from [Y’, B’-Y’, R’-Y’] components ranging [0 … +1]:
601 601
219Y’
= 16 + ( 219⋅
Y’ )
112 601
CB= 128+
B’ Y’
0 886 ( − )
Eq 25.5
.
112 601
CR= 128+
( R’ − Y’
0. 701 )
CHAPTER 25 COMPONENT VIDEO COLOR CODING FOR SDTV 307
Cy
Mg
B
+112 CB axis