DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 23.3 Rec. 709
transfer function is
used in SDTV and HDTV.
Video signal, V’
ITU-R Rec. BT.709, Basic parameter
values for the HDTV standard
for the studio and for international
programme exchange.
The symbol L suggests linear. Take
care not to confuse it with lightness,
L*. The symbol V’ suggests
voltage, or video.
1.0
0.8
0.6
0.4
0.2
0.081
0
0
0.018
Linear segment,
slope 4.5
Power function segment,
exponent 0.45
0.2 0.4 0.6 0.8 1.0
Tristimulus value, L (relative)
Rec. 709 transfer function
Figure 23.3 illustrates the transfer function defined by
the international Rec. 709 standard for high-definition
television (HDTV). It is based upon a pure power function
with an exponent of 0.45. Theoretically, a pure
power function suffices for gamma correction; however,
the slope of a pure power function (whose exponent is
less than unity) is infinite at zero. In a practical system
such as a television camera, in order to minimize noise
in dark regions of the picture it is necessary to limit the
slope (gain) of the function near black. Rec. 709 specifies
a slope of 4.5 below a tristimulus value of +0.018,
and scales and offsets the pure power function segment
of the curve to maintain function and tangent continuity
at the breakpoint.
In this equation the tristimulus (linear light) component
is denoted L, and the resulting gamma-corrected
video signal – one of R’, G’, or B’ components – is
denoted with a prime symbol, V’ 709. R, G, and B are
processed through identical functions to obtain R’, G’,
and B’:
⎧⎪
4. 5L; 0 ≤ L<
0. 018
V'709
= ⎨ 045 .
Eq 23.2
⎩⎪ 1. 099L −0. 099; 0. 018 ≤ L≤1
The Rec. 709 equation includes an exponent of 0.45.
However, the effect of the scale factor and offset terms
CHAPTER 23 GAMMA 263