DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Eq 22.11
Eq 22.12
Eq 22.13
As an example, here is the transform from SMPTE
RP 145 RGB (e.g., SMPTE 240M) to Rec. 709 RGB:
⎡R709⎤
⎡ 0. 939555 0. 050173 0. 010272⎤
⎡R145⎤
⎢ ⎥ ⎢
⎥ ⎢ ⎥
⎢G709⎥
= ⎢ 0. 017775 0. 965795 0. 016430⎥
• ⎢G145⎥
⎢
⎣
B ⎥ ⎢
709⎦
⎣
−0. 001622 −0.
004371 1. 005993⎥
⎢
⎦ ⎣
B ⎥
145⎦
This matrix transforms EBU 3213 RGB to Rec. 709:
⎡R709⎤
⎡1.
044036 −0.
044036 0 ⎤ ⎡R
⎤
EBU
⎢ ⎥ ⎢
⎥ ⎢ ⎥
⎢G709⎥
= ⎢0
1 0 ⎥ • ⎢GEBU⎥
⎢
⎣
B ⎥ ⎢
709⎦
⎣
0 0. 011797 0. 988203⎥
⎢
⎦ ⎣
B ⎥
EBU⎦
To transform typical Sony Trinitron RGB, with D 65 white
reference, to Rec. 709, use this transform:
⎡R709⎤
⎡1.068706
−0.078595
0.009890⎤
⎡RSONY⎤
⎢ ⎥ ⎢
⎥ ⎢ ⎥
⎢G709⎥
= ⎢0.024110
0.960070 0.015819⎥
• ⎢GSONY⎥
⎢
⎣
B ⎥ ⎢
⎥ ⎢
709⎦
⎣
0.001735 0.029748 0.968517
⎦ ⎣
B ⎥
SONY⎦
Transforming among RGB systems may lead to an out of
gamut RGB result, where one or more RGB components
are negative or greater than unity.
These transformations produce accurate results only
when applied to tristimulus (linear-light) components.
In principle, to transform nonlinear R’G’B’ from one
primary system to another requires application of the
inverse transfer function to recover the tristimulus
values, computation of the matrix multiplication, then
reapplication of the transfer function. However, the
transformation matrices of Equations 22.11, 22.12, and
22.13 are similar to the identity matrix: The diagonal
terms are nearly unity, and the off-diagonal terms are
nearly zero. In these cases, if the transform is computed
in the nonlinear (gamma-corrected) R’G’B’ domain, the
resulting errors will be small.
Camera white reference
There is an implicit assumption in television that the
camera operates as if the scene were illuminated by
a source having the chromaticity of CIE D65. In practice,
television studios are often lit by tungsten lamps,
and scene illumination is often deficient in the shortwave
(blue) region of the spectrum. This situation is
CHAPTER 22 COLOR SCIENCE FOR VIDEO 253