DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

XYZ
or R 1G 1B 1
TRISTIMULUS 3×3
(“LINEAR MATRIX”)
-1
[T
1 ]
I use T 1 -1 to denote the encoding
“linear matrix,” to conform to the
notation of Luminance coefficients,
on page 250.
RGB
TRANSFER
FUNCTION
γ E ≈0.5
NONLINEAR
3×3
[ P ]
CHROMA
SUBSAMPLING
R’G’B’ Y’CBCR Y’CBCR
e.g., 4:2:2
Figure 24.7 Luma/color difference encoder. involves the four stages summarized in this block
diagram. First, linear-light (tristimulus) input signals are transformed through the “linear” matrix
T 1 -1 to produce RGB coded to the interchange primaries. Gamma correction is then applied. The
matrix P then produces luma and two color differences. The color difference (chroma) signals are
then subsampled; luma undergoes a compensating delay.
Interchange primaries are also
called transmission primaries.
necessary to insert a 3×3 matrix that transforms from
the interchange primaries to the image display primaries.
(See page 252.)
Figure 24.7 above summarizes luma/color difference
encoding. If image data originated in linear XYZ components,
a 3×3 matrix transform (T 1 -1 ) would be applied to
obtain linear RGB having chromaticities and white reference
of the interchange primaries. For Rec. 709 interchange
primaries standard for SDTV and HDTV, the
matrix would be that of Equation 22.9, on page 251.
More typically, image data originates in some devicedependent
space that I denote R 1 G 1 B 1 , and the 3×3
“linear matrix” transform (T 1 -1 ) is determined by the
camera designer. See the sequence of Figures 22.3
through 22.8, starting on page 244, and the accompanying
text and captions, to gain an appreciation for how
such a matrix might be crafted. Practical cameras do not
have spectral sensitivities that are linear combinations
of the CIE color matching functions, so they are not
properly characterized by chromaticities. Nonetheless,
once a linear matrix to a set of interchange primaries
has been chosen, Equation 22.10 can be used to derive
equivalent sensor primaries (the “taking primaries”).
Once the linear matrix has been applied, each of the
components is subject to a nonlinear transfer function
(gamma correction) that produces nonlinear R’G’B’.
These components are transformed through a 3×3
294 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES