DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Eq 22.10
RGB components where one or more components are
negative or greater than unity.
Any RGB image data, or any matrix that purports to
relate RGB to XYZ, should indicate the chromaticities of
the RGB primaries involved. If you encounter a matrix
transform or image data without reference to any
primary chromaticities, be very suspicious! Its originator
may be unaware that RGB values must be associated
with chromaticity specifications in order to have
meaning for accurate color.
Noise due to matrixing
Even if it were possible to display colors in the outer
reaches of the chromaticity diagram, there would be
a great practical disadvantage in doing so. Consider
a camera that acquires XYZ tristimulus components,
then transforms to Rec. 709 RGB according to
Equation 22.9. The coefficient 3.240479 in the upper
left-hand corner of the matrix in that equation determines
the contribution from X at the camera into the
red signal. An X component acquired with 1 mV of
noise will inject 3.24 mV of noise into red: There is
a noise penalty associated with the larger coefficients in
the transform, and this penalty is quite significant in the
design of a high-quality camera.
Transforms among RGB systems
RGB values in a system employing one set of primaries
can be transformed to another set by a 3×3 linear-light
matrix transform.
[R, G, B] tristimulus values in a source space (denoted
with the subscript s) can be transformed into [R, G, B]
tristimulus values in a destination space (denoted with
the subscript d), using matrices T s and T d computed
from the corresponding chromaticities and white
points:
⎡Rd
⎤
⎡Rs
⎤
⎢ ⎥ −1
⎢ ⎥
⎢Gd
⎥ = T •T G
d s •⎢s⎥
⎢
⎣
B ⎥
⎢
d⎦
⎣
B ⎥
s ⎦
252 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES