DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Michael Brill and R.W.G. Hunt
argue that R, G, and B tristimulus
values have no units. See Hunt,
R.W.G., “The Heights of the CIE
Colour-Matching Functions,” in
Color Research and Application,
22 (5): 337 (Oct. 1997).
The column vectors of the matrix in Equation 22.2 give,
for each primary, the weights of each of the three
discrete wavelengths that are required to display unit
XYZ tristimulus values. The color-matching functions for
CIE XYZ are shown in Figure 22.3, CMFs for CIE XYZ
primaries, on page 244. Opposite those functions, in
Figure 22.4, is the corresponding set of primary SPDs.
As expected, the display primaries have some negative
spectral components: The primary SPDs are nonphysical.
Any set of primaries that reproduces color from
XYZ tristimulus values is necessarily supersaturated,
more saturated than any realizable SPD could be.
To determine a set of physical SPDs that will reproduce
color when driven from XYZ, consider the problem in
the other direction: Given a set of physically realizable
display primaries, what CMFs are suitable to directly
reproduce color using mixtures of these primaries?
In this case the matrix that relates RGB components to
CIE XYZ tristimulus values is all-positive, but the CMFs
required for analysis of the scene have negative
portions: The analysis filters are nonrealizable.
Figure 22.6 shows a set of primary SPDs conformant to
SMPTE 240M, similar to Rec. 709. Many different SPDs
can produce an exact match to these chromaticities.
The set shown is from a Sony Trinitron monitor.
Figure 22.5 shows the corresponding color-matching
functions. As expected, the CMFs have negative lobes
and are therefore not directly realizable.
We conclude that we can use physically realizable
analysis CMFs, as in the first example, where XYZ
components are displayed directly. But this requires
nonphysical display primary SPDs. Or we can use physical
display primary SPDs, but this requires nonphysical
analysis CMFs. As a consequence of the way color
vision works, there is no set of nonnegative display
primary SPDs that corresponds to an all-positive set of
analysis functions.
The escape from this conundrum is to impose a 3×3
matrix multiplication in the processing of the camera
signals, instead of using the camera signals to directly
242 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES