Page 127 - Computational Colour Science Using MATLAB

114 CHARACTERIZATION OF COMPUTER DISPLAYS
practice, a relationship of the form shown as Equation (7.3) is used to map the
N
N
normalized DAC values (d /(2 1), d /(2 1), and d /(2 1)) to the linearized
N
g
r
b
normalized DAC values (R, G, and B). Thus, for the red channel the following
equation can be used,
N
R ¼ðad r =ð2 1Þþð1 aÞÞ , ð7:4Þ
g
where the normalization procedure requires that the system gain and offset are
equal to unity. Since there are three model parameters but only two degrees of
freedom, a minimum of two radiometric measurements are required per channel.
The advantage of minimizing the number of measurements required to
characterize the monitor is important since it is widely recognized that when
making the measurements a time of at least 80 s must be allowed for the colour to
stabilize (Berns et al., 1993a, 1993b). It is only practicable to allow this time for
relatively small numbers of measurements. Berns et al. (1993a) recommend
measuring neutral colours where the load is placed equally across all three
channels rather than highly chromatic colours where the load is placed on only
one of the gun amplifiers. As few as two neutral colours need be measured in
order to be able to determine the parameters of Equation (7.4) for all three
channels.

7.4 Device-independent transformation

Once the GOG model [Equation (7.4)] has been used to linearize the DAC
values, the values can be related to tristimulus values using a simple linear
transform,

2 3 2 32 3
X X r,max X g,max X b,max R
Y r,max Y g,max Y b,max 5 G 5,
6 7 6 76 7
4 Y 5 ¼ 4 4 ð7:5Þ
Z Z r,max Z g,max Z b,max B

where RGB are the linearized and normalized (in the range 0–1) DAC values.
Three measurements are required in order to specify the system matrix for
Equation (7.5). The tristimulus values XYZ must be measured for each of the
N
guns at the maximum DAC value (2 1, where N is the number of bits in the
DAC). The XYZ values of the red gun at maximum intensity form the first
column of the system matrix [Equation (7.5)] and the XYZ values for the green
and blue guns form the second and third columns, respectively. Once each of the
guns has been measured for maximum DAC values the system matrix for
Equation (7.5) is known.