A First Course in FUZZY and NEURAL CONTROL

8.3. COLOR QUALITY PROCESSING 261

These equations, given in [7], are:

X−X 0 =(X−X 1 )∆C 1 +(X−X 2 )∆C 2 +(X−X 3 )∆C 3 (8.1)

Y−Y 0 =(Y−Y 1 )∆C 1 +(Y−Y 2 )∆C 2 +(Y−Y 3 )∆C 3

Z−Z 0 =(Z−Z 1 )∆C 1 +(Z−Z 2 )∆C 2 +(Z−Z 3 )∆C 3

Equations 8.1 can be rewritten as

X =

X 0 −X 1 ∆C 1 −X 2 ∆C 2 −X 3 ∆C 3

1 −∆C 1 −∆C 2 −∆C 3

(8.2)

X =

Y 0 −Y 1 ∆C 1 −Y 2 ∆C 2 −Y 3 ∆C 3

1 −∆C 1 −∆C 2 −∆C 3

Z =

Z 0 −Z 1 ∆C 1 −Z 2 ∆C 2 −Z 3 ∆C 3

1 −∆C 1 −∆C 2 −∆C 3

The evaluation of Equations 8.2 to obtain the tristimulus values of the sample
require a set of nine look-up tables, namely, (X 1 versusC 1 ), (X 1 versusC 2 ),
(X 1 versusC 3 ), ..., (Z 3 versusC 3 ) that have to be experimentally determined
for a given sample. The tristimulus valuesX,Y,andZof the sample are then
compared with that of the standard, namely,X 0 ,Y 0 ,andZ 0. If the difference
in tristimulus values between the standard and that of the sample is within the
acceptable tolerance, the colorant concentrations will result in a match between
the standard and the sample. If not, a new change in colorant concentration is
computed and added to the previously computed values ofC 1 ,C 2 ,andC 3.

Simulation results Figures 8.10 and 8.11 illustrate simulation results for a
case where the initial colorantsC 1 ,C 2 ,andC 3 , and the tristimulus valuesX 0 ,
Y 0 ,andZ 0 are specified.

Figure 8.10. Convergence of colorant concentrations to yield desiredX 0 ,Y 0 ,

andZ 0

For the purpose of simulation, values of the colorants that are smaller than
those of the standard are chosen initially and their tristimulus values are deter-
mined as a representative description of the sample. It is clear from the results
that the colorant concentrations are incrementally adjusted following each itera-
tion to yield ultimately the desired tristimulus values of the standard. It should