8.3. COLOR QUALITY PROCESSING 259
Figure 8.7 Triangular membership functions defining the inputs and the output
The fuzzy control surface for the set associations described in the preceding
table is shown in Figure 8.8.
Figure 8.8 Fuzzy control surface using triangular membership functionsFigure 8.9 illustrates the overall schematic of the fuzzy logic-based color match-
ing scheme. Consider, for example, the outputs corresponding to the FAMs
marked 1, 2, and 3. Note that the output of each FAM is the change in colorant
AC 1. It is natural, in this case, to select the minimum value of the three outputs
to reduce the possibility of overshoot in the net colorant concentration. As such,
the minimum value of the outputs from each set of FAMs in Figure 8.9 are used
to update the colorant concentrations. This update is computed by adding the
change in colorant concentration to the previously computed value of colorant
concentration. These are shown in Figure 8.9 by the summing junctions where
C 1 =C 1 +∆C 1 ,C 2 =C 2 +∆C 2 ,andC 3 =C 3 +∆C 3.
In an experimental setup, after computing the colorant concentrations, the
colorants are mixed and applied to the appropriate sample/substrate and a spec-
trophotometric analysis is conducted. The resulting reflectance curves provide
a basis for determining the new tristimulus values, namely,X,Y,andZ.Note
that in the spectrophotometric analysis, all nonlinearities attributable to the