Assume that a 999 CMY to L*a*b* characterization LUT is measured for a digital color printer. This LUT is used to compute the CMY values corresponding to the gray values of ai* ¼ bi* ¼ 0, Li* ¼ 15 þ 10i, i ¼ 1, 2, . . . ,6. The ICI algorithm (Section 6.4.3) is used to find the right combination of the CMY values.

The results are shown in Table 8.4. Note that since ICI is an iterative technique, the iterations are terminated once the error or number of iterations reach a predefined threshold. Hence, exact gray with ai* ¼ bi* ¼ 0 may not be achieved.

Table 8.5 shows the three gray-balance TRC functions. Figures 8.6 through 8.8 show the plots of the cyan, magenta, and yellow gray-balanced TRCs, respectively.

The available seven data points on the TRCs are marked by a circle and the other values are obtained through linear interpolation (for internal points)

or linear extrapolation (for external points). Note that since smooth TRCs are constructed, the final TRCs do not pass through the data points, particularly in the shadow region. This has the effect of making gray balance less accurate in those regions, but may be essential to reproduce smooth, contourless shadow colors.

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TABLE 8.4 Input CMY Values that Generate Gray L* a* b* C M Y 324 25 0.005 0.005 235.25 237.18 221.58 35 0 -0.002 203.44 200.61 187.41 45 0.003 0.004 164.89 169.45 155.1 55 -0.002 -0.003 131.58 129.78 132.97 65 0.002 0.003 97.88 104.02 104.85 75 0.0017 0.001 68.48 70.85 68.73 TABLE 8.5 Three Gray-Balance TRCS D*=Cin Min Yin Cout Mout Yout 191 235.25 237.18 221.58 166 203.44 200.61 187.41 140 164.891 169.45 155.1 115 131.58 129.78 132.97 89 97.88 104.02 104.85 64 68.48 70.85 68.73