Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 387

TABLE 7.11 (continued)
Example Illustrating the Convergence of a Ray between x 0 ¼ [L 0 ¼50, a 0 ¼0,
b 0 ¼0] and x c ¼ [L c ¼80, a c ¼50, b c ¼30] for Colors between 0 and 50
Iteration# Best CMYK

L * a * b *

Color# 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 C M Y K

34 60.20 17.00 10.20 5.85 2.34 0.95 0.38 0.15 0.06 0.02 0.01 0.00 0.00 66.70 123.93 101.10 40.85

35 60.50 17.50 10.50 5.74 2.35 0.95 0.38 0.15 0.06 0.02 0.01 0.00 0.00 65.85 125.02 101.57 39.28

36 60.80 18.00 10.80 5.49 2.28 0.93 0.38 0.15 0.06 0.02 0.01 0.00 0.00 65.84 126.46 102.43 37.08

37 61.10 18.50 11.10 5.74 2.39 0.98 0.40 0.16 0.06 0.03 0.01 0.00 0.00 65.38 127.61 103.05 35.26

38 61.40 19.00 11.40 5.23 2.17 0.89 0.36 0.14 0.06 0.02 0.01 0.00 0.00 64.83 128.72 103.63 33.52

39 61.70 19.50 11.70 5.50 2.28 0.92 0.37 0.15 0.06 0.02 0.01 0.00 0.00 63.52 129.45 103.81 32.39

40 62.00 20.00 12.00 4.92 2.02 0.82 0.33 0.13 0.06 0.03 0.02 0.01 0.00 64.24 131.15 105.14 29.57

41 62.30 20.50 12.30 5.52 2.26 0.90 0.38 0.19 0.09 0.05 0.02 0.01 0.01 62.80 131.84 105.26 28.25

42 62.60 21.00 12.60 5.14 2.13 0.89 0.42 0.20 0.09 0.05 0.02 0.01 0.01 61.87 132.76 105.70 26.50

43 62.90 21.50 12.90 5.25 2.19 0.98 0.46 0.22 0.11 0.05 0.03 0.01 0.01 60.75 133.57 106.04 24.88

44 63.20 22.00 13.20 4.37 1.89 0.94 0.47 0.24 0.12 0.06 0.03 0.02 0.01 60.73 135.18 107.09 22.10

45 63.50 22.50 13.50 4.96 2.16 1.06 0.52 0.26 0.13 0.07 0.03 0.02 0.01 59.25 136.04 107.22 20.90

46 63.80 23.00 13.80 4.78 2.22 1.08 0.53 0.26 0.13 0.07 0.03 0.02 0.01 58.42 137.28 107.77 19.00

47 64.10 23.50 14.10 4.44 2.17 1.07 0.52 0.26 0.13 0.07 0.04 0.02 0.01 57.62 138.44 108.23 17.05

48 64.40 24.00 14.40 4.15 2.03 0.99 0.49 0.25 0.13 0.06 0.03 0.02 0.01 56.46 139.40 108.49 15.49

49 64.70 24.50 14.70 4.76 2.31 1.12 0.55 0.27 0.11 0.04 0.02 0.01 0.00 55.10 140.25 108.63 14.46

50 65.00 25.00 15.00 4.16 2.08 1.05 0.43 0.17 0.06 0.02 0.01 0.00 0.00 54.81 141.69 109.43 12.70

The CMYK values achieved during convergence are also shown in last four
columns corresponding to each row. They are the best CMYK values for the chosen
GCR used to determine the nominal CMYK that give the minimum D E a * error. In

other words, these values represent the best CMYK values for minimum D E a * (for

both in & out-of-gamut colors). From this table, it is also easy to nd the mapped

CMYK values for the node color, x c , when the node color is projected along the ray in
the ray-based gamut mapping. As is the case in gamut clipping method one of the

ray-based approaches the gamut-mapped color will be on the surface when this
approach is used. This is obtained when the ray penetrates the surface. It is equal
to 77th color in Table 7.12. The CMYK values of the nearest out-of-gamut node give
the gamut-mapped CMYK values for the node color x c when the mapping is done
along the ray. In gamut compression method

—

the
gamut-mapped colors are moved inward along the ray to the nearest node with a
scaling associated with the local region of the gamut. A ray-based control model can
also be used to perform an accurate linear mapping for the compression algorithms.
Thus, in Table 7.12 (see marked boxes), the node color, x c (1) is out-of-gamut
by 15.79

— another ray-based approach —

D E a * , (2) can be gamut mapped with minimum D E a * with a gamut-mapped

CMYK value of C ¼ 0, (3) can be gamut mapped

along the ray on the gamut surface with a gamut-mapped CMYK value of C ¼

0, M ¼ 169.76, Y ¼ 110.61, K ¼

0,

M ¼ 0, and (4) can be mapped inward along the ray as in

compression methods (e.g., say for example, x c can be mapped to color# 72 with a
gamut-mapped CMYK value of C ¼

150.98, Y ¼ 103.28, K ¼

7.94, M ¼ 148.99, Y ¼ 103.93, K ¼ 2.51).