Interpolation of Multidimensional Functions - Control of Color Imaging Systems: Analysis and Design - page 265

Example 6.6

3 forward printer map LUT (CMY!L* a* b *)
given in Table 6.8. Use the Shepard interpolation algorithm to

Consider a CMY printer with the 3 3

nd

(a) The CMY corresponding to L* ¼ 50, a* ¼ 30, and b* ¼ 40. Use m¼ 2 and

2.
(b) The CMY corresponding to L*

p¼

¼ 50, a* ¼ 80, and b* ¼ 14. Use m¼ 2

and p¼ 2.

S OLUTION

P i¼ 1 y i d m P 27

i¼

P 27
i¼

k 2

1 y i d 2

1 CMY i k

[50 30 40] L*a*b i *

y ¼

i
P i¼1 d m

i

(a) ¼ ¼

P 27
i¼

P 27
i¼

k 2

1 d 2

k [50 30 40] L*a*b i *

i i 1

¼ [98 : 27 161 : 53 176 : 64]

TABLE 6.8
33 Forward Printer MAP

C M Y L* a* b*

0 0 0 100 0.04 0.00

0 0 127.5 94.49 5.38 50.30

0 0 255 94.96 8.59 100.00

0 127.5 0 75.04 43.12 8.91

0 127.5 127.5 74.41 34.79 34.04

0 127.5 255 74.12 29.53 75.96

0 255 0 53.82 86.18 14.25

0 255 127.5 55.69 75.09 20.86

0 255 255 55.16 70.02 49.03

21.68 29.70

127.5 0 0 73.27

127.5 0 127.5 71.72 31.65 16.27

127.5 0 255 70.49 37.09 59.89

127.5 127.5 0 55.41 19.06 35.43

127.5 127.5 127.5 56.37 8.82 5.92

127.5 127.5 255 55.38 3.27 42.27

127.5 255 0 37.93 59.71 40.59

127.5 255 127.5 40.09 50.02 4.48

127.5 255 255 40.70 44.69 24.55

255 0 0 54.56 38.18 55.13

255 0 127.5 54.37 54.87 9.70

255 0 255 54.54 61.72 34.77

255 127.5 0 39.35 2.52 57.00

255 127.5 127.5 40.61 15.15 17.88

255 127.5 255 41.46 22.62 17.91

255 255 0 24.98 42.17 57.67

255 255 127.5 26.93 28.03 26.23

255 255 255 30.04 23.55 1.02