Interpolation of Multidimensional Functions - Control of Color Imaging Systems: Analysis and Design - page 297

TABLE 6.19 (continued)
Three-Dimensional LUT
C

M Y L* a* b*

170 170 170 45.60 9.06 5.44

170 170 255 45.80 6.20 26.89

170 255 0 32.07 53.10 47.14

170 255 85 34.28 44.77 22.91

170 255 170 35.64 40.48 3.57

170 255 255 36.49 37.66 13.50

255 0 0 54.56 38.18 55.13

255 0 85 54.79 51.25 24.05

255 0 170 54.76 57.79 4.20

255 0 255 54.54 61.72 34.77

255 85 0 44.41 12.50 55.51

255 85 85 45.39 24.51 27.21

255 85 170 45.94 30.78 2.37

255 85 255 46.10 34.92 23.72

255 170 0 35.67 11.46 56.40

255 170 85 37.20 0.42 30.48

255 170 170 38.40 5.71 7.77

255 170 255 39.12 10.12 14.22

255 255 0 24.98 42.17 57.67

35.15

255 255 85 26.99 33.01

255 255 170 28.80 27.68 16.30

255 255 255 30.04 23.55 1.02

6.6 Repeat Problem 6.3 using
(a) Tetrahedral interpolation
(b) Shepard interpolation
(c) Moving matrix

6.7 Show that the Shepard interpolation algorithm given by

8
<

P i ¼ 1 y i d m

P N
i ¼ 1 d m

if d i 6¼ 0 for all i

i

y ¼

:

i

y j if d j ¼ 0 for some j

will result in a differentiable function if parameter m> 1.

6.8 Assume that we have a CMY ! L*a*b* printer characterization function with
Jacobian J at the nominal value CMY ¼

[120 67 145] given by

2
4

3
5

0 : 1586 0 : 1223 0 : 0075

J ¼ q Lab

q CMY ¼

0 : 1267 0 : 3146 0 : 0299

0 : 1292 0 : 0480 0 : 4026