Interpolation of Multidimensional Functions - Control of Color Imaging Systems: Analysis and Design - page 295

Createa1-DLUTofsize10 2 by uniformly sampling the function from 0 to 1.

(a) Use linear interpolation to estimate the values of the function at x 1 ¼ 0.234

0.568. What is the resulting MSE?
(b) Repeat part a using cubic interpolation.

and x 2 ¼

6.2 Consider the 1-D LUT shown in Table 6.18.
(a) Use linear interpolation to estimate the value of the function at x ¼ 3.8.

(b) Repeat part a using
(i) The Shepard technique (use L 1 norm and m¼ 1)

(ii) The moving matrix with parameters m¼ 2 and e ¼ 0

6.3 Consider the 2-D function given by

ln ( x þ

x þ y þ xy 1 : 8 z ¼ f ( x, y ) ¼ 1 ) 0 x, y 1

10 by uniformly sampling the
function from 0 to 1 in both directions. The total number of grid points
is 100.
(b) Use bilinear interpolation to estimate the values of the function at x ¼

(a) Create a 2-D LUT of size 10

0.25

and y ¼ 0.68. What is the resulting MSE?

6.4 Consider the 3-D function

g ¼ f ( x, y, z ) ¼ ( xz þ yz þ xyz þ 1 )ln( xyz þ 1 ) 0 x, y, z 1

12 by uniformly sampling the
function from 0 to 1 in all directions. The total number of grid points is
1728.
(b) Use trilinear interpolation to estimate the values of the function at x ¼

(a) Create a 3-D LUT of size 12 12

0.75,

0.896. What is the resulting MSE?
(c) Repeat part b for the point with coordinates x ¼

y ¼ 0.68, and z ¼

0.75, y ¼ 0.75, and z ¼ 1.

What is the resulting MSE?

6.5 Consider a CMY printer characterized through the 3-D LUT given in
Table 6.19.
(a) Use trilinear interpolation to

find the L*a*b* values corresponding to the

following CMY patches:

Patch 1: CMY1 ¼ [ 20 20 20 ]

Patch 2: CMY2 ¼ [ 40 40 40 ]

Patch 3: CMY3 ¼ [ 60 60 60 ]

Patch 4: CMY4 ¼ [ 80 80 80 ]

(b) Is this printer gray balanced?