Image Processing Reference
In-Depth Information
Hence,
p ¼p 000 þp x xx 0
x 1 x 0 þp y yy 0
y 1 y 0 þp z z z 0
z 1 z 0
2
4
3
5 þ
2
4
3
5 þ
2
4
3
5 þ
2
4
3
5
82
:
98
14
:
48
10
:
33
0
:
77
67
0
128
85
54
0
¼
29
:
86
0
14
:
27
85
23
:
94
0
7
:
78
85
170
85
7
:
28
18
:
14
5
:
66
30
:
44
Therefore,
2
4
3
5
65
:
85
p ¼
25
:
78
5
:
10
6.2.4 S EQUENTIAL L INEAR I NTERPOLATION
Uniformly sampled LUTs do not use the color space ef
ciently. For example, a
3-D uniformly sampled L*a*b*toCMY LUT used to characterize a digital printer will
havemany colors that are outside the printer gamut. Therefore, if one can optimally place
the grid points to achieve good approximations of the multidimensional functions, then
the color space is optimally utilized and the resulting mean-square error (MSE) due to
interpolation will be small. The sequential linear interpolation (SLI) is an optimal
approach for approximating multidimensional functions by selecting the location
of the grid points in a sequential form suitable for sequential interpolation [3].
Here we assume that the grid points have already been selected optimally
according to the SLI algorithm and only discuss the SLI. For the 1-D functions,
the approach is similar to linear interpolation; therefore, we consider 2-D functions
and extend the results to 3-D. Let y ¼ f(x)
¼ f(x 1 , x 2 ) be a nonlinear function of the
two variables x 1 and x 2 . Figure 6.11 shows an SLI grid structure LUT of size 19.
To interpolate a grid point p ¼
rst
project this point to the two nearest grid lines to the right and left of p, as shown in
Figure 6.12.
One-dimensional linear interpolation is used to estimate the values of the
function, y R and y L , at points p R and p L , respectively. They are given by
[x 1
x 2 ] that is not part of the LUT, we
y R ¼ w R fp R ðÞþ
ð
1
w R
Þ fp R ðÞ
(
6
:
17
)
and
y L ¼ w L fp L ðÞþ
ð
w L
Þ fp L ðÞ
(
:
)
1
6
18
Search WWH ::




Custom Search