Image Processing Reference
In-Depth Information
Equation 6.28 is used to solve for A. The result is
A
¼
SP
1
(
6
:
29
)
where
X
N
W
i
y
i
x
i
S
¼
i
¼
1
X
N
W
i
x
i
x
i
P
¼
i
¼
1
The weight Wi
i
is a function of the distance from the input point x to all the points
x
i
in the LUT. It is inversely proportional to the distance, which gives more weight to
the points closer to the desired point and less weight to points that are farther away
from the desired point. The weight Wi
i
is given by
1
d
i
þ e
W
i
¼
(
6
:
30
)
where d
i
¼k
x
x
i
k
is the Euclidean norm distance. The variable parameters of this
algorithm are
m
and
e
. These two parameters affect the locality of the regression.
Large values of
give Wi
i
more local behavior, which means
that only points closest to the desired point will be considered as signi
m
and small values of
e
cant points.
We now consider a sample example.
Example 6.7
Consider the 1-D function y¼P(x) given by the LUT shown in Table 6.9.
Use the moving-matrix approach, interpolate, and compute the corresponding
value of P(x)atx ¼
10
4
.
0.5. Use
m¼
2 and
e ¼
S
OLUTION
1
d
i
þ e
¼
1
1
W
i
¼
0001
¼
i ¼
1, 2,
...
,10
2
2
j
x x
i
j
þ
0
:
j
0
:
5
x
i
j
þ
0
:
0001
TABLE 6.9
One-Dimensional Function LUT
x
0
0.07
0.27
0.34
0.41
0.55
0.66
0.80
0.89
1
y
0.523
0.461
0.0079
0.0334
0.0266
0.279
0.419
0.545
0.702
1
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