Image Processing Reference
In-Depth Information
Therefore,
[CMY]
¼
[98
:
27 161
:
53 176
:
64]
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 80
14]
L*a*b
i
*
i
P
i¼1
d
m
i
y ¼
(b)
¼
P
27
i¼
¼
P
27
i¼
k
2
1
d
2
k
[50 80
14]
L*a*b
i
*
i
i
1
¼
[27
:
35 240
:
57 26
:
81]
Therefore,
[CMY]
¼
[27
:
35 240
:
57 26
:
81]
6.3.2 M
OVING
-M
ATRIX
I
NTERPOLATION
The moving-matrix approach is another nonlinear technique for interpolation of
irregularly spaced or scattered multidimensional data [5]. It is based on weighted
least-square regression. The interpolated value
y at point x is given as
y
¼
Ax
(
6
:
25
)
where
x
¼
[x 1]
T
is the augmented vector x
A is the transformation matrix of size M
(M
þ
1)
If quadratic, cubic, or other terms are included, then the number of terms in the
augmented vector and the transformation matrix correspondingly increase.
The transformation matrix A is obtained by minimizing the weighted square error
given by
X
N
2
W
i
y
i
Ax
i
E
¼
k
k
(
6
:
26
)
i
¼
1
The above expression for E can be expanded as
X
X
2A
X
W
i
x
i
y
i
þ
A
X
N
N
N
N
Þ
T
¼
W
i
y
i
y
i
W
i
x
i
x
i
A
T
E
¼
W
i
y
i
Ax
i
ð
Þ
y
i
Ax
i
ð
i
¼
1
i
¼
1
i
¼
1
i
¼
1
(
6
:
27
)
Differentiating the above equation with respect to A and setting it equal to zero yields
2
X
2A
X
N
N
q
E
q
A
¼
W
i
y
i
x
i
þ
W
i
x
i
x
i
¼
0
(
6
:
28
)
i
¼
1
i
¼
1
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