Information Technology Reference
In-Depth Information
β
1
(
m
) is expanded as follows:
d
dx
μ
mt
(
x
)
2
X
/
L
i
=1
∑
β
1
(
m
)=κ
1
x
∈
B
[
i
]
X
/
L
i
=1
∑
2
κ
1
B
[
i
]
{
μ
mt
(
x
)
−
μ
mt
(
x
−
1)
}
x
∈
X
/
L
i
=1
∑
X
/
L
i
=1
∑
X
/
L
i
=1
∑
x
∈
B
[
i
]
μ
mt
(
x
)
2
+κ
1
x
∈
B
[
i
]
μ
mt
(
x
−
1)
2
= κ
1
−
2κ
1
x
∈
B
[
i
]
{
μ
mt
(
x
)μ
mt
(
x
−
1)
}
X
/
L
i
=1
∑
X
/
L
i
=1
∑
x
∈
B
[
i
]
μ
mt
(
x
)
2
2κ
1
−
2κ
1
x
∈
B
[
i
]
{
μ
mt
(
x
)μ
mt
(
x
−
1)
}
ρ
i
>
j
η
i
,
j
ρ
|
d
i
−
d
j
|
In the above approximation, we assume that
m
s
(1
κ
1
2
σ
−
ρ
)
1
−
ρ
−
m
2
κ
1
is statistically independent of
μ
mt
(
x
),
and we use the following homogeneous model
X
/
L
i
=1
∑
2
=
s
x
∈
B
[
i
]
{
f
t
(
x
)
}
σ
X
/
L
i
=1
∑
2
s
k
B
[
i
]
{
f
t
(
x
)
f
t
(
x
+
k
)
}
=
σ
ρ
x
∈
and the following approximation
X
/
L
i
=1
∑
B
[
i
]
{
f
t
(
x
+
d
i
(
x
))
f
t
(
x
+
d
j
(
x
))
}
x
∈
X
/
L
i
=1
∑
f
t
(
x
+
d
i
)
f
t
(
x
+
d
j
)
η
x
∈
B
[
i
]
{
}
i
,
j
d
i
−
d
j
|
s
ρ
|
=
η
σ
i
,
j
where
d
i
and
d
j
are the mean values of
d
m
[
i
](
x
) and
d
m
[
j
](
x
) , respectively, and
η
i
,
j
is a parameter to approximate
d
m
[
i
](
x
) and
d
m
[
j
](
x
) using mean displacement (
d
i
and
d
j
).
We can assume that
ρ
is less than but close to one, since
ρ
is the autocorrelation
coefficient of the image signal. Thus, we have
1
−
ρ
ρ
1
.
