Information Technology Reference
In-Depth Information
By defining
F
0
c
h
∑
ξ
ξ
2
as
κ
1
, we have the following approximation:
X
/
L
i
=1
∑
[
i
](
x
)
2
κ
1
F
−
2
B
[
i
]
ζ
(7)
x
∈
X
/
L
i
=1
Next, we consider the relationship between
∑
x
∈
B
[
i
]
ζ
[
i
](
x
) and frame-rate. Ex-
∑
panding
F
[
i
](
x
)
2
X
/
L
i
=1
∑
∑
x
∈
B
[
i
]
ζ
,wehave
X
/
L
i
=1
∑
F
[
i
](
x
)
2
B
[
i
]
ζ
x
∈
X
/
L
i
=1
∑
X
/
L
i
=1
∑
ζ
F
[
i
](
x
)
2
+
∑
F
[
i
](
x
)
F
[
i
](
x
)
=
=
x
ζ
ζ
(8)
x
∈
B
[
i
]
,
x
x
∈
B
[
i
]
x
∈
B
[
i
]
F
[
i
](
x
) is displacement estimation error, defined as follows:
where
ζ
F
[
i
](
x
)=
d
F
[
i
](
x
)
d
F
[
i
]
ζ
−
The first term of equation (8) can be approximated as shown in (6).
About the second term of equation (8), from the Schwarz inequality approach,
we have the following inequality:
X
/
L
i
=1
∑
F
[
i
](
x
)
2
∑
F
[
i
](
x
)
=
x
ζ
ζ
x
∈
B
[
i
]
,
x
x
∈
B
[
i
]
X
/
L
i
=1
∑
F
[
i
](
x
)
2
X
/
L
ζ
ζ
F
[
i
](
x
)
2
i
=1
∑
≤
x
∈
B
[
i
]
,
x
x
∈
B
[
i
]
=
x
F
−
2
F
0
c
h
2
ξ
ξ
2
ξ
ξ
)
2
(
ξ
=
x
−
where
ξ
=
x
−
x
c
[
i
] and
x
c
[
i
]. From the above inequalities, we have
F
−
2
F
0
c
h
X
/
L
i
=1
∑
∑
F
[
i
](
x
)
F
[
i
](
x
)
ξ
ξ
ξ
x
∈
B
[
i
]
,
x
=
x
ζ
ζ
θ
2
(
ξ
)
2
x
∈
B
[
i
]
where
is a constant in the range -1 to 1.
By inserting the above approximation and approximation (6) into equation (8),
we get
θ
⎧
⎨
⎩
ξ
ξ
ξ
)
2
⎫
X
/
L
i
=1
∑
F
[
i
](
x
)
2
ξ
ξ
2
⎬
⎭
F
−
2
F
0
c
h
2
+
ξ
B
[
i
]
ζ
θ
(
x
∈
