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y
=
1
f
s
]
−
μ
f
s
f
s
]
−
μ
f
s
n
x
=
1
n
[
,
[
−
,
−
∑
∑
x
y
x
i
y
k
C
ff
[
i
,
k
]=
(6.37)
2
˃
f
s
×
n
×
n
2
f
s
where
μ
f
s
and
˃
are the mean and the variance of the reference image
{
f
s
[
i
,
k
]
}
,
respectively. Furthermore, the
sequence in Eq. (
6.36
) is a feature sequence
whose elements in descending order are obtained from the cross-covariance matrix
between two images:
{
q
2
[
k
]
}
{
f
s
[
i
,
k
]
}
and
{
g
s
[
i
,
k
]
}
; that is,
C
f g
[
i
,
k
]
defined as [
171
]:
1
f
s
[
]
−
μ
f
s
g
s
[
]
−
μ
g
s
n
x
n
y
∑
∑
x
,
y
x
−
i
,
y
−
k
=
1
=
C
f g
[
i
,
k
]=
(6.38)
˃
f
s
×
˃
g
s
×
n
×
n
where
μ
g
s
and
˃
g
s
are the mean and the standard deviation of the reference image
{
, respectively. It may be observed that if the cross-covariance coefficient
CCC
s
approaches unity, both images absolutely agree with each other.
The current region,
g
s
[
i
,
k
]
}
R
s
is then classified as either relevant or non-relevant
according to the value of
CCC
s
(
f
s
,
g
s
)
relative to a threshold value of
ʾ
COV
.This
results in:
I
=
{
s
:
CCC
s
≥
ʾ
COV
}
(6.39)
∈
{
}
where
I
is the set of selected indices and
s
1
,...,
S
.ByEq.(
6.39
), we can
define all the relevant image regions as:
R
=
R
(6.40)
s
s
∈I
and the resulting output image lattice containing those relevant points can be
obtained from:
X
=
(
)
∈ R
i
,
k
)
:
(
i
,
k
(6.41)
Finally, the normalized versions of the reference image and the target image are
obtained by:
f
[
]
=
f
)
∈ X
i
,
k
[
i
,
k
]
:
(
i
,
k
(6.42)
g
[
]
=
g
[
)
∈ X
i
,
k
i
,
k
]
:
(
i
,
k
(6.43)
In the normalized images, pixels located outside the relevant region, that is, at
position
)
∈ X
, are set to zero.
(
i
,
k
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