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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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