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Fig. 6.3
Flow diagram describing automatic matching of cartridge base case images
represent the pixel indices. The two images are enhanced by the contrast scale
relative to each other. This scale follows the energy of the signal (i.e.
l
2-norm),
which is shown as follows:
round
(
a
×
f
[
i
,
k
])
T
[
f
[
i
,
k
]] =
,∀
(
i
,
k
)
(6.1)
f
[
i
,
k
]
round
(
a
×
g
[
i
,
k
])
T
[
g
[
i
,
k
]] =
,∀
(
i
,
k
)
(6.2)
g
[
i
,
k
]
where
T
is the transformation function,
a
is the average of the
l
2-norm of
{
f
[
i
,
k
]
}
and
. Based on Eqs. (
6.1
) and (
6.2
), the energies of the two images are
adjusted to the same base line, using the averaging of the
l
2-norm.
In the second step, image registration is used in the geometric transformation
of the image
{
g
[
i
,
k
]
}
. The image is adjusted according to translation, rotation, and
scaling. The registration uses the image
{
g
[
i
,
k
]
}
{
f
[
i
,
k
]
}
as the reference image and adjusts
the image
{
g
[
i
,
k
]
}
. We denote
{
g
[
i
,
k
]
}
as the geometric transformation of
{
g
[
i
,
k
]
}
.
As a result, as shown in Fig.
6.3
, the image
{
g
[
i
,
k
]
}
is adjusted according to the
reference image
, with the same translation, rotation, and scaling.
In the third step, the two images are matched by a correlator. The correlator
utilizes the cross-correlation coefficient of the two images, which is defined as [
171
]:
{
f
[
i
,
k
]
}
1
f
]
−
μ
f
g
]
−
μ
g
M
i
N
k
[
i
,
k
[
i
,
k
∑
∑
=
1
=
C
(
f
,
g
)=
(6.3)
˃
f
×
˃
g
×
M
×
N
The
C
value in Eq. (
6.3
) is the normalized cross-correlation coefficient of the two
images:
{
f
[
i
,
k
]
}
and
{
g
[
i
,
k
]
}
of size
M
×
N
. In addition, both
˃
f
and
˃
g
values are
the standard deviations of the two images. Moreover, both
μ
f
and
μ
g
values are the
mean of the two images. It follows from Eq. (
6.3
) that
|
C
| ≤
1.If
|
C
|
=
1 then both
{
f
[
i
,
k
]
}
and
{
g
[
i
,
k
]
}
images agree with each other; however, if
|
C
|
=
0 then both
{
f
[
i
,
k
]
}
and
{
g
[
i
,
k
]
}
images disagree with each other.
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