Database Reference
In-Depth Information
r
,
ʸ
)=
In log-polar coordinates [
174
], the logarithm of the radius axis is taken by:
(
(
log
r
,
ʸ
)
. Thus the relationship in Eq. (
6.28
) can be viewed in the logarithmic
scale as:
M
G
r
,
ʸ
=
M
F
r
−
ʱ
,
ʸ
−
ʸ
0
(6.29)
From the relationship of their magnitude spectra, Eq. (
6.29
) can be viewed as the
function with independent variables in Cartesian space with
r
=
ʸ
=
k
,
same as for Eq. (
6.4
). Thus, the phase correlation technique can be applied using
Eq. (
6.12
) followed by the inverse Fourier transform Eq. (
6.14
). This results in the
delta function,
i
and
ʴ
r
−
ʱ
,
ʸ
−
ʸ
0
N
2
(6.30)
where
r
=
ʱ
=
,
log
r
and
log
ʱ
. It is observed that the maximum value of this
0
and
r
=
ʱ
.
ʸ
=
ʸ
function is attained when
6.2.4
Registration Accuracy
In order to measure the efficiency of the algorithm for automatic alignment of the
cartridge base case images using the phase-correlation technique, the following
mean square error was employed:
i
k
2
(
g
[
i
,
k
]
−
g
[
i
,
k
])
ˁ
m
=
∑
∑
=
1
=
1
×
100 %
(6.31)
2
i
N
k
=
1
(
g
[
i
,
k
])
∑
∑
=
1
where
g
are respectively the grayscales of the target image and
the reference image after they were geometrically transformed with registration
parameters (i.e. translation, rotation, and scaling). In addition, the error of the
estimated parameters between the reference image and the target image was
measured by
[
i
,
k
]
and
g
[
i
,
k
]
ˁ
p
,
2
j
(
q
[
j
]
−
q
[
j
])
ˁ
p
=
∑
=
1
×
100 %
(6.32)
K
j
2
(
q
[
j
])
∑
=
1
where
q
are the parameters used for geometric transformation between the
reference image and the target image;
q
[
j
]
are the parameters used for geometric
transformation estimated using the phase-correlation technique; and
K
is the total
number of parameters used for the experiment.
In the experiment, the test was conducted for three cases of translation, rotation,
and scaling. The first case estimated the parameters for translation. In Fig.
6.4
,a
reference image of size 480
[
j
]
×
640 was translated from 0 to 40 pixels, increasing
Search WWH ::
Custom Search