Information Technology Reference
In-Depth Information
Ta b l e 1
Properties of derived filters
Filter
J
J
1
SNR
Num. o f Pixels
Sqr 3
×
3
.000778989
.40310040
4.51
9
Sqr 4
×
4
.000016162
.18895918
6.76
16
Sqr 5
×
5
.000000376
.11585859
9.12
25
Hex 1
.001432490
.74197938
4.51
7
Hex
√
3
.000017713
.51425309
7.41
13
Hex 2
.000000086
.25649444
10.75
19
7.2
Localization
How the elements of a filter are “balanced” is evaluated next. In particular, how
close to the center of a filter are the element values spread is investigated here. If the
element values gather close to the center, the filter focuses on the information close
to the center.
Localization on square lattices is defined as
≡
∑
m
,
n
P
sqr
mn
d
m
,
n
∑
m
,
n
P
sqr
Loc
sqr
,
(77)
mn
where
P
sqr
mn
2
2
=
(
h
i
(
m
,
n
))
+(
h
j
(
m
,
n
))
,
(78)
where
h
i
(
are the elements of the gradient filters derived in the
x
and
y
directions, respectively, and
d
m
,
n
is distance from the center of the filter.
Moreover, the localization on hexagonal lattices is defined as
m
,
n
)
and
h
j
(
m
,
n
)
≡
∑
m
,
n
P
hex
mn
d
m
,
n
∑
m
,
n
P
hex
Loc
hex
,
(79)
mn
where
2
3
h
a
(
2
1
2
(
P
hex
mn
=
m
,
n
)+
h
b
(
m
,
n
)
−
h
c
(
m
,
n
))
2
1
/
2
1
√
3
(
+
h
b
(
m
,
n
)+
h
c
(
m
,
n
))
,
(80)
where
h
a
(
m
,
n
)
,
h
b
(
m
,
n
)
and
h
c
(
m
,
n
)
are the elements of the gradient filters derived
in the 0
◦
,
60
◦
and 120
◦
directions, respectively.
The resultant localizations are listed in Table 2 with resultant
SNR
,andtheyare
plotted in Figure 5. It is clear that the smaller the filter is, the better its localization
is. At the same time, the larger the filter is, the better the
SNR
is. Accordingly, there
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