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Since our hexagonal filter assumes that the element values are distributed as
shown in Figure 4(a), these above-described Staunton filters are not derived. How-
ever,
h
d
derived by (111), and
h
e
and
h
f
derived by rotating
h
d
give filters with the
same shape as the Staunton filters, though the element values are not the same. On
the other hand, filters that have the same proportion of elements as
h
a
,
h
b
and
h
c
can
be derived from
p
a
,
p
b
and
p
c
by
1
√
3
(
p
d
=
p
a
+
p
b
)
,
(114)
1
√
3
(
p
e
=
p
b
+
p
c
)
,
(115)
1
√
3
(
p
f
=
p
c
−
p
a
)
.
(116)
Our equation for deriving gradient intensity (93) can be rewritten as
2
3
2
f
r
+
2
1
√
3
(
1
2
1
2
(
Int
hex
(
f
)=
f
s
−
f
t
)
+
f
s
+
f
t
)
(117)
4
9
f
r
+
1
2
3
f
s
+
f
t
1
4
(
1
f
s
−
f
t
)
=
f
r
f
s
−
f
r
f
t
+
2
f
s
f
t
+
+
2
f
s
f
t
+
1
9
(
1
2
4
f
r
+
4
f
s
+
4
f
t
+
=
4
f
r
f
s
+
4
f
s
f
t
−
4
f
r
f
t
)
3
f
r
+
f
r
)
2
1
2
f
s
+
=
f
r
f
s
+
f
t
(
f
t
+
f
s
−
2
3
(
2
f
r
+
f
s
+
=
f
r
f
s
)
,
which is the same as (112) except for the constant coefficient. The gradient intensity
detecting equation with Staunton filters can therefore detect gradient intensities with
the same accuracy as our filters.
a
-
-
-
0
0
-a
a
-
a-
0
0
0
0
0
-a
a-
a-
a-
0
0
a=1
p
a
p
b
p
c
Fig. 7
Staunton filters[23].The original
p
c
has opposite sign.
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