Image Processing Reference
In-Depth Information
Fig. 4.14.
Computation of Euler Number: (
a
)variables;(
b
)equations.
E
[18
]
=
L−
1
M−
1
N−
1
{
x
0
[
1
−
x
1
(
1
−
x
4
·
x
5
)
i
=2
j
=2
k
=2
7
−
x
2
(
1
−
x
1
·
x
3
)
−
x
4
(
1
−
x
2
·
x
6
)
−
x
i
]
}
i
=0
3
x
m
·
x
7
−m
·
x
else
]
.
+
[
(4.45)
m
=0
E
[26]
=
L−
1
M−
1
N−
1
{
x
0
[
1
−
x
1
(
1
−
x
4
·
x
5
)
i
=2
j
=2
k
=2
7
−
x
2
(
1
−
x
1
·
x
3
)
−
x
4
(
1
−
x
2
·
x
6
)
−
x
i
]
}
,
(4.46)
i
=0
x
else
x
else
) means the product of all six values
where
x
i
=
1
−
x
i
and
(
x
i
s
(
x
i
s) such that
i
=
0
,
1
,...,
7
,i
=
m, i
=
7
−
m
.
(Proof)[6-c case] Considering simplexes in Fig. 4.5,
Number of 0-simplex =
i
x
0
j
k
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