Image Processing Reference
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(ii) Pattern matching can be used if the number of relating local patterns is
low (one or two, for example) and their structure is simple.
(iii) If the conditions match as in (ii) and are expressed in a well-defined
mathematical form, pseudo-Boolean equations will be effectively used in
(i) and (ii).
(iv) Tests for features of a projection graph are realized effectively by examin-
ing logical expressions such as a kind of a decision tree or pseudo-Boolean
expressions, if features are simple (e.g., existence of an isolated point).
(v) The adjacency matrix will be used if tests of complicated characteristics
are necessary such as detection of a path of the given length.
Generation of a projection graph and its use for the deletability test are
given in [Yonekura82b, Yonekura82c].
Algorithm 4.2 (Deletability test -
6
-connectivity case).
(1) Calculate the connectivity number
Nc
(6)
(
x
x
)at
.
Go to (2), if
Nc
(6)
(
x
x
)=
1
.Otherwise,
is not deletable.
(2) Denoting by
n
(
x
x
) the number of 1-voxels in the 6-neighborhood of
,
x
is not deletable, if
n
(
x
≤
(i)
)
3
(ii) Go to (3), if
n
(
x
)=
4
(iii) Go to (4), if
n
(
x
)=
5
)=
6
(3) Calculate the following equation
s
(
(iv) Go to (5), if
n
(
x
x
)
)=
k∈S
1
s
(
x
[
x
h,k
+1
·
x
h,k
·
x
h,k
+2
·
x
h,
0
·
x
2
,k
·
x
2
,k
+1
·
x
2
,k
+2
]
,
(4.50)
h
=1
,
3
where
x
a,b
=
1
−
x
a,b
,
S
1
=
{
1
,
3
,
5
,
7
}
.
x
is not deletable, if
s
(
x
)=
1
;
x
is deletable, otherwise.
(4) Calculate the above
s
(
x
).
x
) = 1; otherwise generate the projection graph
[Yonekura80b, Yonekura80c, Yonekura82a] of
is not deletable, if
s
(
x
is not deletable,
if the graph has an isolated node (a node connected to no other node next
to an edge),
x
. Then,
x
is deletable otherwise.
(5) Generate the projection graph
G
(
x
x
)of
x
.Then
x
is deletable, if the graph
G
(
)
is connected or not is known using the following: Denoting the adjacency
matrix (6
x
) is connected;
x
is not deletable, otherwise. Whether the graph
G
(
x
×
6) of a graph
G
(
x
)by
M
,calculate
N
=
M
(
I
+
M
(
I
+
M
(
I
+
M
(
I
+
M
))))
,
(4.51)
where
I
is the identity matrix.
Then
) is not connected), if any element of the
value
0
exists in
N
.Otherwise
x
is not deletable (
G
(
x
x
is deletable [Yonekura80a, Yonekura80b,
Yonekura80c, Yonekura82c].
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