Image Processing Reference
In-Depth Information
FIGURE 1.15: A 2-D point set in a grid.
iteration consists of three scans for deleting border points. One additional scan
is required to check the safe deletion condition for Front and Back border
points. However, in the 3-D neighborhood, for each type of edge point the
safe point condition should be checked in four different neighboring planes.
For example, for the left- edge point the planes containing both the v
4
and v
0
points are considered. They are shown in Fig. 1.17. In each of these planes,
the safe point condition should be true for the safe removal of the point. The
condition is stated below:
C
4
= C
(a)
4
.C
(b
4
.C
(c
4
.C
(d)
4
where,
C
(a)
4
= v
0
.(v
1
+ v
2
+ v
6
+ v
7
).(v
2
+ v
3
).(v
6
+ v
5
)
(1.2)
C
(b)
4
= v
0
.(u
0
+ u
8
+ w
0
+ w
8
).(u
8
+ u
4
).(w
8
+ w
4
)
(1.3)
C
(c)
4
= v
0
.(u
1
+ u
2
+ w
7
+ w
6
).(u
2
+ u
3
).(w
6
+ w
5
)
(1.4)
C
(d)
4
= v
0
.(w
1
+ w
2
+ u
7
+ u
6
).(w
2
+ w
3
).(u
6
+ u
5
)
(1.5)
The skeleton obtained by the above algorithm preserves the 26-
connectivity of the pattern. A typical result is shown in Fig. 1.18.
