Image Processing Reference
In-Depth Information
v
1
v
3
v
2
v
0
p
v
4
v
7
v
5
v
6
FIGURE 1.12: The Boolean neighbors of p.
Using the above characterization, it is possible to delete simple border
points iteratively till no more deletion is possible. In addition, care should
be taken so that a foreground component does not get eroded. This would
result in a skeleton of the pattern. Let us consider the technique proposed in
[156]. Let us denote the neighbors of a point p with a set of Boolean variables
v
0
,v
2
,...,v
7
as shown in Fig. 1.12, such that a background pixel assumes the
value false, otherwise it is true for a foreground pixel. The safe point thinning
algorithm (SPTA) [156] works in an (8,4) digital grid, and characterizes a
border pixel into any of the four types, namely left, right, bottom, and top.
For example, a foreground pixel p is a left-border pixel, if v
4
∈ N
8
(p) is false.
Similarly other types of border pixels are also defined, when any of v
0
, v
6
,
and v
2
is false. Naccache and Shinghal showed four neighboring conditions for
which a point should not be deleted as it would either destroy the connectivity
of the pattern, or erode the pattern completely. These conditions are shown
in Fig. 1.13. In the figure, the foreground pixels are shown with dark circles,
background pixels with empty circles, and the dotted circles denote 'don't care'
states. A left border pixel is simple or safe for deletion when the following
Boolean expression (refer Eq. (1.1)) is false.
C
4
= v
0
.(v
1
+ v
2
+ v
6
+ v
7
).(v
2
+ v
3
).(v
6
+ v
5
)
(1.1)
In the above equation, '.' and '+' denote 'Boolean AND' and 'Boolean
OR' operations, respectively. Similarly, Boolean conditions for other types
of border points could be derived to check whether they are simple. Using
