Image Processing Reference
In-Depth Information
P1
P2
P3
P8
P0
P4
P7
P6
P5
(a)
(b)
Fig. 3.2
(a) Enumeration of the pixels in a 3
×
3 neighborhood. (b) An example of 3
×
3
neighborhood where the central pixel
P
0has
B
(
P
0
)=
3and
C
(
P
0
)=
1.
P
8 of its eight neighbor pix-
els is considered, as shown in Fig. 3.2 (a). As usual, for each
i
Given a pixel
P
0, a clockwise enumeration
P
1
,...,
,
Pi
is
considered as a Boolean variable, with the (truth) value 1 if
Pi
is
black
and0if
Pi
is
white
.
In order to decide if a pixel
P
0 is deleted in the corresponding iteration subcycle,
two parameters are evaluated:
∈{
1
,...,
8
}
i
=
8
B
(
P
0
)=
∑
1
Pi
i
=
C
(
P
0
)=(
¬
P
2
∧
(
P
3
∨
P
4
))+(
¬
P
4
∧
(
P
5
∨
P
6
))
+(
¬
P
6
∧
(
P
7
∨
P
8
))+(
¬
P
8
∧
(
P
1
∨
P
2
))
eval-
uates the
connectivity
of the pixel
P
0. Notice that for isolated black pixels, the con-
nectivity is 0. If the pixel is surrounded by eight black pixels, the connectivity is also
0. According to the Guo and Hall algorithm, in each iteration, an evaluated black
pixel
P
0 is deleted (changed to white) if and only if all of the following conditions
are satisfied.
B
(
P
0
)
counts how many pixels in the neighborhood of
P
0 are black.
C
(
P
0
)
Guo and Hall Conditions
(
)
>
1.
B
P
0
1;
(
)=
2.
C
1; This condition is necessary for preserving local connectivity when
P
is deleted.
P
0
3.
(
FALSE
; Intuitively, this condition
is satisfied if
P
0 is not the central pixel of a
cross
.
P
1
∧
P
3
∧
P
5
∧
P
7
)
∨
(
P
2
∧
P
4
∧
P
6
∧
P
8
)=
For example, let us consider as
P
0 the central pixel in the image of Fig. 3.2 (b). In
this case,
B
1, and the third condition is also satisfied. Hence,
P
0 will be deleted in the corresponding subcycle iteration.
(
P
0
)=
3
>
1,
C
(
P
0
)=
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