Master Thesis - Department of Computer Science

P 9
P 8
P
7
(i−1, j+1)
P 2
P 1
P 6
P 3
(i−1, j−1) (i, j−1) (i+1, j−1)
(i−1, j)
(i, j)
(i, j+1)
P 4
(i+1, j)
P 5
(i+1, j+1)
Figure A.13: The locations of the nine pixels in a window.
is used in the thinning process, where P1 is the center pixel and P2, ..., P9 are its
neighbors. Let P ′
i be the pixel value of Pi. The method consists of two iterations
applied to any pixels with a pixel value 1, and determines whether a center point
must be to preserved or deleted. In the first iteration, the center point is deleted
from the image, if the following conditions are satisfied:
(a) 2 ≤ N(P1) ≤ 6;
(b) S(P1) = 1;
(c) P ′ 2 ∗ P ′ 4 ∗ P ′ 6
= 0;
(d) P ′ 4 ∗ P ′ 6 ∗ P ′ 8 = 0;
where N(P1) is the number of nonzero neighbors of P1, that is, N(P1) = P ′ 2 +
P ′ 3 + ... + P ′ 9 and S(P1) is the number of transitions from 0 to 1 for the order set
{P ′ 2 , P ′ 3 , ..., P ′ 9 }. N(P1) = 0, N(P1) = 1, and N(P1) > 6 are corresponding to the
center pixel P1 is an isolation point, end point and intermediate point, respectively.
If S(P1) > 1, the center point P1 is a bridge that preserves the connectivity of a
skeleton. For these four cases, the center pixel P1 will not be deleted to break the
skeleton.
In the second iteration, the conditions (a) and (b) remain the same, conditions
(c) and (d) are modified as follows:
(c’) P ′ 2 ∗ P ′ 4 ∗ P ′ 8
(d’) P ′ 2 ∗ P ′ 6 ∗ P ′ 8
= 0;
= 0;
Conditions (c) and (d) for the first iteration are used to remove south-east bound-
ary points and north-west corner points which are not skeletal pixels. Similarly, con-
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