Master Thesis - Department of Computer Science

(a)
6
7
0
1
2
5
6
7
0
1
2
3
5
3
4
4
(i, j)
4
4
(b)
3
5
3
2 1
1
0 0
7
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(c)
Average local
intensity is
minimum
Average local
intensity is
maximum
Figure A.11: (a) The eight directions; (b) The 9 × 9 mask for computing slit-sums;
(c) For ridge pixels, average local intensity or slit-sum is minimum along the direction
of the ridge and maximum along the normal direction of ridge.
A slit-sum method with local threshold proposed by Stock and Swonger [118] is
used to binarize a image. This method uses pixel alignment along eight (8) discrete
directions, 0, π/8, 2π/8, ..., 7π/8 (see Fig. A.11(a)) and a 9×9 mask (see Fig. A.11(b))
to center at the pixel of interest. The basic idea here is that for each pixel that
belongs to ridge line, there exists an orientation whose average local intensity is lower
than those of remaining orientations (see Fig. A.11(c)). The gray-level values along
eight directions are added respectively to obtain each slit-sum by using the following
equations,
S0 = H(i, j + 4) + H(i, j + 2) + H(i, j − 2) + H(i, j − 4),
S1 = H(i − 2, j + 4) + H(i − 1, j + 2) + H(i + 1, j − 2) + H(i + 2, j − 4),
S2 = H(i − 4, j + 4) + H(i − 2, j + 2) + H(i + 2, j − 2) + H(i + 4, j − 4),
S3 = H(i − 4, j + 2) + H(i − 2, j + 1) + H(i + 2, j − 1) + H(i + 4, j − 2),
S4 = H(i − 4, j) + H(i − 2, j) + H(i + 2, j) + H(i + 4, j),
S5 = H(i − 4, j − 2) + H(i − 2, j − 1) + H(i + 2, j + 1) + H(i + 4, j + 2),
S6 = H(i − 4, j − 4) + H(i − 2, j − 2) + H(i + 2, j + 2) + H(i + 4, j + 4),
S7 = H(i − 2, j − 4) + H(i − 1, j − 2) + H(i + 1, j + 2) + H(i + 2, j + 4).
where S0, S1, ..., S7 represent the sum of gray-level values for eight discrete di-
rection (slit). Let Smax, Smin and Ssum be the maximum, minimum and sum of the
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