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