Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
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(a) cn(p) = 2 (b) cn(p) = 1 (c) cn(p) = 3<br />
Figure 2.8: (a) Intra-ridge pixel; (b) Termination minutia; (c) Bifurcation minutia<br />
number different from 2. The crossing number [6] cn(p) <strong>of</strong> a pixel p in a binary image<br />
is defined as half the sum <strong>of</strong> the differences between pairs <strong>of</strong> adjacent pixels in the<br />
8-neighborhood <strong>of</strong> p:<br />
cn(p) = 1<br />
2<br />
�<br />
i=1,..,8<br />
|val(pi mod 8) − val(pi−1)|. (2.20)<br />
where p0, . . . , p7 are the pixels belonging to an ordered sequence <strong>of</strong> pixels defining<br />
the 8-neighborhood <strong>of</strong> p and val(p) ∈ {0, 1} is the pixel value. It is simple to note<br />
(Fig. 2.8) that for a pixel p with val(p) = 1, it:<br />
• is an intermediate ridge point if cn(p) = 2;<br />
• corresponds to a termination minutia if cn(p) = 3;<br />
• defines a more complex minutia (bifurcation, crossover, etc.) if cn(p) ≥ 3<br />
Leung et al.’s [76] method extracts the minutiae from thinned binary images but,<br />
instead <strong>of</strong> using the crossing number, they use a three-layer perceptron neural net-<br />
work. In some approaches, minutiae are detected from binary images without any<br />
intermediate thinning. Weber [129] first performed an image enhancement by band-<br />
pass filtering in the frequency domain and then did binarization via local threshold.<br />
Finally, the minutiae are detected from the thick binary ridges through a ridge track-<br />
ing algorithm. Szekély and Szekély [121] developed a minutiae detection technique<br />
based on the computation <strong>of</strong> the orientation image divergence.<br />
Miao and Maltoni [82] proposed a direct gray-scale minutiae extraction algorithm,<br />
where the basic idea was to tract the ridge lines in a gray-scale image by “sailing”,<br />
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