Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
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another intrinsic property <strong>of</strong> a fingerprint image. The steps for obtaining frequency<br />
image, F , is as follows:<br />
1. Divide G into blocks <strong>of</strong> size W × W (16 × 16).<br />
2. For each block centered at pixel (i, j), compute an orientation window <strong>of</strong> size<br />
H × W (32 × 16) that is defined in the ridge coordinate system (see Fig. A.5).<br />
3. For each block centered at pixel (i, j), compute the x-signature,<br />
X[0], X[1], . . . , X(H − 1), <strong>of</strong> the ridges and valleys within the orientated win-<br />
dow, where,<br />
X[k] = 1<br />
W<br />
u = i +<br />
v = j +<br />
W −1<br />
�<br />
d=0<br />
G(u, v), k = 0, 1, ..., H − 1, (A.12)<br />
�<br />
d − W<br />
�<br />
�<br />
cos O(i, j) + k −<br />
2<br />
H<br />
�<br />
sin O(i, j), (A.13)<br />
2<br />
�<br />
d − W<br />
�<br />
� �<br />
H<br />
sin O(i, j) + − k cos O(i, j). (A.14)<br />
2<br />
2<br />
If no minutiae and singular points appear in the orientated window, the x-<br />
signature forms a discrete sinusoidal-shape wave, which has the same frequency<br />
as that <strong>of</strong> the ridges and valleys. Let T (i, j) be the average number <strong>of</strong> pixels<br />
between two consecutive peaks in x-signature, then the frequency Ω(i, j) is<br />
computed as: Ω(i, j) = 1/T (i, j). If no consecutive peaks can be detected from<br />
the x-signature, then the frequency is assigned a value <strong>of</strong> -1 to differentiate it<br />
from valid frequency values.<br />
4. For a fingerprint image scanned at a fixed resolution like 500dpi, the value <strong>of</strong><br />
the frequency lies in certain range ([1/3, 1/25] for 500dpi). So any estimated<br />
frequency out <strong>of</strong> this range will be assigned a value <strong>of</strong> -1 to indicate invalid<br />
frequency.<br />
5. The blocks containing minutiae and/or singular points will provide a well-<br />
defined sinusoidal-shaped wave. So, the frequency values for these blocks need<br />
to be interpolated from the frequency <strong>of</strong> the neighboring blocks which have a<br />
well-defined frequency. The interpolation is performed as follows:<br />
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