Master Thesis - Department of Computer Science

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