Master Thesis - Department of Computer Science

(a) (b)
Figure A.6: Frequency images (after filtering) of two input fingerprints shown in
Fig. A.2.
where φ is the orientation of the Gabor filter, f is the frequency of a sinusoidal plane
wave, and δx and δy are the space constants of the Gaussian envelope along x and y
axes, respectively. The modulation transfer function (MTF) of the Gabor filter can
be represented as,
H(u, v : φ, f) =
�
2πδxδyexp − 1
�
(uφ − u0)
2
2
δ2 +
u
(vφ − v0) 2
δ2 +
��
v
�
2πδxδyexp −
(A.22)
1
�
(uφ + u0)
2
2
δ2 +
u
(vφ + v0) 2
δ2 ��
,
v
(A.23)
uφ = u cos φ + v sin φ, (A.24)
vφ = −u sin φ + v cos φ, (A.25)
u0 =
2π cos φ
,
f
(A.26)
v0 =
2π sin φ
.
f
(A.27)
where δu = 1/2πδx and δv = 1/2πδy. To apply Gabor filters to an image, three
parameters must be specified:
• The frequency, f,
• The filter orientation φ, and
• The standard deviations of the Gaussian envelope, δx and δy.
In this case, the frequency of the filter is given by local ridge frequency and the
orientation by local ridge orientation. The selection of the values of δx and δy involves
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