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2.2 The Extraction of 2-D Wavelet Decomposition Coecients
Wavelets transform booms as a signal processing approach of transform domain
in field of computer vision and image processing. With regard to wavelet, an ex-
tension of traditional Fourier transforms, its multi-resolution analysis has a good
time-frequency characteristic so that it is feasible to process stationary signals,
e.g. finger texture image. It is worth to say that wavelet coecients can be con-
sidered as features in parallel fusion schemes. Concretely, a finger texture image
is decomposed into four sub-images by Wavelets decomposition (Fig.1), which
are approximation coecients, horizontal coecients, vertical coecients, and
diagonal detailed coecients. The fig.1 proposes a 2D Wavelet Decomposition
at level 2, and there are 4 sub-images with a scale of 1/4 on the left top corner.
Each pixel of sub-images, i.e. coecients with the scale of 1/4, are utilized for
feature selection of parallel fusion because of its uniqueness, so as to perform
biometric verification.
Fig. 1.
2D wavelet decomposition at level 2 for finger texture image
2.3 Parallel Fusion
Suppose that
A
and
B
in which are respectively feature vectors extracted from
two traits, e.g. face, fingerprint etc. The parallel fusion is in the form of
c
l
=
{a
1
+
ib
1
,a
l
2
+
ib
l
2
, ···}
where
c
l
denotes as a complex vector, and
i
2
=
1. Provided
that
m>n
,where
m, n
are subscripts of
a
l
m
and
b
l
n
, i.e. the numbers of samples,
then set 0 as
b
l
n
+1
,b
l
n
+2
, ···,b
l
m
, i.e.
c
l
=
−
{a
1
+
ib
1
,a
l
2
+
ib
l
2
, ··· a
l
n
+1
,a
l
n
+2
···
a
l
m
}
; vice versa. According to quaternion [5,9], we make use of four wavelet
decomposition coecients i.e. approximation coecient, horizontal coecient,
vertical coecient, and diagonal detailed coecient as parallel features. That
is to say, a quaternion is constructed as
W
=
w
1
+
w
2
i
+
w
3
j
+
w
4
k
,where
w
1
,w
2
,w
3
,w
4
are such four coecients separately.
3 Our Algorithm
Basically, proposed algorithm workflow is illustrated in the fig. 2. In the phase
of preprocessing, our ROI extraction method is proposed. Since feature extrac-
tion, 4 wavelet decomposition coecients have been obtained by 2 level wavelets
decomposition for composing a quaternion as the parallel fusion. Then match-
ing module proposes matching between template quaternion and test one from
which can gain a matching score. This score can be discriminated by the specific
threshold as the decision.
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