Information Technology Reference

In-Depth Information

features of the same sample have not identical number, e.g.
m>n
. If assign 0

as
b
l
n
+1
,b
l
n
+2
, ···,b
l
m
, this method will be lack of physical significance. Here our

algorithms enable to avoid this problem because each sub-image pixel has four

coecients for fusion at the same time.

3.3

Quaternion Euclidean Product Distance

As mentioned section above, we here make QEPD available as matching score.

The relationship between QEP and quaternion modulus has been discussed in the

section 2.1, thus consider two quaternions, for an arbitrary pixel corresponding

to 4 separable wavelets decomposition coecients sub-image, which the former

is from this pixel as the template,
P
=
a
+
bi
+
cj
+
dk
and the latter is from

the tester, in which
Q
=
t
+
xi
+
yj
+
zk
. Ideally, if
P
=
Q
such that
PP
=

2
,

where is a particular case of QEP. We can estimate the difference between the

template quaternion matrix and the tester one by QEPD
D
(
PP,|PQ|

|P |

)asa

discriminant distance. Notice that the template quaternion matrix and tester

matrix refer to a matrix stores the value of
PP
corresponding to each pixel

of the subimage and a matrix with all of

|PQ|

corresponding to these pixels

respectively. Such two matrices have the same size as the subimage above. In

which

is the modulus of Quaternion Euclidean product, and the operator
D

is certain kind of distance, e.g.
L
1
norm,
L
∞
norm distance, Euclidean distance

etc. In our scheme, Euclidean distance is chosen as the operator
D
. The reason

use the modulus of
PQ
is that the multiplication of two different quaternions

is a quaternion (equation (9)), combined (3) and (6), so that it is impossible to

compare directly with
PP
. From the equation,
PQ
is not a scalar.

|PQ|

PQ
=(
a − bi − cj − dk
)(
t
+
xi
+
yj
+
zk
)

=(
at
+
bx
+
cy
+
dz
)+(
ax − bt − cz
+
dy
)
i

+(
ay
+
bz − ct − dx
)
j
+(
az − by
+
cx − dt
)
k

(9)

Therefore, the similarity between template and tester QEPD
D
(
PP,|PQ|

)is

obtained by Euclidean distance between the matrix of the absolute value of the

equation (9) and that of template's modulus square

2
.

|P |

3.4

QEPD Matching

We make 2-D wavelets decomposition feature as parallel fusion discussed in the

subsection 3.2. After fusion, we employ QEPD for matching. Suppose
A
and
B

as two finger texture feature quaternion vectors for each pixel of the subimage,

A
=

where
a, b, c, d
are wavelets decomposition coecients

respectively. The same is true like
B
=

{a
+
bi
+
cj
+
dk}

{t
+
xi
+
yj
+
zk}

. According to QEPD

D
(
PP,|PQ|

) , a matching score table (Table 1) is listed from the following Finger

texture ROI image (Fig.4):

From the table 1, QEPD matching scores are calculated by each two samples.

The most intra-class scores of this QEPD matching score estimated in our ex-

periment, usually span from 0 to 0.32, and majority of inter-class scores from

Search WWH ::

Custom Search