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s
∈=
[0,1],
i
1, 2,
N
K
, then the final marks after fusion are between 0 and 1. For
a two-class classification problem, score based max rule is totally the same as deci-
sion level rule OR. Also, min rule is the same as AND, and median rule is the same as
majority vote rule. According to the greatest similarity principle and expression (6),
max rule may perform better than other rules. In our experiment we find that max rule
has a better performance than other rules.
If
3 Multiple Templates Selection Analyze
3.1 Templates Selection and Multibiometrics
Biometric recognition systems usually keep several templates and execute multiple
matches in authentication for an individual. The system validates a person's identity
by comparing the captured biometric data with his own biometric templates stored in
the database. Systems which keep more than one template for each individual may be
classified as a kind of multisample system. Based on the theory of multibiometrics,
multiple templates can gain high matching accuracy. Consider a two-class classifica-
tion problem and a multiclassifier system consisting of N classifiers (assume N is
odd); the majority vote rule classifies an input pattern as belonging to the class that
obtains at least K=(N+1)/2 votes. If p is the probability that a single classifier per-
forms correctly, then the probability of the multiclassifier is as follows [9]:
N
∑
PN
()
=
() 1
Nm Nm
m
p
−
p
−
)
(7)
mK
=
The formula (1) assumes that the classifiers themselves are statistically independent.
However, multiple templates come from the same biometric trait, which can not be
independent in practice. Anyway, multiple templates can improve the accuracy of
biometric system, but how many templates are suitable and how do multiple templates
achieve better performance can be a problem. In this paper, we studied the two prob-
lems and got some useful conclusions.
3.2 A Model of Template Selection
The problem of template selection may be posed as follows: Choose K(K<N) biomet-
ric templates from N biometric samples captured from users during the enrollment
which can represent the variability as well as the typicality observed in the N biomet-
ric samples best.
Definition 1: During the enrollment, the user inputs N biometric samples i
1
,i
2
,
…
,i
N
.
After feature extraction, N candidate feature templates t
1
,t
2
,
,t
N
are available. Score
matrix S
N×N
is constructed in which the item s
m,n
represents the match score between
the template t
m
and the input sample i
n
. In our experiment, all the match scores are
between 0 and 1. It should be noticed that s
m,n
may not be equal to s
n,m
because the
feature template has less information than its sample after feature extraction.
…
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