Studies of Fingerprint Template Selection and Update - Advances in Computational Science and Engineering - page 152

The problem of multi-template system can be described as follows:
Given N fingerprint templates T i (i=1,2,…N) which are N templates from N the
same finger, and the input fingerprint I 1 . N match scores s i (i=1,2,…N) represent the
similarity between T i (i=1,2,…N) and I 1 . We assume that the N templates from person
A and the input fingerprints from person B. We need to identify if B and A are the
same person. In our experiments, all the match scores from the same matcher are
between 0 and 1, so we need not transform the match scores. Different from Kittler'
rule which is based on Bayesian decision theory, we try to find the fusion rules based
on similarity between A and B based on the N score marks. That is to say we try to
find a new match score which represents similarity between A and B based on the N
match scores. According to the greatest similarity model, the match score between A
and B is apt to be bigger.
There are usually three kinds of score fusion rules: density based rules, transforma-
tion based rules and classifier based rules [10]. In this paper, we pay attention to
transformation based rules which are also called fixed fusion rules. Kittler et al. [15]
proposed a set of fusion strategies namely, sum, product, min, max, median and ma-
jority vote rules. We study the fusion rules based on the similarity model. In our pa-
per, the definition of the five fixed fusion rules: sum, max, min, median and product
are as follows.
sum:

1

N

∑

s = s

(1)

sum i

N

i = 1

product:

N

∏

1/ N

s = ( s )

(2)

product i

i = 1

max:

N

s = max( s )

(3)

max i

i = 1

min:

N

s = min( s )

(4)

min i

i = 1

median:

N

s edian s
=

= ()

(5)

median i

i 1

It is not difficult to prove (6).

s ≥≥ s s ≥ s s ≥ s ≥ s

and

(6)

max sum product min max median min