Studies of Fingerprint Template Selection and Update - Advances in Computational Science and Engineering - page 154

Definition 2: The distance between biometric feature templates set A and biometric
samples set B is:

∑

dAB (, ) = 1 − s

(8)

mn ,

∀∈∀∈

t

AiB ,

m n

The K templates selected is denoted as template set T K and the left N-K samples is
denoted as input set I N-K . For the future inputs i N+1 ,i N+2 ,

denoted as set I N + , our aim
is that the distance between T K and I N + denoted as d(T k ,I N-K ) should be minimized.
However, the future inputs are not available. So replace the set I N + with the left sam-
ples set I N-K , the problem is now to choose the K templates that make d(T k ,I N-K )
minimized. We define the match score between set A and set B as follows:

…

∑

sAB (, ) = s

(9)

mn
t Ai B

,

∀∈ ∀∈ ,

m n

Finally, substituting formula (9) into formula (8) , we obtain formula (10) where
N(A) and N(B) refers to the numbers of elements in set A and B.
(, ) dAB NA NB sAB = ()* () − (, )

(10)

Finally, we obtain the follow formula:

dT I (, ) = K N K sT I *( − ) (, − ) (11)

kNK − kNK −

K(N-K) is constant in template selection. Therefore the model is to select K tem-
plates from N input samples which make s(T k ,I N-K )maximized. To express simply,
we call the model maximized score model and record the maximized s(T K ,I N-K ) as
Max(T K ).

3.3 How Many Templates Should Be Selected?

It is a key issue that how many templates should be selected. There are at least three
factors to be considered to decide the value of K. First, the aim of template selection
is to reduce the number of templates and to keep good performance at the same time.
Second, although we say that storage and parallel processing technique progress
greatly, the memory space and CPU speed is not unlimited and more space and higher
CPU speed means more cost. We should make a tradeoff between the templates num-
ber and the cost. Third, according to the maximized score model, we should make the
s(T K ,I N-K ) maximized on condition that I N-K represents the future inputs set I N + . There-
fore, N-K should be large enough so that I N-K can represent I N + . In practice, s m,n and
s n,m are usually very similar. So given s m,n = s n,m , Max(T K ) = Max(T N-K ). That means
choose K templates are the same with N-K templates according to the maximized
score model. So we suggest K [N/2] if N is large enough. Also, from Table 1 in

section 5, we can find that the EER is decreased begin slowly when K

≤

≥ 4. In our ex-

periment, 3~5 templates are suitable when N=8.