Master Thesis - Department of Computer Science

Genuine
Impostor
Scores Scores
1
0
1
0
No of Samples GD
b
1 No of Samples
(a)
Figure 3.7: Area difference between genuine and impostor distribution with their
ideal counterparts.
GDi and IDi, can written as,
GDi = {m(rs)(ij) | i = r , j = 1, 2, ..., n and s = 1, 2, ..., p} (3.2)
IDi = {m(rs)(ij) | i �= r, r = 1, 2, ..., C, j = 1, 2, ..., n and s = 1, 2, ..., p} (3.3)
We have formulated four different criteria for measuring goatishness and lambish-
ness for a person. Ideally, all elements of the confusion matrix for a genuine subject
should be one (1) whereas, elements for impostor subjects should be zero (0). We
have tried to measure the amount of deviations of genuine and impostor distribu-
tions from their ideal counterparts. The criteria need to be minimized for choosing
appropriate subbands. The criteria are described below:
3.3.1 Criteria used for measuring Goatishness and Lambishness
• First Criterion (C1): Let the number of elements in the genuine and impostor
sets be b GD = n ∗ p and b ID = n ∗ (C − 1) ∗ p, respectively irrespective of
any subject. Taking the elements along x-axis, if we plot the scores of the
genuine samples we obtain a multimodal hill-shaped curve (genuine distribu-
tion). The difference in area between this and the ideal curve gives the measure
of deviation for genuine distribution from its ideal counterpart. For impostor
distribution, the measure is the area under impostor curve (see Figure 3.7).
So goatishness and lambishness measures for i th subject denoted as Gi and Li,
55
1
(b)
ID
b