Single-sensor hand and footprint-based multimodal biometric ...

2.1 Identification versus Verification
Definition 2.1.4 (Verification system). Given a biometric sample X ∈ X and a
claimed identity i ∈ {1, . . . , m}, a verification system is a function V : X × M →
{genuine, imposter} determining whether the claim is true by returning the class
genuine or whether the claim is false by returning imposter, based on a threshold η:
V (X, mi) :=
�
genuine, if S(E(X), ii) ≥ η;
imposter, otherwise.
2. Identification: Only the acquired biometric sample is used for reliable determination
of the identity of the access claiming person. Thus, screening against all stored
reference templates (one-to-many comparison) is needed, see [14].
Definition 2.1.5 (Identification system). Given a biometric sample X ∈ X , an
identification system is a function I : X → M ∪ {reject} determining the identity
mi, i ∈ {1, . . . , m} if existing or the state reject in case of no suitable identity can be
determined:
⎧
⎨ mi, if i = arg max{S(E(X),
ij)} ∧ S(E(X), ii) ≥ η;
I(X) :=
j
⎩
reject, otherwise.
Apart from this definition of identification systems, the following variants exist [1]:
sometimes the whole set of matching identities, i.e. the set {mi : S(E(X), ii) ≥ η},
is considered (threshold-based identification). Another variant, not necessarily based
on scores, is rank-based identification where the matcher is expected to return a
fixed size k-dimensional ranking vector (mπ(1), mπ(2), . . . , mπ(k)) with π a permutation
of {1, . . . , m}. Finally, there are also hybrid approaches returning a variable-sized
ranking vector of maximum length k containing only templates exceeding the defined
threshold.
It is clear, that running systems in identification mode is more challenging for the following
reasons:
• Security: System error rates largely depend on the number of enroled members.
This circumstance is illustrated by the following experiment: assuming a system
operates at 0.1% False Accept Rate (FAR, the rate of falsely accepted imposter
authentication attempts) with a member database size of n = 250, a single imposter
trying to cheat the system will be lucky in approximately 1 − 0.999 250 ≈ 22.13%
of the cases (assuming a simplified model with equal FAR for each identity in the
system database [1]). However, using a database size of n = 2500 the probability of
being falsely accepted increases to 91.8%;
• Performance: The number of necessary comparisons increases with the number
of enroled members. Large databases, such as the FBI Integrated Automated Fingerprint
Identification System [48] with fingerprints of over 47 million subjects as of
July 2007, need fast matching algorithms in order to be able to respond in reasonable
time.
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