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

FNMR =
�η
−∞
2.3 System performance
P (s|H0) ds. (2.4)
The selection of an arbitrary operating point, i.e. tuple (FMR, FNMR)η of FMR and
FNMR values for some fixed threshold η, is typically insufficient for comparison. Instead,
different algorithms are compared using the set of all possible operating points depicted
in the form of a Receiver Operating Characteristics (ROC) curve [1] (see Figure 2.2).
Alternatively, for performance comparison the following indicators are frequently adopted
(see also the Fingerprint Verification Competition 2006 [50]):
• Equal Error Rate (EER): the value such that FMR = FNMR;
• Zero False Match Rate (ZeroFMR): the lowest FNMR for FMR = 0%;
• Zero False Non-Match Rate (ZeroFNMR): the lowest FMR for FNMR = 0%;
• Minimum Half Total Error Rate (MinHTER): the global minimum value of the
following function [30]:
HTER(t) :=
FMR(t) + FNMR(t)
. (2.5)
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As can be seen in Figure 2.2, each of these performance indicators refers to a single point in
the ROC curve: PEER is the intersection of the ROC curve with the first median and corresponds
to the EER indicator. Analogously PZeroFNMR and PZeroFMR refer to ZeroFNMR
and ZeroFMR and can be identified as intersections of the ROC curve with the y-axis (and
x-axis respectively) with closest distance to the origin. Finally, PMinHTER corresponds to
the operating point where the half of the sum of coordinates is a minimum.
It should be pointed out that, for identification systems, the situation is slightly different.
Here, using the notions above, the hypotheses could be reformulated as follows:
H0 : ∃M ∈ M : X ≡ M, i.e. there exists an enroled template with the same identity;
(2.6)
Ha : ∀M ∈ M : X �≡ M, i.e. within M no template with the same identity exists. (2.7)
Within this context, a False Accept occurs, if X is found to be matched with a template
of an enroled member mi ∈ M, while in reality it is an imposter and False Rejects
denote falsely rejected genuine authentication attempts. Matching with multiple (correct
or incorrect) candidates is ignored in this case.
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