FACIAL SOFT BIOMETRICS - Library of Ph.D. Theses | EURASIP

8reduced computational complexity comes with restrictions on the size of an authentication group.It becomes apparent that a measure of performance must go beyond the classical biometric equalerror rate of the employed detectors and include a different and new parametrization. Our generalinterest here is to provide insightful mathematical analysis of reliability of general soft biometricsystems, as well as to concisely describe the asymptotic behavior of pertinent statistical parametersthat are identified to directly affect performance. Albeit its asymptotic and mathematicalnature, the approach aims to provide simple expressions that can yield insight into handling reallife surveillance systems.We introduce the setting of interest, which corresponds to the general scenario where, out of alarge population, an authentication group is randomly extracted as a random set of n people, outof which one person is picked for identification (and is different from all the other members ofthe authentication group). We note that this general scenario is consistent with both, the case ofperson verification as well as of identification. A general soft-biometric system employs detectionthat relates toλsoft biometric traits (hair color, skin color, etc), where each traiti,i = 1,2,...,λ,is subdivided into µ i trait instances, i.e., each trait i can take one of µ i values. We henceforthdenote as category to be any λ-tuple of different trait-instances, and we let Φ = {φ i } ρ i=1 definea set of all ρ categories, i.e., the set of all ρ combinations of soft-biometric trait-instances. Thenumber of ρ, that the system is endowed with, is given byρ = Π λ i=1µ i (1)In this setting we elaborate on pertinent factors, such as those of the authentication group,traits, traits instances, overall categories and their interrelations. We then proceed to introduce andexplain the event of collision, which is of significant character when employing SBSs for personidentification. event where any two or more subjects belong in the same category φ. Focusing ona specific subject, we say that this subject experiences interference if he/she belongs in a categorywhich also includes other subjects from the authentication group. In regards to this, we are interestedin gaining insight on two probability measures. The first measure is the probability p(n;ρ)that the authentication group of size n, chosen randomly from a large population of subjects, issuch that there exist two subjects within the group that collide. We briefly note the relationship ofp(n;ρ) to the famous birthday paradox. For the other measure of system reliability, we considerthe case where an authentication group of size n is chosen randomly from a large population ofsubjects, and where a randomly chosen subject from within this authentication group, collideswith another member of the same group. We denote this probability asq(n), and note that clearlyq(n) < p(n). To clarify, p(n) describes the probability that interference exists, even though itmight not cause error, whereas q(n) describes the probability of an interference induced error.Example: In a group of N subjects p(n) would describe the probability that any two subjects willbelong to the same category φ x . On the other handq(n) reflects the probability that a specific subjectwill interfere with one or more of theN−1 remaining subjects. In the following we provide asimulation of the probability of identification error, in the setting of interest, under the assumptionthat the errors are due to interference, i.e., under the assumptions that errors only happen if andonly if the chosen subject shares the same category with another person from the randomly chosenauthentication group. This corresponds to the setting where the soft-biometric approach cannotprovide conclusive identification. In the simulation, the larger population consisted of 646 peoplefrom the FERET database, and the simulation was run for different sizes n of the authenticationgroup. The probability of identification error is described in the following figure.As a measure of the importance of each trait, Figure 1 describes the collision probability whendifferent traits are removed. The presence of moustache and beard seem to have the least influenceon the detection results, whereas hair and eye color have the highest impact on distinctiveness.