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

38 3. BAG OF FACIAL SOFT BIOMETRICS FOR HUMAN IDENTIFICATIONIn other words the bound in Lemma 5 implies that, a reduction of the relative-throughput fromits maximal value of n/ρ ≈ 1 to a sufficiently smaller n/ρ ≈ 1 2, for high enough ρ, results in asubstantial and exponential reduction in the probability of interference, from P(h = 1) ≈ ρ −ρɛ toP(h = 1 2 ) ≈ ρ−ρ(5 4 +ɛ 2 ) .We have up to now focused on the interference limited scenario, where errors occur only due tomore than one subject belonging to one category. In the next section 3.5.4 we consider estimationerror and a more pragmatic way to improve the overall reliability of a SBS.3.5.4 Estimation reliabilityIn the aforementioned operational setting of interest, the reliability of an SBS captures theprobability of false identification of a randomly chosen person out of a random set of n subjects.In such a setting, the reliability of an SBS is generally related to:– the number of categories that the system can identify.– the degree with which these features/categories represent the chosen set (of subjects) overwhich identification will take place– n, where a higher n corresponds to identifying a person among an increasingly large set ofpossibly similar-looking people– robustness with which these categories can be detectedWe here proceed to study the general SBS error probability, containing inevitably all abovementioned factors including the algorithmic categorization error–probabilities. With other wordswe examine, the re–identification error probability, regardless of the underlying source, which canbe both due to misclassifcation or due to interference.Given the knowledge of the population statistics and moreover the exact algorithmic reliabilities(true detection rates and additionally the confusion probabilities), we can use a maximum–likelihood (ML) optimizing rule to compute the maximal posterior probability for each category.We note here that the ML optimizing rule for the most probable category in which a chosen subjectbelongs, is given by:ˆφ = argmax φ∈Φ P(φ)·P(y/φ), (3.27)wherey is the observation vector,P(φ) is the pdf of the set of categories over the given population(note ∑ ρß=1 P(φ i) = 1), and P(y/φ) the probability that y is observed, given that the subjectbelongs in category φ.3.5.4.1 Improving SBS reliabilityIn the most common case of a training set, which provides insufficient information on all confusionfactors as of all P(y/φ), we can find heuristic rules to combat the overall error probabilityP err . Given the large amount of empty categories, see the distribution of over-all-categories inthe FERET population in Figure 3.1, and furthermore the above presented correlations betweentraits, certain misclassifications can be identified and reconciled. An example for a heuristic errorconciliation attempt can be the following.Example 6 We take into account the given large FERET population and the SBS presented insection 3.3.1. We simulate again the same identification scenario, where here we simulate an estimationerror of 10% for the color soft biometric traits (hair, skin and eye color). When fusing thetraits on decision level (hard fusion) those errors naturally add up. That is why a soft decision,taking into account the confidence levels of the extracted features and also the reliability of the