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

59for one person, for trait t, t = 1,2,··· ,T . At the same time Let N fr be the average complexityassociated with the face recognition algorithm, per person. Given a naive way of pruning, weconclude that the overall computational complexity N is given asN = nT∑N t +|S|N fr , (4.31)i=1which reflects the fact that the categorization algorithms for the T traits would be employed on npeople, and the computationally expensive face recognition algorithm would be employed only on|S| people. We relate this computational complexity N to the computational complexity requiredif only the face recognition system was employed on the entire v. Towards this we have thefollowing.Proposition 2 Pruning results in a computational cost reduction to a fraction of nN fr that isequal to∑EN Ti=1=N t+p T Ep. (4.32)nN fr N frExample: We proceed with the evaluation of our presented SBSs with three different estimatedrelationships between the computational complexity of the face recognition system N fr ,and that of implementing a trait, i.e., toN t .Complexity Reduction1.110.90.80.70.6N fr/N t=70.5N /N =4.6 fr tN /N =3.5 fr t0.42e m g 4e mg 2emSB System2eg 2emg 4emgFigure 4.12: Complexity cost reduction provided by the presented SBSs. In the above, the ratioN fr /N t varies.Figure 4.12 reflects on the computational cost reduction of the proposed SBSs. In this contextthe best systems are ‘4e’ and ‘4emg’, which reduce the computational cost by more than half. Thesystem ‘4e’ specifically has very low complexity, since the computation involves just one trait,but where the four categories are sufficient to increase the gain, and hence reduce the numberof people on which the face recognition system is applied. Similarly system ‘4emg’ achievesgood complexity, mainly because of its high pruning gain, which substantially reduces the costof applying the face recognition system. Also interesting to see is the cost increase for systems‘m’ and ‘mg’. This means that those systems reduce the initial database insufficiently and cannotjustify their computational costs.