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56 4. SEARCH PRUNING IN VIDEO SURVEILLANCE SYSTEMS0.60.5pruning Gain r(vt)0.40.30.20.10 5 10 15 20 25 30Realization tFigure 4.8: SBS ‘mg’, n=50, target subjectv ′ belongs to categoryC ′ =“no moustache - no glasses".0.60.5pruning Gain r(vt)0.40.30.20.10 5 10 15 20 25 30Realization tFigure 4.9: SBS ‘mg’, n=200, target subject v ′ belongs to category C ′ =“no moustache - noglasses”.the other more common case where v ′ belongs in the category of people without glasses andmoustache. The operating ranges of the pruning gain reflects directly the distinctiveness of thetarget subject, given in both cases the same population and system characteristics.4.7 Average case analysis of gain, reliability and computational-costeffects of pruning4.7.1 Average pruning gain and related errorWe proceed with presenting a concise description of the average gain of an SBS, where thegain r(v) is averaged over all possible authentication groups v, and over the randomness of thecategorization errors w, as elaborated in 4.3.The following describes the average gain and reliability of an SBS.Proposition 1 An SBS system endowed with a categorization confusion matrixEand error vectore, and operating over a general population with statistics given by p, allows for a probability of