## 1 Introduction  
Many developers of biometric systems start with modest samples before general deployment. However, they are interested in how their systems will work with much larger samples. To assist them, we evaluated the effect of gallery size on biometric performance. We start with the hypothesis that as gallery size increases, more information is required to achieve any particular level of performance. We will be addressing performance in terms of identification rate, specifically Rank-1 Identification Rate (Rank-1 IR), and also in terms of ROC-based measures such as EER. (All error rates rates are expressed as percent in the present study). It is well known from empirical studies that the Rank-1 IR declines with increasing gallery size and that this relationship is linear in log(gallery size) (see Figure 1) [1; 2; 3] We will attempt to further describe this relationship, and also show that the decrease in Rank-1 IR can be reversed with the addition of new information. [PERSON] et al. 2010 [2] conducted a theoretical analysis of this issue using extreme-value theory. They develop large sample approximations to illustrate how Rank-1 IR should change with gallery size. Their basic result (assuming independence of the probe scores against different imposters) gives a linear relationship in log(gallery size) to the first order. The authors show that their theoretical result does not match up well with empirical results. However, they indicate that this was likely due to dependence among the probe-imposter scores due to image quality; a modification using a categorization of image quality provides a much better fit to the empirical results. The end of their paper talks about the \"open\"-set case where ROC-curves tend to be utilized. They indicate that asymptotic theory suggests ROC metrics should depend on the tail of the imposter score distribution; no empirical comparisons are provided. Our work complements that of [PERSON] et al. (2010) [2] in that we provide extensive empirical evidence regarding the effect of gallery size. Our results support their theoretical suggestion of a log-linear relationship. We also probe the importance of feature reliability (i.e., temporal persistence) among the features used to define the score. We also perform an extensive empirical analysis of the effect of gallery size on ROC-curves. Although [PERSON] et al. (2010) [2] emphasize the important role of the tails of the similarity score distributions, in the present study we emphasize the role of the spread (i.e., inter-quartile range (IQR)) of the similarity score distributions. There is little published research on the impact of increasing gallery size on ROC-based measures such as EER, aside from the work of [PERSON] et al. 2010 [2], noted above. Although it is well established that increasing the number of subjects will decrease the confidence limits on any ROC-curves produced [4; 5], this evidence does not imply anything about the central tendency of any estimated error rate. We were interested in evaluating the influence of changes in gallery size on a large scale (up to 100,000 subjects). For reasons of convenience, availability and control, we employed synthetic data sets. However, at each step in the analysis, we provide comparison analyses for a real face-recognition data set (MORPH-II) [6] with \(N\) = 13,930 subjects. The real face recognition data allowed us to evaluate if the substantive findings with synthetic data were replicated in real biometric data. In Section 2 of the manuscript, we present a method for creating synthetic data sets with a number of properties that are helpful for studying biometric performance. Because the data are synthetic, we are able to control the degree of temporal persistence of the features while also ensuring that features are approximately independent of each other and thus  
Figure 1: Probability of detection at Rank-1 IR as a function of more than 600,000 plain index fingers [1] (See Figure 19). Note the log scale for the \(x\)-axis. Probe set size was 1000 subjects.