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We investigate the existence of quality measures for face recognition. First, we introduce the concept of an oracle for image quality in the context of face recognition. Next we introduce greedy pruned ordering (GPO) as an approximation to an image quality oracle. GPO analysis provides an estimated upper bound for quality measures, given a face recognition algorithm and data set. We then assess the performance of 12 commonly proposed face image quality measures against this standard. In addition, we investigate the potential for learning new quality measures via supervised learning. Finally, we show that GPO analysis is applicable to other biometrics.