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This paper introduces the concept of biometric-completeness. A problem is biometric-complete if solving the problem is ldquoequivalentrdquo to solving a biometric recognition problem. The concept of biometric-completeness is modeled on the informal concept of artificial intelligence (AI) completeness. The concept of biometric-completeness is illustrated by showing a formal equivalence between biometric recognition and quality assessment of biometric samples. The model allows for the inclusion of quality of biometric samples in verification decisions. The model includes most methods for incorporating quality into biometric systems. The key result in this paper shows that finding the perfect quality measure for any algorithm is equivalent to finding the perfect verification algorithm. Two results that follow from the main result are: finding the perfect quality measure is equivalent to solving the open-set and closed-set identification problems; and that a universal perfect quality measure cannot exist.