The relation between the ROC curve and the CMC

The Cumulative Match Curve (CMC) is used as a measure of 1 identification system performance. It judges the ranking capabilities of an identification system. The Receiver Operating Characteristic curve (ROC curve) of a verification system, on the other hand, expresses the quality of a 1:1 matcher. The ROC plots the False Accept Rate (FAR) of a 1:1 matcher versus the False Reject Rate (FRR) of the matcher. We show that the CMC is also related to the FAR and FRR of a 1:1 matcher, i.e., the matcher that is used to rank the candidates by sorting the scores. This has as a consequence that when a 1:1 matcher is used for identification, that is, for sorting match scores from high to low, the CMC does not offer any additional information beyond the FAR and FRR curves. The CMC is just another way of displaying the data and can be computed from the FAR and FRR.