The Relation Between the ROC Curve and the CMC

The Cumulative Match Curve (CMC) is used as a measure of 1:m 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.

By: R. M. Bolle; J. H. Connell; S. Pankanti; N. K. Ratha; A. W. Senior

Published in: RC23885 in 2006


This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.


Questions about this service can be mailed to .