FMR, FNMR, FPIR and FNIR: the four face recognition error rates, as NIST defines them

This page belongs to the face recognition section and defines the terms that the face verification metrics page and every NIST results table rely on.

01Why four error rates and not one?

Every face recognition decision is a score compared with a threshold, and every threshold produces two kinds of mistake. NISTIR 8280 puts it in two sentences: "A genuine score below threshold yields a false negative outcome, and an imposter score at or above threshold, a false positive outcome" (Grother, Ngan and Hanaoka, 2019). A single accuracy number hides which of the two it is counting and where the threshold sat.

The count doubles because face recognition is two tasks. Verification compares one photo with one claimed identity; identification searches one photo against a gallery of N identities and returns candidates. The report notes that "The ISO/IEC 19795-1 performance testing and reporting standard requires different metrics to be reported for identification and verification implementations", so the two errors each get a verification name and an identification name. That gives four rates, drawn from one threshold in the figure below.

02What are FMR and FNMR?

The NIST FRTE 1:1 page defines both in one place: "FNMR is the proportion of mated comparisons below a threshold set to achieve the false match rate (FMR) specified. FMR is the proportion of impostor comparisons at or above that threshold" (NIST FRTE 1:1 Verification, read 9 November 2026). A mated comparison is two images of the same person; an impostor comparison is two images of different people.

NISTIR 8280 section 3.1 gives the same definitions as formulas. From a vector of N genuine scores, FNMR at threshold T is the fraction below T; from a vector of M impostor scores, FMR at T is the fraction above it. The report also explains how thresholds are chosen for a table: "We typically generate a set of thresholds from quantiles of the observed imposter scores", spaced evenly on a logarithmic scale, because "typical operations target false match rates spanning several decades 10^-6 to as high as 10^-2". A published FNMR therefore always comes with the FMR its threshold was set to reach. On the FRTE 1:1 page the ordering column is FNMR at FMR equal to one in a million on the Visa-Border dataset.

03What are FPIR and FNIR?

The FRTE 1:N page defines the identification pair: "FNIR is the proportion of mated searches failing to return the mate above threshold. FPIR is the proportion of non-mated searches producing one or more candidates above threshold" (NIST FRTE 1:N Identification, read 9 November 2026). In the main 1:N table the threshold is set for each algorithm and each column so that FPIR equals 0.003, and the FNIR at that threshold is what the cell shows.

NISTIR 8280 section 3.2 adds two details that the short definitions leave out. FPIR can be computed from the highest-scoring non-mate candidate in each search, so rank 2 and below do not matter for it. FNIR has three arguments, N, R and T: a mate counts as missed if it falls outside the top R ranks or scores below T, and "a mate that is not reported on a candidate list is treated the same as a miss arising from face finding failure", so a template that could not be made is a miss too. The hit rate many practitioners quote, the true positive identification rate, is simply one minus FNIR.

04How does the threshold connect the four?

One algorithm has one threshold in operation, and NISTIR 8280 stresses that this is where most academic reporting goes wrong: "the vast majority of biometric systems are configured with a fixed threshold against which all comparisons are made", yet most studies report "false negative rates at fixed false positive rates rather than at fixed thresholds", which hides movement in the false positive rate between groups. Moving the threshold up lowers FMR and FPIR and raises FNMR and FNIR at the same time; there is no setting that lowers all four.

That coupling is why the NISTIR 8280 report reports both rates for each demographic group at the same threshold, and why its headline finding is a false positive one: false match rates that "often vary by factors of 10 to beyond 100 times" across groups while false negatives vary "by factors below 3". Any demographic comparison that quotes one rate without the other is incomplete by the report's own standard.

05Where does the investigation mode fit?

When the threshold is set to zero the definitions still hold but FPIR stops being informative. The 1:N page's investigation tables set "the threshold is set to zero and the algorithm returns a fixed number (50) of candidates", and in that mode FNIR becomes "the proportion of mated searches for which the algorithm does not place the correct candidate at rank 1". Every non-mated search returns 50 candidates, so FPIR is 100 percent by construction and the burden moves to the human reviewer. Reading a 1:N table means checking which of the two modes a column reports before comparing numbers.

06How these rates compare with detection metrics

Deepfake detection uses the same threshold sweep but names it differently: true positive and false positive rates on an ROC curve, summarised as AUC, or an equal error rate where the two mistakes balance. FMR and FNMR are the recognition names for the two points on that curve at one threshold; FPIR and FNIR are their search equivalents. The same trap applies in both fields: a detector such as GenConViT reports an AUC of 99.3 percent averaged over its own test sets, a figure that says nothing about where its threshold would sit in use. The face recognition technology overview places these rates in the full pipeline, and the NIST evaluations page shows where each one appears in a published table.