Face verification metrics: TAR at FAR, 1:1 and 1:N, and how to read the table

This page is part of the face recognition section. The ICCV 2021 masked face recognition challenge that this domain once hosted scored its entries this way, and the metrics page in the deepfake section explains the same curve under its other name.

01What face verification measures

Every comparison of two faces ends in a score, usually the cosine similarity between two embedding vectors. On its own the score means nothing; it becomes a decision only when compared with a threshold. Set the threshold high and few impostor pairs get through, but more genuine pairs are rejected; set it low and the reverse. A verification benchmark therefore needs two kinds of pair, genuine (same person) and impostor (different people), and it sweeps the threshold across the scores of both to trace the trade-off. Labeled Faces in the Wild, with 13,233 images of 5,749 people, fixed 6,000 such pairs and asked for the accuracy at the best threshold, which is why its numbers saturated; later benchmarks report points on the curve instead.

021:1 verification versus 1:N identification

Verification is one to one: is this the person on this document? Identification is one to many: who in this gallery, if anyone, is this probe? The second is built from many instances of the first, which is why its error rates grow with the size of the gallery, and why the two are reported with different vocabularies. NIST's evaluations state the 1:1 quantities as false non-match rate (FNMR), "the proportion of mated comparisons below a threshold set to achieve the false match rate (FMR) specified", and the 1:N quantities as false negative identification rate (FNIR) and false positive identification rate (FPIR), with FPIR defined as "the proportion of non-mated searches producing one or more candidates above threshold" (NIST FRTE 1:1, 1:N). Academic papers more often write TAR and FAR for the same 1:1 quantities, and rank-1 accuracy for identification. The NIST evaluations page explains how those reports are laid out, and the demographic differentials page shows why the two error types have to be reported separately: NIST found them to differ by group in very different degrees.

03TAR at a fixed FAR

Why the operating point matters

The false accept rate is the error a deployment has to bound, because it is the error that lets the wrong person in. A result is therefore stated at a fixed FAR: 1 in 100, 1 in 10,000, 1 in 1,000,000. The true accept rate at FAR 1e-4 and at FAR 1e-6 can differ by many points for the same system, so two TAR figures are comparable only when their FARs match, and a TAR without a FAR is not a result. The same system can also show very different TARs on two test sets at the same FAR, because the impostor pairs in one set may be harder, so the test set is part of the number too.

Reading a TAR at FAR row

A representative line from a 2020 training-set paper reads "97.2% TAR on IJB-C at FAR=10^-4" (arXiv 2010.05222). Read it as four fields: the metric is TAR; the operating point is a FAR of one in ten thousand; the test set is IJB-C, which holds 3,531 subjects, 21,294 still images and 117,542 video frames and whose distribution NIST ended in March 2023; and the system is whatever the paper trained. Change any field and the 97.2 is a different number. The ICCV 2021 masked face recognition report scored its WebFace260M track the same way, with the additional constraint of an inference time budget under the FRUITS protocol, so that a slower model could not buy accuracy with time (arXiv 2108.07189).

04Loss functions and why they appear in tables

Face recognition results tables often list a loss function where one would expect a model name: ArcFace, CosFace, SphereFace. The reason is that the backbone network is usually a standard ResNet and the thing a paper contributes is the training objective that shapes the embedding space, pulling images of one identity together and pushing identities apart by a margin. ArcFace, introduced at CVPR 2019 (arXiv 1801.07698), adds an angular margin to the classification loss and became the default; the "ArcFace" in a table row means a ResNet trained with that loss on a named training set, and the training set is as much part of the result as the loss. The WebFace260M paper's claim that WebFace42M cut the relative failure rate on IJB-C by 40% is a claim about data, measured with the same kind of loss (arXiv 2103.04098); the dataset page covers it.

05The same curve for deepfake detectors

Sweep a deepfake detector's threshold and the same curve appears with the axes renamed: true positive rate against false positive rate, called an ROC curve, with its area, AUC, as the usual summary and the equal error rate as the point where misses equal false alarms. The translation is exact: TAR is the true positive rate on genuine pairs, FAR the false positive rate on impostor pairs. The difference is convention, recognition fixes the operating point and detection averages over it, and the difference in what each field needs: a deployment must bound false accepts, while a benchmark comparison across detectors wants a threshold-free number. The metrics page takes the detection side, and the bridge page follows the shared pipeline that produces both scores.