Choosing a face-match threshold: FMR, FNMR, and operating points

Every face API returns a similarity score, and every team asks the same question: what score counts as a match? The honest answer is that it depends on your photos and the cost of each kind of error. Let's make that concrete.

The two errors you're trading off

You cannot minimize both at once. A signup verification step wants a low FMR (don't accept a mismatched selfie, even if it occasionally sends a real user to manual review). An event photo gallery tolerates a higher FMR behind a confirm step, because missing someone's photos is worse than showing one extra to confirm.

How to actually pick the number

1. Build a validation set from your own consented images: pairs you know are the same person (positives) and pairs you know are different (negatives). Size it for the error rate you need to measure — a very low target FMR needs *many thousands* of negative pairs, because you can't measure a 1-in-10,000 rate with only a few hundred.
2. Score every pair with the API's compare/search and record the similarity.
3. Plot FMR and FNMR against threshold. You'll see two curves crossing — the shape is specific to your data (posed selfies and casual candids behave very differently).
4. Choose the operating point by the cost of each error in your product, not by the crossover.
5. For 1:N search, validate at gallery scale. Pairwise FMR understates false-identification risk when a probe is compared against thousands of faces — the chance of *some* wrong match grows with gallery size. Measure identification error against realistic gallery sizes, not just pair-at-a-time.
6. Re-validate when your image mix or the model version changes.

# similarity is SightRadar's native 0-1 score, so sweep 0.00..0.99.
# (On AWS Rekognition, Similarity is 0-100 — sweep 0..100 instead.)
def sweep(pairs):  # pairs: [(similarity, is_same_person), ...]
    neg = sum(1 for _, same in pairs if not same) or 1
    pos = sum(1 for _, same in pairs if same) or 1
    for i in range(0, 100):
        t = i / 100
        fm = sum(1 for s, same in pairs if s >= t and not same)
        fnm = sum(1 for s, same in pairs if s < t and same)
        print(f"t={t:.2f}  FMR={fm/neg:.4f}  FNMR={fnm/pos:.4f}")

The two-tier reveal pattern

For 1:N search (find-my-photos), you don't need a single line. Use two: an auto threshold high enough to reveal immediately, and a lower review threshold whose matches are shown behind a "confirm it's you" step. This gives high recall without auto-revealing a stranger's photos to the wrong person. SightRadar labels each match auto or review for exactly this; a client that ignores the label sees every match as auto.