Multimodal Biometric Fusion Lab (2D)

Fusion Rule

Fingerprint threshold t₁ 0.55

Face threshold t₂ 0.55

Fingerprint weight w 0.50

Fused threshold t 0.55

Live Metrics

Combined FAR

0.0%

Combined FRR

0.0%

Accepted impostors

0 / 0

Rejected genuine

0 / 0

Approx. EER

–

Overall accuracy

0.0%

Genuine user attempt

Impostor attempt

Drag inside the score plane to move the boundary directly.

How it works

Every biometric match produces a similarity score in [0,1]. A genuine user's fingerprint and face scores cluster high; an impostor's cluster low, but the two distributions always overlap — that overlap is what causes False Accepts and False Rejects. Multimodal systems combine two independent scores (s₁ = fingerprint, s₂ = face) to shrink that overlap:

AND rule:      accept ⇔ s1 ≥ t1  AND  s2 ≥ t2
OR rule:       accept ⇔ s1 ≥ t1  OR   s2 ≥ t2
Weighted sum:  f = w·s1 + (1-w)·s2
               accept ⇔ f ≥ t

Each of 400 simulated genuine sessions and 400 impostor sessions draws (s1, s2) from Gaussian score models per modality. The decision rule slices this 2D score plane — shown on the left as a live scatter with a draggable boundary — into an accept region and a reject region. The right-hand panel sweeps the fused threshold from 0 to 1 and traces how FAR and FRR move in opposite directions, crossing at the Equal Error Rate:

FAR = impostors accepted / total impostors
FRR = genuine rejected  / total genuine
EER = threshold where FAR ≈ FRR (the crossover point)

AND drives FAR down (harder to spoof both sensors) but raises FRR (easier to lock out the real user). OR does the opposite — convenient, but a spoofed single modality gets through. Weighted score fusion lets you trade the two off continuously and, tuned well, beats either single modality's Equal Error Rate — this is why production authentication (Face ID + passcode fallback, fingerprint + behavioral checks) layers modalities instead of trusting one sensor alone.

Score plane (drag to move boundary)

FAR / FRR vs. fused threshold

Rule: Weighted score sum Genuine: 400 · Impostor: 400