Blog - Signature verification — telling genuine from forgery

Signature verification is a behavioral biometric. The practical split is offline (scanned image) vs online (tablet trajectory: $x,y,t$, pressure).

Offline: signature as an image

From a bitmap we extract skeleton, contour, Hu moments, stroke-orientation histograms. It works, but static shape is easier to forge than dynamics.

Similarity of feature vectors $u,v$ is often cosine:

$$s(u,v) = \frac{u^\top v}{\|u\|\,\|v\|}$$

Online: time and pressure

The signal is a sequence $p_k = (x_k, y_k, t_k, p_k)$. Compare sequences with DTW or a Siamese/LSTM embedding.

DTW recurrence between sequences $A,B$:

$$D(i,j) = d(a_i,b_j) + \min\{D(i-1,j), D(i,j-1), D(i-1,j-1)\}$$

Smaller normalized $D(|A|,|B|)$ means closer signatures.

Decision pipeline

What exposes a forger?

1. Timing — unnaturally uniform speed.
2. Pressure — missing natural drops on pen-ups.
3. Stroke order — different motion topology with similar appearance.

That is why online verification usually beats offline FAR at the same UX budget.

Takeaway

Effective signature verification leans on dynamics, not shape alone. If you can capture online signals — do; the image is plan B.