*2.4. Two-Stage Online Signature Verification*

The forgery can be classified to be two types, named skilled forgery and random one. In real applications, random forgeries appear more frequently while skilled forgeries occur less. On the other hand, skilled forgeries are much more difficult to be verified correctly. In this paper, we propose a method using shape contexts and function features as well as a two-stage strategy for accurate online signature verification. The shape context-based verification module is firstly used to reject obvious random forgeries quickly while the function features-based verification module is applied to re-check the signatures survived from the previous module. In this way, the whole system can achieve higher accuracy and consume less computation cost at the mean time.

Two metrics named FRR (False Reject Rate) and FAR (False Accept Rate) have been widely used to evaluate signature verification system. For cascade structure applied in our method, the relationship of FRR and FAR between the sub-verification modules and the whole system are showed in Table 3, where *p* denotes the reject percentage of first sub-verification module. Obviously, *p* takes the value smaller than 1.

$$\begin{aligned} r\_1 &< r\_2 \Rightarrow pr\_1 + (1-p)r\_2 < r\_2\\ p &< 1 \Rightarrow (1-p)a\_2 < a\_2 \end{aligned} \tag{13}$$

**Table 3.** FRR and FAR of individual verification modules and cascade system.


It can be seen that the performance of the cascade system depends on the thresholds of two sub-verification modules. If *p* < 1 and *r*<sup>1</sup> is set to be smaller than *r*2, the cascade system can achieve better performance than the sub-verification modules in terms of false acceptance rate, which is illustrated in Equation (13).
