2.2.5. Similarity Measure

The similarity measure *Score* of two signature curves is calculated as follows:

$$\begin{cases} Score = w\_b \cdot LSC + w\_b \cdot GSC \\ LSC = \frac{1}{N} \sum\_{i=1}^{K} (0.2sx\_i + 0.3sy\_i + 0.5IVR\_i) \\ GSC = g(M/N) \\ w\_a + w\_b = 1, w\_a \ge 0, w\_b \ge 0 \end{cases} \tag{14}$$

where *LSC* and *GSC* are local similarity score and global similarity score, respectively, while *wa* and *wb* are the corresponding weights. *M* and *N* are the lengths of the reference signature and the comparison signature, respectively.

Here:

$$\text{g}(\mathbf{x}) = \begin{cases} 0 & \mathbf{x} < 0.5\\ 100 \times \exp(-2(\mathbf{x} - \mathbf{1})^2) & 0.5 \le \mathbf{x} \le 2\\ 0 & \mathbf{x} > 2 \end{cases} \tag{15}$$

is used to calculate score of the writing time ratio of two origin signatures.

The calculation of the weight is calculated by enumeration, where *wa* = 0.85 and *wb* = 0.15, and the detailed process is shown in the next Section 3.4.

It is considered that threshold ε of the signature verification system is 60 in many cases, and when *Score* is greater than 60, it may be distinguished into a genuine signature, and below 60 may be considered as a forged signature.

This is similar to the 100 point test. Passing more than 60 points is a pass, and below 60 is a failure. Of course, accurately determining the threshold is also a problem that needs to be studied in depth. For each user's signature threshold determination, some other real registration signatures or even skilled forged signatures are needed. As a single template signature authentication system, only a reasonable threshold is given here, which is one of the key issues that need to be studied in the future.

## **3. Experiments**

In this section, experiments to evaluate the efficacy of the four datasets are described and signature verification performances are reported.
