**1. Introduction**

Biometric authentication has always been a field of primary concern in the security application field [1,2]. Person authentication or verification using handwritten signatures is one of the most widely researched behavior-biometrics and the most popular method for identity verification [3]. Usually, signature verification systems can be divided into two categories, namely, off-line and on-line systems, which have a significant difference. Dynamic signatures are too difficult to imitate and forge, even for skilled forgers [4] because they are unique and consistent for a given period. Compared with off-line signatures [5], online signatures are more robust and gain a higher level of security by monitoring dynamic features like time series of position trajectories, pressure, altitude, and azimuth. There is a tendency to recover online signatures from offline signature images [6].

Online signature verification can basically be viewed as a problem of similarity discrimination, whereby a decision must be made about whether a given online signature corresponds to the claimed identity or not. In a signature verification system, we compare the features of a test signature against those from a set of genuine signatures of an enrolled user, which can be called reference signatures

or template signatures. By stable and discriminative feature extraction and selection, there are two approaches to identify the authenticity of a signature, which can be called the function approach and the parameter approach.

Signature verification methods based on the parameter approach include the statistical classification [7,8], neural network [9], support vector machine (SVM) [10], Bayesian decision [11] and features cluster [12], where some global or local features derived from the original signature signal, e.g., average speed, pressure, the number of strokes, etc., constitute signature feature patterns or feature vectors.

The signature verification system based on a function considers each signature signal as a function of time and verifies the signer by comparing the reference signature with the test signature directly. Usually, matching procedures or special function parameter calculations are a need between signatures, requiring more time and space. The common approaches include Dynamic Time Wrapping (DTW) [13], its improved version [14–19] and the hidden Markov model (HMM) [20,21].

Bonus template matching approaches are considered, and a longest common subsequences (LCSS) combined elastic distance metrics is also used [22]. A discrete cosine transform (DCT) [23] has been applied to 44 time signals. A multi-section vector quantization (VQ) approach [24] has been suggested where all signatures are represented by vectors of the same length. Similar methods such as the Fourier description [25], wavelet packet and discrete wavelet transform (DWT) [26] have been presented too.

A function-based system utilizes all original information about the signature, and shows better performance than parameter-based systems. Nowadays, fusion for improving verification accuracy has become a promising trend, and a combination of parametric approaches and functional approaches is often adopted in literature [16–18,27].
