# Online Signature Verification Systems on a Low-Cost FPGA
## 2 Signature Verification Algorithm  
Signature biometric systems are usually based on two phases: enrollment and verification. At the enrollment phase, the system is trained for a genuine user who provides several signatures to extract a set of distinguishing features, which is stored as the user dataset. During the verification phase, a new signature is presented, and its features are extracted and matched against the previously stored one. Then, by computing a similarity score that is compared with a threshold value, the signature is classified as genuine or counterfeit.  
Most online signature verification techniques can be classified as template, statistical or structural matching [13; 14]. Template matching is a straightforward comparison of samples from the genuine user and the presented signature, which are usually pre-aligned by a DTW algorithm [15]. In statistical matching, the most salient behavioral signature features are compared and scored by means of a neural network, a hidden Markov model or a GMM (Gaussian Mixture Models). Structural matching is based on syntactic approaches for representing signatures that are compared through graph or tree techniques.  
The signature verification algorithm consists of four stages: pre-processing, DTW, extraction of features and GMM matching, as depicted in Figure 1. The initial pre-processing applies a set of transformations on the captured signature, as resampling, centering and rotating the shape, and normalization. The resulting data are a set of 256-width vectors containing normalized samples. Then, a DTW algorithm computes the optimal alignment between the time-dependent samples of the processed signature and the enrolled template.  
Finally, a set of statistical features are extracted from the aligned signature, known as pseudo-distances, to execute a GMM model that calculates a distance score.  
The dataset of an enrolled user on the implemented online signature system [16] is composed of a signature template and its GMM parameters. The signature template consists of 256-width vectors containing normalized samples (x-y coordinates, pressure, angles). A set of distinctive features from the signature are selected to generate a GMM model. The parameters of the optimal GMM model for each enrolled user are computed by the expectation-maximization (EM) algorithm [17] with a public signature database [18]. The database contains 25 genuine signatures and 25 skilled forgeries for 100 different users. Basically, the implemented algorithm is an improved version of the presented one [19] by adding dynamic features, such as speeds and accelerations, at the GMM matching.  
The algorithm performance was tested by the public database available in [18]. The DET (Detection Error Tradeoff) curve, shown in Figure 2, represents the relationship between FMR (False Match Rate) and FNMR (False Non-Match Rate) for different threshold decision values [16; 19]. The EER (Equal Error Rate) achieved by the proposed online signature algorithm is 2.74%, which is a competitive performance when compared to other biometric modalities presented in some competitions [20].