Handwritten Signature Verification by Multiple Reference Sets D. Impedovo(^)(§), R. Modugno(*)(§),G. Pirlo(*)(§) , E. Stasolla(*) (§) (*)
Dipartimento di Informatica – Università degli Studi di Bari – Via Orabona 4–Bari – Italy Dipartimento di Elettrotecnica ed Elettronica–Politecnico di Bari – Via Orabona 4–Bari – Italy (§) Centro “Rete Puglia” - Università degli Studi di Bari – Via G. Petroni 15/F.1–Bari – Italy
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[email protected]} Abstract This paper presents a new approach for on-line handwritten signature verification, which exploits the potential of multiple reference sets. Preliminarily, system performance is estimated using different sets of reference signatures for each writer. Successively, reference sets leading to diverse system behaviors are enrolled into the personal knowledge-base and used in a multi-stage verification process. The experimental results show the effectiveness of the proposed approach, compared to traditional techniques. Keywords: Biometry, Classification, Dynamic Signature, Signature Verification, Multi-expert system.
1. Introduction The development of the e-society is strongly dependent on the possibility to fully exploit potentials of internetworking. In other words it is necessary for more and more people to use the net for performing all the daily activities and operations, such as teamwork cooperation and distance learning, banking transactions and fund transfers, access to information resources, etc. Therefore there is a growing need for secure personal verification. Automatic personal verification systems can be categorized on the basis of the means they use for personal verification: physical mechanisms belonging to the individual (i.e. key or badge), information (i.e. password, numeric string, key-phrase) and biometric characteristics (i.e. speech, finger-print, palm-print, signature) [1, 2, 3]. Compared to personal verification systems based on physical mechanisms and information, the main advantage of biometric systems is that biometric characteristics cannot be lost, stolen or forgotten [4, 5]. Furthermore, among the various biometrics, handwritten signature verification has the advantage that signature has long been established as one of the widespread means for personal verification in our daily life; it is well-recognized by legal and financial institutions and well-accepted by users [1,4,6,7]. Therefore, the field of signature verification has attracted many researchers which are interested not only to the scientific challenges but also to the
valuable applications this field offers [8, 9]. Several excellent survey papers report the progress in the field of automatic signature verification [10, 11, 12, 13, 14, 15]. Recently, the extraordinary growth of the internet has augmented the interest toward automatic signature verification, as demonstrated by the creation of specific laws and regulations, approved in many countries and the attention to the standardization of signature data interchange formats by various important associations and institutes [16, 17, 18]. Therefore, along with these important results, signature verification technologies are becoming much more profitable solutions for a wide range of commercial applications such as banking, insurance, health care, ID-security, document management, e-commerce and retail point-of-sale (POS) [19, 20, 21, 22, 23]. However, many efforts are still necessary to perform automatic signature verification effectively. In fact, automatic signature verification is a complex task that involves many biophysical and psychological aspects related to human behavior as well as many engineering issues [24, 25, 26, 27, 28, 29]. A handwritten signature is the result of a complex process based on a sequence of actions stored into the brain and realized by the writing system of the signer (arms and hands) through ballistic-like movements. Thus, signatures of the same person can considerably differ depending on the physical and psychological condition of the writer. Two types of variability must be considered [9, 10]: short–period and long-period variability. Short-period variability is evident on a day-to-day basis, it is mainly due to the psychological condition of the writer and on the writing conditions (posture of the writer, type of pen and paper, size of the writing area, etc.). Longperiod variability is due to the modifications of the physical writing system of the signer as well as of the sequence of actions stored in his/her brain [10, 11]. So far, many efforts have been devoted to automatic signature verification systems using different function-based and parameter-based features as well as advanced techniques for signature comparison [9, 10, 13, 14, 15]. Anyway, whatever feature set and comparison technique is considered, the performance of signature verification systems is strictly dependent on the type and quality of information
used for reference and on the way in which it is organized and exploited for verification. So far, two different strategies have been addressed for reference information construction and management [30]. A first strategy uses a single prototype of genuine signatures for each writer, and several techniques have been proposed for the development of the optimal average prototype for a signer and for determining the optimal threshold representing the personal variability in signing, by shape and dynamic feature combination [30], time- and position-based averaging [31]. A second strategy uses a set of genuine signatures for reference. In this case a crucial problem concerns the selection, among the samples available, of the optimal subset of reference signatures that represents the signature of an individual in the best way. In fact, it is worth noting that the number of authentic signatures, acquired during the enrolment phase, is generally larger than the number of reference signatures employed in the verification process. When static signature verification is considered, the validity of the reference model is evaluated according to specific quality criterion, as for instance the intra-class variability that should be as low as possible [32, 33]. In dynamic signature verification, the selection of the best sub-set of reference signature has been determined on the basis of the stability regions in the signatures of the sub-set, determined by a well-defined index of local stability [34, 35, 36]. Of course, the selection of the best subset of reference signature can be avoided at the cost of using multiple models for signature verification [37, 38, 39], also by considering synthetic signatures generated from the existing ones by convolutions [40], elastic matching [41] and perturbations [42]. This paper presents a new approach for on-line handwritten signature verification, which exploits potential of multiple reference sets leading to diverse system behaviors. In a preliminary phase, system performance is estimated using different subsets of reference signatures extracted from the available set of authentic signatures. Subsets leading to diverse system behavior – estimated by means of well-suited optimality functions - are considered for reference and used in a multi-stage verification process. The experimental result shows the potential of the proposed approach with respect to traditional strategies for reference information selection.
2. Analysis of Reference Sets In this paper the analysis of different sets of genuine signatures is performed on the basis of their effectiveness, when used as reference. The process of signature verification can be considered as a function D(•), that associates a Boolean value to each input signature Si: D(Si)=“G” if the signature is considered to be genuine; D(Si)=“F” if the signature is considered to be a forgery. Of course, the signature verification process can produce two types of errors: the Type I errors - that concern with the false rejection of genuine signatures, and the Type II errors that concern with the false acceptance of forged signatures.
Therefore, the False Rejection Rate (FRR) and the False Acceptance Rate (FAR) are the most diffuse estimators of the accuracy of a signature verification system [9, 10]. In many practical applications a trade-off between the two error types must be defined since any reduction of FAR increases FRR, and vice-versa. For this purpose the Total Error Rate (TER), that is defined as FRR+FAR, is also widely considered as a measure of the overall error of the system [42]. Now, let Sr : { Sri | i=1,2,…,Nr} be the set of genuine signatures available for reference and let us consider the problem concerning with the selection of the best subset of k reference signatures Sr,k, from Sr. Traditionally, this can be done by the analysis of the subset Sr,kTER for which the TER is minimum (see Figure 1) [42]. In other word let Sg = { Sgi | i=1,2,…,Ng} and Sf = { Sfi | i=1,2,…,Nf} be respectively a set of genuine and forgery signatures, the set Sr,kTER is considered as the set for which it is minimum the function OTER(Sr,k) = ( FRRr,k + FARr,k )
(1)
where:
FAR r ,k
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1 ⋅ card S ig D S ig = F , (2) g N 1 = f ⋅ card S i f D S i f = G . (3) N
FRR r ,k =
Obviously, when Sr,kTER is considered, the function D TER(•), that associates to each input signature Si a Boolean value, can be rewritten as: Dr,kTER(Si)=“G” if the signature is considered to be genuine; Dr,kTER(Si)=“F” if the signature is considered to be a forgery. r,k
In this paper, starting from the consideration that the characteristics of different subsets can be exploited to improve the overall verification accuracy, a two-level verification strategy is considered (see Figure 2). At the first level the following subsets are considered: ¾ Sr,kFRR: the subset for which it is minimum the value of the optimality function OFRR(Sr,k) = αFRR•FRRr,k + βFRR •FARr,k ,
(4)
where αFRR and βFRR weight the cost of False Rejection Errors and False Acceptance Errors (in this case αFRR>> βFRR ). In this case the function Dr,kFRR (•), that associates to each input signature Si a Boolean value can be rewritten as: Dr,kFRR(Si)=“G” if the signature is considered to be genuine; Dr,kFRR(Si)=“F” if the signature is considered to be a forgery.
¾ Sr,kFAR: the subset for which it is minimum the value of the optimality function OFAR(Sr,k) = αFAR• FRRr,k + βFAR • FARr,k ,
(5)
where αFAR and βFAR weight the cost of False Rejection Errors and False Acceptance Errors (in this case αFAR
