Legendre polynomials based feature extraction for online signature verification. Consistency analysis of feature combinations
Introduction
Automatic signature verification has long been considered an important research area in the field of biometrics [1], [2], [3], [4]. Signature verification is the most popular method for identity verification. Signatures are recognized as a legal means of verifying an individual's identity by financial and administrative institutions. In addition, it is a non-invasive biometric technique, and people are familiar with the use of signatures for identity verification in their everyday life.
Two categories of signature verification systems can be distinguished taking into account the acquisition device, namely, offline and online systems. For offline verification systems, only the image of the signature is available, while for online systems, dynamic information acquired during the signing process, such as x and y pen coordinates and pen pressure, is available. The interest in the online approach for signature verification has increased in recent years due to the widespread use of electronic pen-input devices, such as digitizer tablets and PDAs. In addition, it would be reasonable to expect that the incorporation of dynamic information acquired during the signing process would make signatures more difficult to forge and, in this way, the online verification systems more reliable than the offline ones.
In online systems, the signature is parameterized by several discrete time functions, e.g., pen coordinates, pen pressure and, when available, pen inclination angles. Researchers have long argued about the effectiveness of these different time functions for verification purposes. During the First International Signature Verification Competition (SVC2004), the results using only pen coordinates outperformed those adding pen pressure and pen inclination angles [5]. Since then, several works have been presented concerning the best set of features to model the signatures. In [6], the authors state that using only pen coordinates leads to better results than incorporating the pen pressure. The time variability between training and testing data acquisition sessions is considered in [7], where it is concluded that pen pressure is the most unreliable feature, pen inclination angles are too unstable, and pen coordinates are the most robust time functions in the presence of a long term time variability. On the other hand, some works show improvements when combining pen coordinates with pen pressure and inclination angles [8]. The conflicting results observed in the literature make the discussion still open. In a preliminary work by the present authors [9], some feature combinations based on the pen coordinates and the pen pressure, are studied. The conclusions in [9] are in line with the idea that combining pen coordinates with the pen pressure leads to a verification performance improvement.
A desirable property for any feature is to have high consistency in the sense that the feature values of the genuine signatures should be close to each other while the ones of genuine and forged signatures should be not. A well defined consistency model would allow to quantify the discriminative power of the features and to predict their effectiveness for verification purposes. A consistency model was first introduced in [10], [11]. In [10], the consistency model is used to select an optimal subset of global features from a larger global feature set. In [11], several local and global features are compared on the basis of their consistency, resulting pen coordinates and some derived features the most reliable ones. The lack of a widely used consistency model in the literature, makes its study an interesting issue. In [9], a new consistency factor is introduced. The proposed feature combinations are compared based on their consistency factor values, being the feature combinations containing the pen pressure the most reliable ones.
An important factor that deserves more investigation is the influence of the cultural origin of the signatures in the performance of the verification systems. To the best of the authors’ knowledge, there are not many works in the literature that consider non-Western signatures such as Chinese, Japanese, Arabic, etc. In [12], an updated survey of non-English and non-Latin signature verification systems can be found. Non-Western signatures do have different shapes and the writing style is different to the Western one. For instance, the Chinese handwriting style consists of one or more multi-trace characters, most of them being phono-semantic compounds, composed by two parts: the radical, which is often a simplified pictograph and suggests the character's general meaning and a phonetic indicator. Originally, Chinese pictographs conveyed their meaning through pictorial resemblance to a physical object. Although in modern Chinese this resemblance is no longer clear, Chinese characters are still pictorial symbols. Among the literature of non-Western signature verification, more attention has been given to Chinese signatures than to Japanese, Arabic, Persian or Indian signatures. Offline [13], [14], as well as online [15] verification systems have been presented in the literature for Chinese signature verification. Further, the Signature Verification Competition for Online and Offline Skilled Forgeries (SigComp2011) held within ICDAR 2011 [16], introduced a new Database containing Chinese signatures, encouraging the researches to work on this type of data. On the other hand, Japanese and Arabic signatures, among others, have not been investigated so much. Japanese signatures consist of different component characters spaced from each other. There is not much work done on this type of data [17], [18], and it is mostly focused in offline data. Arabic script is written from right to left in a cursive style. Although a lot of research has been carried out on Arabic handwriting recognition, not much work has been carried out on Arabic signature verification. In [19], an offline verification system for Arabic signatures is presented. For a verification system to have a widespread acceptance it should take into account these different writing styles. As pointed out in [12], there are still many challenges in this research area.
In this paper, the coefficients in the Legendre series approximations of the time functions associated with the signatures are used as features to model them. The time functions considered in this paper are the pen coordinates, pressure, velocities and acceleration, as well as the log curvature radius, which are the most commonly used functions in the literature for online signature verification [20], [21]. A consistency factor is proposed to quantify the discriminative power of different combinations of the time functions related to the signing process. Two different signature styles are considered, namely, Western and Chinese, of a publicly available Signature Database. Two state-of-the-art classifiers, namely, Support Vector Machines (SVMs) and Random Forests (RFs), are used to perform the verification experiments.
This approach of representing the time functions using Legendre polynomials was first introduced by the present authors in the conference paper [9]. Only few feature combinations were studied there, and a qualitative study of the consistency of the feature combinations was performed. In the present paper, more time functions are considered and a thorough analysis of all the possible feature combinations is carried out. In addition, a quantitative study correlating the consistency factor with the verification errors is performed.
The main contributions of this paper are the following:
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A feature extraction approach based on Legendre series representation of the time functions associated with the signatures is proposed. To the best of the authors’ knowledge this is the first time that this approach is used in the context of signature verification.
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A consistency factor is proposed to quantify the discriminative power of different combinations of the time functions associated with the signing process. A thorough study of all the possible feature combinations is carried out, and the pros and cons of these different combinations are analyzed.
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A quantitative study of the relationship between the proposed consistency factor and the verification performance of a feature combination is performed based on correlation analysis.
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The experiments are performed on one of the most recent signature datasets, containing Western and Chinese signatures, which have been used in one of the latest signature verification competitions. To quantify the verification performance, the EER (Equal Error Rate) and the cost of the log-likelihood ratios are reported.
The paper is organized as follows. The feature extraction approach is described in Section 2. In Section 3 the proposed consistency model is introduced. In Section 4 the Database is described. Section 5 is devoted to the description of the experiments, in particular, 5.1 Consistency computation, 5.2 Verification performance evaluation focus on the consistency computation and the verification experiments, respectively. In Section 6 the results are presented and discussed. Finally, some concluding remarks are given in Section 7.
Section snippets
Feature extraction
Several methods have been proposed in the literature for online signature verification. They differ basically in the way they perform the feature extraction and in the classification approach they employ. The different features can be classified into local features, calculated for each point in the time sequence, and global features, calculated from the whole signature. Many researchers accept that approaches based on local features achieve better performance than the ones based on global
Consistency measure
An important property of a feature is its discriminative capability. Features associated with genuine signatures should be close to each other while distances between features associated with genuine and forged signatures should be relatively large. This property is usually called consistency of the feature.
A measure of consistency based on the features would be difficult to compute since they may have different lengths. It is then more reasonable to define a consistency measure based on the
Signature database
The publicly available SigComp2011 Dataset [31] presented within ICDAR 2011 is used. It has two separate datasets, one containing genuine and forged Western signatures (Dutch ones) and the other one containing genuine and forged Chinese signatures. The available forgeries are skilled forgeries, which are simulated signatures in which forgers (different signers than the reference one) are allowed to practice the reference signature for as long as they deem it necessary. Fig. 3(a) and (b) shows
Evaluation protocol
In [11], the most common time functions were individually compared based on a consistency model. In this paper, the consistency factor introduced in (13) is used to evaluate the discriminative capability of the feature vectors composed by the Legendre polynomial coefficients associated with all possible combinations of the considered time functions (x, y, p, vx, vy, aT, ).
The correlation between the consistency factor and the corresponding verification error for each feature combination is
Results and discussion
For the sake of compactness of the notation, the different combinations of the considered time functions (x, y, p, vx, vy, aT, ), are coded as indicated in Table 3. Note the reader that whenever the x coordinate is considered, also the y coordinate is included in the combination, since no preferential direction would be expected to exist a priori. The same holds for the x and y velocities.
Conclusions
All the possible feature combinations associated with the most commonly used time functions related to the signing process were analyzed, in order to provide some insight on their actual discriminative power for online signature verification. A consistency factor was defined to quantify the discriminative power of these different feature combinations. A fixed-length representation, based on Legendre polynomials series expansions, was used to represent the time functions associated with the
Conflict of interest
None declared.
Marianela Parodi graduated as Electronic Engineer at the National University of Rosario (UNR), Argentina, in 2009, ranking at the top of her class. She is currently a Engineering Ph.D. Student at the same University, working on Automatic Signature Verification, supported by a Scholarship from CONICET (National Research Council). She is also part time teaching assistant at the UNR.
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Marianela Parodi graduated as Electronic Engineer at the National University of Rosario (UNR), Argentina, in 2009, ranking at the top of her class. She is currently a Engineering Ph.D. Student at the same University, working on Automatic Signature Verification, supported by a Scholarship from CONICET (National Research Council). She is also part time teaching assistant at the UNR.
Juan C. Gómez has an Electronic Engineering degree from the National University of Rosario, Argentina (1983), and a Ph.D. in E&CE from the University of Newcastle, Australia (1998). He is Professor at the UNR and Director of the Laboratory for System Dynamics and Signal Processing. His research interests are in the areas of Multimedia Signal Processing, Pattern Recognition and System Identification.