Classification and Verification of Online Handwritten Signatures with Time Causal Information Theory Quantifiers
Venue: ArXiv

We present a new approach for online handwritten signature classification and verification based on descriptors stemming from Information Theory. The proposal uses the Shannon Entropy, the Statistical Complexity, and the Fisher Information evaluated over the Bandt and Pompe symbolization of the horizontal and vertical coordinates of signatures. These six features are easy and fast to compute, and they are the input to an One Class Support Vector Machine classifier. The results produced surpass state of the art techniques that employ higher dimensional feature spaces which often require specialized software and hardware. We assess the consistency of our proposal with respect to the size of the training sample, and we also use it to classify the signatures into meaningful groups.  The word biometrics is associated to human traits or behaviors which can be measured and used for individual recognition. In fact, the biometry recognition, as a personal authentication signal processing, can be used in applications where users need to be security identified.1 Clearly, these kind of systems can either verify or identify. Two types of biometrics can be defined according to the personal traits considered: physical/physiological or behavioral. Physical/physiological biometrics is about catering the biological traits of users, like fingerprints, iris, face, hand, etc. Behavioral biometrics takes into account dynamic traits of users, such as, voice, handwritten and signature expressions. One of the main advantages of biometric systems is that users do not have to remember passwords or carry access keys. Another important advantage lies in the difficulty to steal, imitate or generate genuine biometric data, leading to enhanced security.1 As mentioned, behavioral biometrics is based on measurements extracted from an activity performed by the user, in conscious or unconscious way, that are inherent to his/her own personality or learned behavior. In this aspect, behavioral biometrics has interesting pros, like user acceptance and cancelability, but it still lacks of some level of the uniqueness physiological biometrics has. Among the pure behavioral biometric traits, the handwritten signature and the way we sign is the one with widest social and legal  6 Identity verification by signature analysis requires no invasive measurements and people are familiar with the use of signatures in their daily life. Also, it is the modality confronted with the highest level of attacks. A signature is a handwritten depiction of someone's name or some other mark of identification written on documents and devices as proof of identification. The formation of signature varies from person to person, or even from the same person due to the psychophysical state of the signer and the conditions under which the signature apposition process occurs. Hilton7 studied how signatures are produced, and found that the signature has at least three attributes: form, movement and variation; being movement the most important, because signatures are produced by moving a writing device. The study also noted that a person's signature does evolve over time and, with the vast majority of users, once the signature style has been established the modifications are usually slight. The movement is produced by muscles of fingers, hand, wrist, and in some writers the arm; these muscles are controlled by nerve impulses. When one person is signing these nerve impulses are controlled by the brain without any particular attention to detail. The signing processes can be described then, at high level, as how the central nervous system (the brain) recovers information from long term memory in which parameters such as size, shape, timing etc. are specified. At the peripheral level, commands are generated for muscles. In consequence, the signing process is believed to be a reflex action (ballistic action8) rather than a deliberate action. Then, the production of genuine signatures is associated to a ballistic handwriting, which is characterized by a spurt of activity, without positional feedback, whereas the production of forgery signature is associated to a deliberate handwriting which is characterized by a conscious attempt to produce a visual pattern with the aid of positional feedback.9, 10 Handwritten signature verification is a problem in which the input signature (a test signature) is classified as genuine or forged. This process is usually performed in three main phases:2 6 Data acquisition and pre processing. Two different categories of systems can be identified, depending on whether there is electronic access to the handwritten process or not. a) Online or dynamic recognition, in which the pen's instantaneous information trajectories, and also information like pressure, speed or pen up movements can be captured. b) Offline or static recognition: those that record signatures as images on paper which can be later digitized by means of a scanner, and processed. In the latter, the pre processing phase involves filtering, noise reduction and smoothing. Online signature verification offers reliable identity protection, as it employs dynamic information not available on the signature image itself but in the process of signing. As a consequence, online signature verification systems usually achieve better accuracy than offline systems. Feature extraction. Two types of features can be used. a) Function features of the signature: time functions whose values constitute the feature set. b) Parameter features: the signature is characterized as a vector of elements, each one representative of the value of the feature. Usually, the last one yields better performance, but it is also time consuming.  In the verification process, the authenticity of the test signature is evaluated by matching it against those stored in the knowledge base developed during the enrollment stage. This process produces a single response that attests to the authenticity of the test signature. When template matching techniques are considered, a questioned sample is matched against templates of authentic/forgery signatures. Distance based classifiers, mostly when parameters are used as features, are usually developed with statistical techniques, e.g. with Mahalanobis and Euclidean distances. The performance of a signature verification system is commonly assessed in terms of the percentage Equal Error Rate. On the one hand, template matching attempts at finding similarities between the input signature and those in a data base. Most approaches use Dynamic Time Warping to perform this match.5, 6 On the other hand, distance based classifiers rely on the use of features derived from the signatures. Two opposite mechanisms describing the signing process can be found in the literature. The nonlinear character and chaotic behavior of several physiological complex processes are well established.11, 12 In particular, Longstaff and Heath13 found evidence of chaotic behavior on the underlying dynamics of time series related to velocity profiles of handwritten texts. Taking into account the inherent behavioral nature of the online signing process, the input information could be associated to deterministic (nonlinear low dimensional chaotic) signals, and the handwritten signature variations as a consequence of chaos (sensibility to initial conditions) In opposition, most of the research in the field of signal verification considers the input information as well described by a random process.2 6 Then, the dynamic input information acquired through a time sampling procedure must be consequently considered as discrete time random sequence. In any case, the signature analysis taken as a time based sequence characterization process is strongly related to the way in which a reference model is established. From the stochastic point of view, Hidden Markov Models are among the most commonly used in the literature, and the ones with the best performance in signature verification.2 6 Our proposal relies on the use of time causal quantifiers based on Information Theory for the characterization of online handwritten signatures: normalized permutation Shannon entropy, permutation statistical complexity and permutation Fisher information measure. These quantifiers have proved to be useful in the identification of chaotic and stochastic dynamics throughout the associated time series.14, 15 Their evaluation is simple and fast, making them apt for the signature verification problem. We apply our proposal to the well know MCYT online signature data base.16 Next section describes the database used in this study, followed by a section where we detail the quantifiers employed and by their application to the data. In addition to the usual data flow, we present an exploratory data analysis (EDA) of the features that enhances their appropriateness for this problem. The expressiveness and usefulness of these descriptors for the problem of online signature classification and verification follows in the sequence: we experiment their application to the test bed.