Research Of Off-line Signature Verification Based On Fuzzy Theory And Movement Relativity Of Images

As one of the biological features used widely in personal identity verification, signature is playing a more and more important role in our modern society. Auto-handwritten signature verification is a challenging topic in the fields of computer vision, image processing, pattern recognition, artificial intelligence and so on, and it is also studied actively and popularly during the recent years. Research on auto-hand written signature verification is indeed significant to both practical application and the development of science and technology. Up to date, research in such field has received many considerable achievements, but some critical problems are still needed to be resolved. In China, it has just begun.In general, auto-handwritten signature verification technique can be divided into two classes, on-line (or dynamic) and off-line (or static) verification. On-line verification takes place as a writer creates his signature on a digital tablet or a similar device to grab dynamic information, while off-line verification is the process of verifying a static signature which is written on white paper and collected by a digital scanner or a video camera. As opposed to the on-line case, off-line signature verification is applied in more fields. However, because of lacking any form of dynamic information during the writing process, it will be more difficult to obtain higher accuracy.There are three main difficulties in signature verification. First of all, genuine signatures are of some uncertainty. No two signatures by the same person are identical in different time or place, which results in some difficulties in classification decision making. Secondly, signatures of different writers have significant diversification, and their feature abstract becomes discord, variable and uncertain. Finally, the number of genuine samples could be insufficient and the forgeries almost absent.The objective of this paper is try to solve these three problems, by which fuzzy modeling integrated with the combined technique of feature extraction is proposed in order to deal with the first two problems. And for the last difficulty, the principle of the movement relativity of images in different coordinates of Euclidian space is presented and applied to build a model of off-line signature verification.Feature extraction and classification decision are the crucial steps of off-line signature verification, which can influence the verification performance greatly. For feature extraction, the appropriate features are our attention to reflect the characteristics of signatures and improve the classification precision. In this paper, the advantage and disadvantage of a large number of features which have been proposed are analyzed firstly. Then several different types of features depending on our verification schemes are extracted in order to obtain the maximum verification quality. These features mainly include global features, which are extracted from a whole signature image, and local features, which are extracted from each sample point. Projection profiles and Hu moments constitute our global features and local features are pixels density, angle feature, gravity center distance and predominant slant. In the whole feature subsets, pseudo-dynamic features are also involved to make up the lacked dynamic information of off-line signatures partly.The task of classification is to judge whether an input signature is a genuine signature or a forgery by comparing it with collected signature samples. As for the uncertainty of the features with insufficient genuine samples and almost absent forgeries, fuzzy modeling is one of the effective methods to deal with the problem. So we focus on building a fuzzy model with the membership function which can reflect the uncertainty of the features for one person and multiple rules for different people. Both of them are of great importance for the stability and correctness of the fuzzy model.Based on the fuzzy membership function, two new schemes of off-line signature verification are devised. The first scheme extracts projection profiles whose variation and uncertainty for the same person are described by fuzzy sets, and builds up an optimal objective function from a suitable membership function. Then dynamic matching algorithm is carried out for training and verification. In addition, the conception of the dynamic threshold decision is presented and discussed for the purpose of reducing random disturbance to verification. The decision threshold consists of two terms. One is the verification point estimated with some training samples, and the other is an offset estimated with the training samples other than those used to improve the correctness of the threshold. In the second scheme, since high frequency coefficients of Discrete Wavelet Transform(DWT) represent features that contain sharper variations in time-resolution, the reconstructed signals are the second features of the adjusted projection profiles. These features can enhance the characteristics of signatures, yet give rise to uncertainty to true signatures. So fuzzy nets are introduced to describe the uncertainty and an objective function is build up to employ verification. In the fuzzy nets, the weight coefficients are constructed using the membership function which can reflect the contribution of the enhanced features to the output.Two databases of English and Chinese signatures are applied to the experiments. The English signature database has been used by other researchers, and the Chinese signature database is created by our laboratory. We adopt false rejection rate, false acceptance rate and the average error rate to evaluate the verification performance. The final verification results of our schemes on membership functions are comparable to the other existing results based on the same English database, whereas our extracted projection profiles are simple and the computational complexity of the proposed schemes is low.The other research work stresses on fuzzy rules which aim at much flexibly dealing with the feature variation of signatures for different people. In contrast to the existing fuzzy model of a single rule, a new verification system based on fuzzy modeling of multiple rules and feature selection are proposed. In this system, the uncertainty of extracted features is described by fuzzy sets and the membership functions are devised to reflect the contribution of different fuzzy rules to verification results. Furthermore, the optimal selecting of multiple rules by the reliable estimate of K-fold cross-validation is introduced to reduce the computational complexity of the entire fuzzy system and improve the verification performance, whose results are better than that of the exisiting fuzzy model of a single rule and the fuzzy model of multiple unoptimizable rules. In the feature selection process, a new selection criterion is proposed based on discriminative measure that can avoid the singular of the covariance matrix. The singular exists when using the selection criterion based on probability density and the number of training signatures is less than or equal to the feature vector dimension. In the end, two types of experiments are performed. The former one without feature selection obtains the average error rates of 11.56% for Chinese database and 12.48% for English database respectively. Unlike the former one, the latter involves fuzzy modeling of a single rule and feature selection, where the training and verification phases are similar to the former one. The average error rates of 9.35% and 10.51% are obtained approximately and about 3% is reduced when compared with the other existing results on the same English signature database, which indicates that our proposed fuzzy model is better than the traditional classifiers in verification performance.In order to solve the difficult problem of the very small number of training samples in off-line signature verification, a new scheme based on the movement relativity of images in different coordinates of Euclidian space is proposed. On modeling off-line signature verification with our presented lemma, the feasibility of this new scheme is firstly evaluated. In the scheme, we can distribute the verification sample and the reference sample into different coordinates and four cases are discussed. Due to the fact that the movement relativity should be smaller or larger when a verification sample is compared to reference samples, an objective function is built up and can be transformed into the optimization problem with restrictions. Experimental results show that this verification system is effective. Also the model is of wide practicability, and it can be extended to the fields of fingerprint identification, face recognition and so on.