Offline Handwritten Signature Verification - Literature Review <s> Mathematical transformations <s> This paper describes an approach to the problem of signature verificzation that treats the signature as a two-dimensional image and uses the Hadamard transform of that image as a means of data reduction and feature selection. This approach does not depend on the language or alphabet used and is general enough to have applications in such areas as cloud pattern surveys, aerial reconnaisance, and human-face recognition. <s> BIB001 </s> Offline Handwritten Signature Verification - Literature Review <s> Mathematical transformations <s> In this paper, a wavelet-based off-line handwritten signature verification system is proposed. The proposed system can automatically identify useful and common features which consistently exist within different signatures of the same person and, based on these features, verify whether a signature is a forgery or not. The system starts with a closed-contour tracing algorithm. The curvature data of the traced closed contours are decomposed into multiresolutional signals using wavelet transforms. Then the zero-crossings corresponding to the curvature data are extracted as features for matching. Moreover, a statistical measurement is devised to decide systematically which closed contours and their associated frequency data of a writer are most stable and discriminating. Based on these data, the optimal threshold value which controls the accuracy of the feature extraction process is calculated. The proposed approach can be applied to both on-line and off-line signature verification systems. Experimental results show that the average success rates for English signatures and Chinese signatures are 92.57% and 93.68%, respectively. <s> BIB002 </s> Offline Handwritten Signature Verification - Literature Review <s> Mathematical transformations <s> A great deal of work has been done in the area of off-line signature verification over the past two decades. Off-line systems are of interest in scenarios where only hard copies of signatures are available, especially where a large number of documents need to be authenticated. This dissertation is inspired by, amongst other things, the potential financial benefits that the automatic clearing of cheques will have for the banking industry. The purpose of this research is to develop a novel, accurate and efficient off-line signature verification system. In this dissertation two systems are developed. The first system uses dynamic time warping (DTW) to match a test signature with an appropriate reference signature. The second system represents each writer’s signature with a hidden Markov model (HMM). Both of these systems use the discrete Radon transform (DRT) to extract a sequence of feature vectors from a signature. The HMM-based system achieves rotation invariance in an efficient and robust way. No alignment of observation sequences is required. In order to ensure rotation invariance, the DTW-based system must first align a test sequence with an appropriate reference sequence, before they are matched. As a result, the HMM-based system is computationally more efficient than the DTW-based system. Experiments are conducted on two different data sets. The systems perform almost equally well, when they are applied to the “Stellenbosch data set”. Equal error rates of approximately 18% and 4.5% respectively, are achieved when only skilled forgeries and only casual forgeries are considered. When the HMM-based system is applied to “Dolfing’s data set” of dynamic signatures, the results compare well with an algorithm by Dolfing which only considers the spatial coordinates of each dynamic signature. In this dissertation it is also demonstrated that the HMM-based system performs better than a typical human being. Existing systems utilise either a technique or features that are fundamentally very different from those used in this dissertation. This is especially the case for the HMM-based system. This implies that it is very likely that a combination of any existing system and the HMM-based system developed in this dissertation, will result in a superior merged system. <s> BIB003 </s> Offline Handwritten Signature Verification - Literature Review <s> Mathematical transformations <s> In this paper, a new offline handwritten signature identification and verification system based on Contourlet transform is proposed. Contourlet transform (CT) is used as feature extractor in proposed system. Signature image is enhanced by removing noise and then it is normalized by size. After preprocessing stage, by applying a special type of Contourlet transform on signature image, related Contourlet coefficients are computed and feature vector is created. Euclidean distance is used as classifier. One of the most important features of proposed system is its independency from signer’s nationality. Experimental results show that proposed system has so reliable results for both Persian and English signatures. <s> BIB004 </s> Offline Handwritten Signature Verification - Literature Review <s> Mathematical transformations <s> In this paper, we propose a new system for identification and verification of offline handwriting signature. The identification allows knowing the owner of such a signature, whereas the verification allows verifying the authenticity of a given signature. In recognition systems, the phase of feature extraction represents the most pertinent step. Therefore, we opted to use the fractal approach which is very sophisticated for objects with irregular forms. In this work, we have implemented three methods for calculating fractal dimensions. Experimental results have been assumed on a large database, namely, “FUM-PHSDB” showing promising result and demonstrating the effectiveness of the proposed system. These experiments show an identification rate of 95% and a verification rate of 83% <s> BIB005
Researchers have used a variety of mathematical transformations as feature extractors. Nemcek and Lin BIB001 investigated the usage of a fast Hadamart transform and spectrum analysis for feature extraction. Pourshahabi et al. BIB004 used a Contourlet transform as feature extraction, stating that it is an appropriate tool for capturing smooth contours. Coetzer et al. BIB003 used the discrete Radon transform to extract sequences of observations, for a subsequent HMM training. Deng et al BIB002 proposed a signature verification system based on the Wavelet transform: first the image is preprocessed to obtain a closed-contour of the signature. For each pixel in the contour, the coordinates (x and y), and the tangential angle are recorded. Each sequence is represented as a one-dimensional signal, and then a discrete wavelet transform is used to decompose the signal. Zouari et al BIB005 has investigate the usage of the Fractal transform for the problem. 