AbstractâSignature verification has been widely applied in financial and legal transactions for authentication and has attracted much attention in the academia ...
The 2014 7th International Congress on Image and Signal Processing
Reliable Offline Signature Verification with Cascade Classifier Ensemble Chen Wang
Bailing Zhang
School of Business Xi’an Jiaotong-Liverpool University Suzhou, 215123, China
Department of Computer Science and Software Engineering Xi’an Jiaotong-Liverpool University Suzhou, 215123, China
Abstract—Signature verification has been widely applied in financial and legal transactions for authentication and has attracted much attention in the academia and industries. In this paper, a two-stage cascade verification system is proposed to minimize the cost of wrong verifications. In the first stage, an improved local mean K-Nearest Neighbor is applied with two reliable parameters to measure the confidence level of the judgment for a testing sample. At the second stage, a multiple expert system is formed with Random Subspace method and the reliability of decisions is evaluated by majority voting. With a testing sample, the first stage classifier will make an evaluation about the confidence level of the verification. If it is reliable enough, the result will be final; otherwise, the sample is rejected by the first stage and passed on to the second for further assessment. In this case, the final result will be the outcome of the second stage when the result has been accepted. Otherwise, this testing sample will be rejected by the whole system. Comparing to a single classifier, the cascade system can reduce the rejection rate with a slight sacrifice of accuracy. The performance of the cascade model is evaluated in terms of the trade-off between the classification accuracy and rejection rate, and the results confirm its effectiveness.
I.
INTRODUCTION
Research on handwritten signature verification has been an important topic in the area of personal authentication. Due to its relatively high reliability and convenience, signatures play an indispensable role in many authentication issues and signature verification has been applied in many fields such as financial and legal transactions. Via analysis of a handwritten signature, the computer program will draw a conclusion about whether if the signature is written by a specific person. Normally, the signature verification problems can be classified into two types: on-line and off-line. On-line systems make use of plenty of dynamic information about the signature, such as time, speed and pressure, which can be easily captured from many mobile signature devices. As for off-line systems, images of handwritten signatures are acquired through scanners or cameras after the handwritings have been finished. In other words, a signature sample is obtained as an image in off-line systems [1 -2]. In comparison to on-line systems, the off-line signature does not provide the dynamic features which are recorded in real time during the process of writing. On-line signature verification systems have been more thoroughly investigated and successfully applied [3]. In practice, the off-
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line signature verification is more challenging due to its absence of additional dynamic features. As a decision-making process, signature verification means that the system can distinguish between genuine and counterfeit signatures by measuring the differences between them. In general, forgery samples can be categorized into random forgery (unprofessional), simple forgery (unprofessional) and skilled forgery (professional). In random forgery, a fake signature is produced without any knowledge of the genuine version. In simple forgery, forgers merely know the name. When comparing with random and simple forgeries, the skilled forgery is closely imitated by forgers who has seen the genuine signature and has had sufficient time to practice. It is obvious that the skilled forgery causes more difficulties during the verification process. Unfortunately, much of previous studies focused on random and simple forgeries [4-5]. In many conventional approaches, signature verification is a typical two-class classification problem involving true and false situations. Initially, the proper type of image features is extracted from the original image in order to render the process more efficient. After that, a testing sample is compared with the samples in the training set and a similarity will be generated according to specific measurement methods. Then the system can make a judgment about which class the test sample belongs to. There are different types of classifiers that can be constructed to implement the above procedure. For instance, support vector machine (SVM), k-nearest neighbor (KNN), Fisher linear discriminant (FLD) and multi-layer perception (MLP) are all well performed in signature verification problem [6]. However, a significant issue arises: is it reasonable to classify any sample into either of two classes? Despite the many progresses that have been made in the field of offline signature verification and the improvement in the accuracy of classification, the applicability of conventional approaches is not quite appropriate in certain situations. Even with extremely low confidence levels, the classifier may still classify a sample into one of the two classes, i.e., true or false. In reality, this behavior can result in serious consequences. To solve this problem, a reject option for classification when the confidence of decision is lower than an acceptable threshold will be quite useful. In other words, specific thresholds can be predefined in the classification algorithm, and once the confidence level is inferior to the defined level the program
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will reject to make a decision. Therefore, the reliability of the verification is improved greatly. This paper aims to develop a new high pperformance and reliable classification approach to deal with sspecial occasions. Based on this, an improved local-mean based nearest neighbor classifier with a reject option is introduced. When a testing sample is inputted into the model, K nearest nneighbors will be selected from each class in our algorithm annd then different classes are reconstructed. A new method to measure the distance between a testing instance and each cclass is applied to improve the accuracy of classification. In adddition, reliability parameters are also used to implement the rejection option which is treated as an extra output from classsifier. Thereafter, users can predefine a desired accuracy rate and dispose the rejected instances with further judgment. Figure 2. A schematic illustrattion of PHOG feature
II.
MODEL DESCRIPTION
A. Feature Extraction (PHOG) The extraction of suitable features from ann image sample to represent the whole image is a crucial step in off-line signature verification. One of the efficient solutions iis to exploit the distribution of edges to represent an image. D Dalal and Triggs raised such a method of feature extraction, naamed Histograms of Oriented Gradients (HOG) [7]. The graadient images of horizontal and vertical direction are illustrated in Fig. 1.
S B. The First Stage of the Cascade System The k-Nearest neighbor (KN NN), as a non-parametric method, is one of the most comm mon algorithms in machine learning and pattern recognition. Mitani M and Hamamoto have proposed a local mean-based nonp parametric classifier which performs quite well in small sample size problems [9]. A training sample set ୧ ൌ ൛ ୧୨ ห ൌ ͳǡ ǥ ǡ ୧ ൟ from or the number of training class ɘ୧ is given and ୧ stands fo samples fromɘ୧ . In this local meean-based KNN method, a testing sample X is assigned to the class ɘୡ through the following steps [9]: Step 1: Select ɀ nearest training samples around X for each class ɘ୧ according to the Euclidean n distance, where the value of r must range from 1 to୧. m vector ɀ୧ is computed Step 2: For each classɘ୧ , a mean ୧ ୧ ୧ from ɀ nearest samplesሼ ୩భ ǡ ୩మ ǡ ǥ ǡ ୩ಋ ሽ:
Figure 1. Signature sample and gradient iimages
Nevertheless, HOG method does noot consider the difference between spatial scales which have ssignificant effects on the classification. As an enhanced m method, Pyramid Histogram of Oriented Gradients (PHOG) is actually a combination of many levels of HOG. The purpose of the PHOG is to take the spatial properties lackiing in HOG into consideration. “Pyramid” refers to the fact thaat the space of an image will be divided and the divisions in eveery axis direction will be doubled when the level increases each ttime. Following the works of Bosch et al. [8], we define the number of levels L as 3 in the implementationn. When L=0, the image is not divided and the whole image can be viewed as one =1, the image is cell with the dimensionality of 8; when L= divided into 4 cells to compute the HOG and the dimensionality is 4*8=32; When L=2, the imagge is divided into 16 cells and the dimensionality is 16*8=128. The dimensionality of the complete feature of onee signature image is 8+32+128=168.
ଵ
ݕ ൌ σୀ ୀଵ ܺೕ
(1)
Step 3: Classify X into class ɘୡ when ୧ ሺ െ ୧ ሻ ሺ െ ୧ ሻ ሺ െ ୡ ሻ ሺ െ ୡ ሻ ൌ
(2)
The local mean-based KNN method m has an outstanding performance on classification when n compared to the primitive KNN method. However, there is i still room for further enhancement of this algorithm. Zhaang and Pan [10] introduced an improved version of local mean-based classifier and applied it on automatic vehicle recognition. In this method, the second step in local mean-based KNN is redefined. Instead of calculating the mean value of severral vectors in each class, an appropriate weight value is supposeed to be selected to compute the mean vector of each class baased on the distance from testing samples to each single nearest neighbors. Such a weight value can play a pivotal role as a diistinguishable indicator and offers an estimated posterior probability.
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Based on the local mean-based KNN, an improved algorithm was proposed by the second author in [10], with details as follows: Step 1: As similar with the first step in local mean-based KNN, ɀ nearest samples ቄ ୧୩భ ǡ ୧୩మ ǡ ǥ ǡ ୧୩ಋ ቅ are chosen from each class ɘ୧ according to Euclidean distance. Step 2: For each neighbor in step 1, a coefficient or membershipρ୧୩ , is defined for the testing instance X by using normalized radial basis functions with the center of nearest training samples such as ୧୩ಋ . In addition another parameter ɐ୧ is the width of Gaussian defined for ɘ୧ and it is normally a small number. ȝik =
ȁȁషౡ ȁȁ2 ሻ మಚమ ȁȁషౢ ȁȁ2 ౡಋ σౢసభ expሺሻ మಚమ
expሺ-
ǡ ൌ ͳǡ ǥ ǡ ஓ ǡ ൌ ͳǡ ǥ ǡ ɘ୧ Ǥ
(3)
Step 3: After obtaining the coefficient ρ୧୩ for each nearest neighbors, the process of reconstruction should be conducted. Actually this step redefines the procedure of calculating the mean vector in the second step of local mean-based KNN. The reconstructed pattern ୧ can be computed as following. ୧ ൌ
ౡ
౨ ρ ଡ଼ σౡసభ ౡ ౡ ౡ
౨ ρ σౢసభ ౢ
ǡ ൌ ͳǡ ǥ ǡ ɘ୧ Ǥ
(4)
In the above equation, the reconstructed pattern ୩୧ can be treated as a unified representative of the nearest neighbors of classɘ୧ . Step 4: This step will give a result of classification through comparing the distance between the delegates of classes ୩୧ of each class ୧ and the testing instance X. The X will be assigned to ɘୡ if ሺ െ ୡ ሻ ሺ െ ୡ ሻ ൌ ୧ ሺ െ ୧ ሻ ሺ െ ୧ ሻ
Figure 3. Two cases of unreliable classification: (a) The testing samples are dramatically far away from the training sets; (b) the testing samples are lying on the classification boundary.
For signature verification, the classification is a typical type of two-class issue. Thus, there are only two outputs of distance in total in this case and we defined them as ୵୧୬ andଶ୵୧୬ . For୵୧୬ , it stands for the distance between testing sample X and the reference sample with the shortest distance, and ଶ୵୧୬ stands for the second smallest distance. It is obvious that the two reliability parameters in two-class classification problems are same because the variable ୫ୟ୶ does not even exist or we can say the variable ୫ୟ୶ equals toଶ୵୧୬ , and therefore the only one reliability parameter in our method is defined as: ɗൌͳെ
౭ మ౭
(9)
According to this parameter, the classifier is able to reject a sample based on its confidence level. A general process of the first stage is illustrated in Fig. 4.
(5)
Let us indicate the definition of the reliability parameters: ɗୟ ൌ ͳ െ
౭ ౣ౮
(6)
Where ୫ୟ୶ is the highest one among the distance gained from the comparison between the testing samples and each training class. As for the other parameter ɗୠ , it is used to judge the similarity between the two most possible results. Obviously, this parameter is determined by two variables: ୵୧୬ andଶ୵୧୬ , where ଶ୵୧୬ is the smallest distance besides ୵୧୬ . ɗୠ ൌ ͳ െ
౭ మ౭
(7)
The classification reliability for the classifier is therefore represented by ɗ ൌ ሼɗୟ ǡ ɗୠ ሽ
(8)
Figure 4. The classification schema for the first stage of cascade system
C. The Second Stage of the Cascade System To design a cascade signature verification system, another classification algorithm is required at the second stage of the system. In our system Support Vector Machine (SVM) is chosen as the main classifier for the second stage of the cascade system. Given the situation of two classes, the SVM method attempts to find the optimal hyperplane which can separate the samples into two classes as much as possible. A linear separation can be done by such classification decision function:
641
ൌ ሺ ȉ ሻ
(10)
And the empirical risks can be minimized aas follows: ଵ
ൌ σ୪୧ୀଵȁሺ୧ ሻ െ ୧ ȁǡ୧ ൌ ሼെͳ ͳǡ ͳሽ ୪
(11)
where l stands for the size of examples. The largest margin of separation betweeen two classes decides the optimal hyperplane under the princciple of structural risk minimization [11]: Minimize:
ଵ ଶ
Subject to: ୧ ሺ ȉ ୧ ሻ ͳǡ ൌ ͳǡ ǥ ǡ
(12)
For a SVM model, the inner products beetween vectors of the feature space and support vectors can be uused to define the kernel function: ሺ୧ ǡ ሻ ൌ ୧
(14)
On the other hand, the function of the nnon-linear case is defined: ሺሻ ൌ ሼȽ σ୪୧ୀଵ ୧ ሺ୧ ǡ ሻ ሽ
(15)
A widely used Gaussian kernel is as follow ws: ሺǡ ሻ ൌ ሺെ
ȁȁ୶ି୷ȁȁమ ଶమ
ሻ
Figure 5. The schema for the secon nd stage of cascade system
(13)
(16)
Our assumption is that the more experts that are together the more rational a decision is made because of a more comprehensive consideration. To create a multti experts system, a common approach is to train members of ennsembles on each subset of a whole vector. Random Subspace m method is such an ensemble method which trains multiple ranndom subsets of feature vectors with a single classificationn algorithm and therefore produces many models [12]. Although the application of SVM ensembbles is not a new idea, it rarely applied in the field of signature vverification. For a training set with dimensionality , a fixed number for the dimensionality of the subspace is selected (nn
