Signature Verification Based On Line Directionality

E. N. Zois, A. A. Nassiopoulos Research Development Telecommunications Laboratory,

Electronics Department, Athens Technological Educational Institution,

12 Ag. Spiridonos Str. 12210, Aegaleo, Greece, elias@ee.teiath.gr, nassiop@teiath.gr

V. Anastassopoulos Electronics Laboratory, Electronics and Computers

Division, Physics Department, University of Patras, 26500.

Patras, Greece vassilis@physics.upatras.gr

Abstract— A novel technique is presented for off-line signature recognition and verification. The feature extraction procedure employs directional-vectors, similar to those used in chain codes, which provide a global measure of the signature image. The signature trace is transformed into the feature vector by measuring the directional strength of line segments having a chessboard distance equal to two. A probabilistic neural topology is employed for the design of the classifier. In order to obtain comparable results, the method was applied to a database already used in the literature. The verification procedure provides low classification error for authentic signatures while it eliminates the forgers.

I. INTRODUCTION Handwritten patterns, which are part of the so-called non-

invasive procedures, have been widely accepted to convey important and sensitive information regarding common and secure transactions [1]. However, they are susceptible to imitating procedures which are well known under the criminologist term forgeries. Among several forms of handwriting, the signature has been found to be the most prone to fraud. This is due to the fact that humans can easily recall their signatures in order to accomplish their everyday transactions like documents and checks [2]. The main reason why persons can use their signature with increased confidence stems from the fact that continuous and iterative training is carried out by writing the same and fixed handwritten symbols. This is an a-priori assumption for the signature verification system, when it is employed to verify the claimed identity. It should provide a relatively fast, economical and confident way to identify the individuals against potential breach efforts [3].

Feature selection in an off-line verification system is a challenging task since the line patterns in the signature may contain symbols of different complexity, from clear and tight letters up to totally unconstrained curves [1]. Many of the approaches that have been reported in the literature treat the signature image as a whole, thus resulting in a global feature extraction procedure [1]. One way to achieve this is to describe the structural relation between the line-primitives that constitute the signature image in terms of geometrical features [4]. The relation between the local handwriting strokes and the global shape of the signature can be derived also using directional groupings [5,6]. In this paper a method

is proposed for verifying handwritten signatures by means of measuring the distribution of elementary line segments along predetermined directions. These elementary line segments possess a chessboard distance (D8) [7, p. 69] equal to two. In order to obtain results comparable with other signature verification techniques, the method is applied to an already used signature database [5].

II. THE DATABASE

A. The database The signature database consists of 20 sets of different

signatures. Each set consists of 24 genuine and 144 forgery signatures. Following K. Huang [5], who has created this database, each volunteer is asked to sign a full page with his own signatures and to imitate up to three pages of other peoples signatures. The forgery samples represent various levels of imitation, ranging from simple freehand up to skilled. The images have been scanned at a resolution of 100 dpi, 8 bit grey scale. Figure 1 provides samples of the acquired images. From an early inspection we can conclude that the database contains signatures of various styles i.e clear and tided, cursive and oriental. For the experiments which have been contacted a portable PC computer has been used (Pentium 4, 2.8 GHz) along with the MATLAB package.

B. Preprocessing For every image a preprocessing step is followed in order

to obtain an output image, which will maximize the amount of utilized information. In order to achieve this, thresholding and thinning procedures have been applied. The resulting binary image, which is one pixel wide, is deemed as insensitive to pen variations like size, color and style [1,2,7]. However, in order to apply the feature extraction method the original image along with the thinned version must be maintained. This results in an increase of the total memory requirements but incorporates significant properties of the original signal into the verification process. The grey level image properties in conjunction with the thinned image provide critical information about the dynamic aspects of the signature image [8,9]. Figure 2 demonstrates the original image, the thinned one and the final version, which is the

This work is co-funded a) by 75% from E.U. and 25% from the Greek Government under the framework of the Education and Initial Vocational Training Program – Archimedes and b) The Research Committee of TEI of Athens under the framework of Project Athena-04.

0-7803-9333-3/05/$20.00 ©2005 IEEE SIPS 2005343

Figure 2. Preprocessing steps of a signature image. a) Original image. b) Thinned image. c) The combined grey scale, one pixel wide image.

Figure 1. Samples from the signature database. The first sample comes from the genuine writer while the second is a forgery. a) Oriental handwriting. b) Cursive and unconstrained handwriting. c) Tight handwriting.

combination of the thinned signature with grey-level values. The resulting image will be referred to as Combined Gray-scale One Pixel wide (CGOP).

III. FEATURE VECTOR GENERATION On each pixel (i,j) that is part of the trace of the CGOP

image, a rectangular grid mask with dimensions 3×5 pixels is applied as shown in Figure 3. Thus, a total of nine positions having a chessboard distance equal to 2 (depicted in the Figure as shaded squares) are enabled. The pixels belonging to all two-step paths that connect the reference pixel (i,j) with each 8D distant pixel (i+k,j+l) are summed in order to create the quantity:

( ) ( )[ ]∑∈⎭⎬⎫

⎩⎨⎧++

+++++= CGOPnj

mi,, ),;,( ljkifnjmiflkjif DDd

(1)

Consequently, depending on the combination of k and l, nine similar quantities are formed corresponding to each specific position (i,j). Accordingly, a nine dimensional feature vector is formed by accumulating the above quantity over all ),( ji points of the CGOP image. The nine feature

components correspond to the different directions which are defined by the following equation:

{ }∑∈

=CGOP i,j

dd (i,j:k,l) flkf ),( (2)

Since fd(-2,0) coincides with fd(0,2), the fd feature vector is reduced to a dimensionality equal to 8. The final feature vector can be normalized to the total sum of the extracted parameters in order to obtain a probabilistic meaning.

IV. THE CLASSIFICATION SCHEME

A. Experimental Protocol In this paper we address the signature verification

according to the following statement. A specific signature sample is classified either as genuine (H1i: the specific i-writer is present) or not (H0i: the specific i-writer is not present). The total error probability, defined by eq. (3), is to be used as an evaluation metric:

)1(21)(

21

dfamfaerror PPPPP −+=+= (3)

where Pfa is the probability to accept hypothesis H1i, while H0i hypothesis is true, Pm is the probability to accept hypothesis H0i, while hypothesis H1i is true, and Pd is the corresponding probability of detection.

For each signature owner an individual classifier is designed, trained and evaluated for both cases of random and skilled forgery. This design strategy offers reduction on the required training samples. Moreover, it can be applied in case that another writer is added to the verification procedure. For the verification stage, the following simplified decision rule is adopted:

):():( 01

0

1

di

H

H

di fHfHi

i

φφ<> (4)

where ):( 1 di fHφ and ):( 0 di fHφ are expressions of the posterior probabilities of the genuine and forgery classes.

fD(i-1,j+1)

fD(i,j) fD(i,j+1) fD(i,j+2)

Fig. 3. Multiple, two-step paths for accessing the pixel fD(i,j+2). All shaded pixels have a chessboard distance D8 equal to 2.

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The problem usually met is the lack of any information about the analytic representation of the conditional probability densities [10]. Thus, a non parametric procedure must be followed in order to derive the two parts of eq. (4).

For each writer the following classification protocol is applied. First, the genuine signature samples of the training set are processed as described in section 2.3 in order to extract the bounding rectangle for each writer. After that, the training samples are converted to the feature vector as described in section 3. Similar procedures have been followed in order to extract the same parameters for the training set with the random forgeries as well as the skilled forgery specimens. These image samples are resized, to the writer class maximum width and length, according to the feature extraction procedure. The features provide the necessary clusters H1i and H0i for each writer.

The population size of both the training and testing set is considered in order to ensure adequate representation of both classes for the evaluation of the total error probability. For training the genuine class the leave-one-out-method has been adopted since the sample population is limited. Perturbation techniques [5, 6] for providing extra signature samples are not used as the resulting signatures might provide correlated results which will degrade the performance of the proposed method. Thus, 23 genuine samples for each writer are employed while the remained sample is applied to the testing phase. For training the forgery class half of the samples (72 signatures) that represent the skilled forgery category are used. The other 72 skilled forgery samples along with the 3864 samples from all other signatures [23 writers × (1 genuine + 6 fraud) classes × 24 (samples/class)] which represent the random forgery category are used at the verification stage. The whole procedure is repeated for all the writers and the experimental results are discussed in section 5.

B. Neural network topology Probabilistic neural networks consist of two layers: a

hidden radial basis layer of p -size pattern neurons and an output competitive layer of c - size class neurons [11], which forms a linear combination of the kernel functions computed by the hidden layer nodes. The kernel function is often approached by using the Gaussian form:

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−−= 2

,1,1,1 2

)()(exp

j

jT

jj

wxwxa

σ, 1,...,2,1 Nj = (5)

while the competitive node equations are provided by:

1,2 ,awy jj = , 2,...,2,1 Nj = (6)

In (5), x is the input pattern which corresponds to the eight-dimensional feature vector, while ja ,1 , jw ,1 are the corresponding output and weighting parameters of the j -th

node in the radial basis layer. In (6), 1a is the vector of all

outputs from the radial basis layer, while jw ,2 and jy are the weighting parameter and the output of the j -th node of the linear layer respectively. The normalization parameter

2jσ in the radial basis layer represents a measure of the

spread of the data in the feature space. This is a critical parameter for designing the training procedure since it can vary between two values. This can be viewed as determining the width of an area in the feature space to which each hidden neuron responds. The spread parameter should be strong enough so that radial neurons respond to overlapping regions of the feature space. Thus, for each writer class we let the spread parameter vary in order to find the best discrimination results. In this design procedure, care must be taken in order not to set the spread parameter to an excessive value, thus leading to a case in which active input regions of the radial neurons overlap throughout the entire feature space. The selection of the spread must provide a generalization to new input vectors. Typical values for the spread parameter are within ten to thirty percent of the maximum cluster distance. The spread value has a twofold meaning; it can be used to provide an additional parameter for the model of each writer and it is also used in order to evaluate the discrimination capability of the network topology. The number of neurons 21, NN in each layer is determined by the number of the test patterns and the number of assigning classes. In our case the number of the radial basis neurons equals 95 (23 genuine + 72 forgery) whereas the number 2N is set to 2 in order to represent the existence or non-existence of the genuine writer.

V. EXPERIMENTAL RESULTS. The above methodology has been applied to the signature

database twenty-four times for each one of the twenty writers as the leave-one-out method indicates. The preliminary results for a subgroup of writers are depicted in Table 1. From the confusion matrix it is noted that the method provides high verification accuracy, especially for the case of the random forgery, where the average error is 0.9%. For the skilled forgery the average error is 9.96%. In order to improve the verification results the bounding rectangle normalization parameters are explored in a more detailed way for the writers who present the highest degree of error. Thus, for the writers 1, 7, 9, 10, 11, 12, 13, 14, 15, 18 and 19 the normalization strategy has been redesigned. Table 2 provides a more detailed insight for a subset of writers who are presenting the largest error rates. The total skilled verification efficiency increases to 94%, whereas the average error for the random forgery samples drops to 0.1%. For example the unacceptable high error rate for the random forgery case between writer 1 and writer 2 is overcome when resizing the bounding rectangle using a resizing ratio of {1.5 x 1.5} for the width and the length. It is noted that the highest errors occur when the signature samples contain a large degree of vertical strikes, while the oriental type signatures and those containing curves are presenting highly efficient verification rates. Compared to results obtained

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from references, one can state that the proposed method provides sufficient and comparable efficiency for a feature vector that carries mostly global information.

TABLE I. PRELIMINARY VERIFICATION RESULTS

Writers 10 11 12 13 14 15

10 0.10 0 0.02 0.01 0 0

11 0 0.14 0 0 0 0

12 0 0.01 0.16 0 0.03 0.08

13 0 0 0 0.22 0 0

14 0 0 0 0 0.10 0

15 0 0.02 0.10 0 0 0.12

TABLE II. IMPROVED VERIFICATION RESULTS

Writers 10 11 12 13 14 15

10 0.10 0 0 0.01 0 0

11 0 0.04 0 0 0 0

12 0 0.01 0.10 0 0.01 0.01

13 0 0 0 0.08 0 0

14 0 0 0 0 0.09 0

15 0 0.02 0.03 0 0 0.09

VI. CONCUSIONS This paper presents a new off-line signature verification

method based on a global feature. This information resembles texture or chain coding techniques and describes the way that the signal is directed throughout the signature image. The method is based on measuring the sum of pixel values along eight predetermined directions. The feature presents low dimensionality thus making it attractive to standard pattern recognition techniques. The proposed feature vector possesses attributes that resemble human perception of curves.

ACKNOWLEDGMENT This work is co-funded a) by 75% from E.U. and 25%

from the Greek Government under the framework of the Education and Initial Vocational Training Program – Archimedes and b) The Research Committee of TEI of Athens under the framework of Project Athena-04.

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[3] A. K. Jain, F. D. Gries, S. D. Connel, On-line signature verification, Pattern Recognition, Vol. 35, pp.2963-2972, 2002.

[4] H. Baltzakis and N. Papamarkos, A new signature verification technique based on a two stage neural network classifier, Engineering Applications of Artificial Intelligence, 14, pp. 95-103, 2001.

[5] K. Huang and H. Yan, Off-line signature verification based on geometric feature extraction and neural network classification, Pattern Recognition, 30 pp. 9-17, 1997.

[6] K. Huang and H. Yan, Off-line signature verification using structural feature correspondence, Pattern Recognition, 35, pp. 2467-2477, 2002.

[7] R. C. Gonzalez and R. Woods, "Digital signal processing", Addison Wisley, Massachusetts, 1993.

[8] Y. Qi, and B.R. Hunt, Signature verification using global and grid features, Pattern Recognition, Vol. 27, 12, 1621-1629, (1994).

[9] J.P. Drouhard, R. Sabourin and M. Godbout, A neural approach to off-line signature verification using directional PDF, Pattern Recognition, Vol. 29, 3, 415-424, (1996).

[10] R.O. Duda, P.E. Hart and D. G. Stork, "Pattern classification and scene analysis", John Wiley and Sons, New York, 2001.

[11] D. R. Hush, B. Horne, Progress in supervised neural networks, IEEE signal procesing magazine, No. 1, pp. 8-39, 1993.

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