Handwritten Signature Recognition using Departure

of Images from Independence

Samir Kumar Bandyopadhyay Member IEEE, Department of Computer

Science and Engineering, University of

Calcutta, Senate House, 87/1 College Street,

Kolkata -700073, India

skb1@vsnl.com

Debnath Bhattacharyya Computer Science and Engineering

Department, Heritage Institute of

Technology, Anandapur,

Kolkata - 700107, India

dippoulami@yahoo.com

Poulami Das Computer Science and Engineering

Department, Heritage Institute of

Technology, Anandapur,

Kolkata - 700107, India

debnathb@gmail.com

Abstract-In this paper we propose a new Handwritten

Signature Recognition Algorithm. The Algorithm is based on

pixel-to-pixel relationship between Images. The Algorithms are

based on extensive statistical analysis, Standard Deviation,

variance and Theory of Cross-Correlation. This is an extension

work of Handwritten Signature Identification.

This Algorithm supports the application environment and

we strongly believe that “User Recognition” could be a solid

platform for future research and study based on statistics and

probability theory.

Keywords: Security, authentication, watermarking,

image analysis, correlation and biometric.

I. INTRODUCTION

Various good techniques of secure transmission of data

are proposed and already taken into practice. Data Hiding is

the process of secretly embedding information inside a data

source without changing its perceptual quality. Digital

watermarking is the process of conveying information by

imperceptibly embedding it into the digital media.

Steganography (covered writing) the process of secretly

embedding information into a data source in such a way its

very existence is concealed. Extraction, Authentication and

Recognition of Data also equally important for security

purpose. The researchers have proposed numerous

authentication and recognition schemes, out of these

Biometric authentications and recognitions are used widely.

Biologically inspired approaches have got better popularity

in research.

The term correlation can also mean the cross-correlation

of two functions or electron correlation in molecular

systems. In probability theory and statistics, correlation, also

called correlation coefficient, indicates the strength and

direction of a linear relationship between two random

variables. In general statistical usage, correlation or co-

relation refers to the departure of two variables from

independence, although correlation does not imply

causation. In this broad sense there are several coefficients,

measuring the degree of correlation, adapted to the nature of

data. A number of different coefficients are used for

different situations. The best known is the Pearson product-

moment correlation coefficient, which is obtained by

dividing the covariance of the two variables by the product

of their standard deviations.

II. EARLIER WORKS

Numerous approaches have been proposed for

Handwritten Signature Identification, Recognition and

Authentication systems. Besides all, one approach that has

shown great promise is the use of Artificial Neural Network

in the Handwritten Signature Identification. An Artificial

Neural Network is trained to identify patterns among

different supplied handwriting samples. Handwritten

signature samples are considered input for the artificial

neural network model and typically weights also supplied for

recognition [3].

According to Berend-Jan van der Zwaag, the used method

in Neural Network is, various characters are taught to the

network in a supervised manner. A character is presented to

the system and is assigned a particular label. Several variant

patterns of the same character are taught to the network

under the same label. Hence the network learns various

possible variations of a single pattern and becomes adaptive

in nature [5].

Debnath Bhattacharyya, Samir Kumar Bandyopadhyay

and Deepsikha Chaudhury, 2007, proposed a scheme where

the Standard Deviation for each byte of the Training Image

Files (sample signatures) is computed and then each

corresponding byte of Test Signature is compared to check

whether it falls within the range of (Mean ± Standard

Deviation ). If 70% cases match, then the Test Signature is

accepted [4].

F. Bartolini, A. Tefas, M. Barni and I. Pitas discussed the

problem of authenticating video surveillance image. After an

introduction motivating the need for a watermarking-based

authentication of VS (video surveillance) sequences, a brief

survey of the main watermarking-based authentication

techniques is presented and the requirements that an

authentication algorithm should satisfy for VS applications

are discussed. A novel algorithm which is suitable for VS

visual data authentication have proposed [6].

Rehab H. Alwan, Fadhil J. Kadhim, and Ahmad T. Al-

Taani, 2005, have explained a method with three main steps.

First, the edge of the image is detected using Sobel mask

filters. Second, the least significant bit LSB of each pixel

is used. Finally, a gray level connectivity is applied using

978-1-4244-1718-6/08/$25.00 ©2008 IEEE Pg 964

a fuzzy approach and the ASCII code is used for

information hiding. The prior bit of the LSB represents the

edged image after gray level connectivity, and the remaining

six bits represent the original image with very little

difference in contrast. The given method embeds three

images in one image and includes, as a special case of data

embedding, information hiding, identifying and

authenticating text embedded within digital images [7].

Yusuk Lim, Changsheng Xu and David Dagan Feng,

2001, described the web-based authentication system

consists of two parts: one is a watermark embedding system

and the other is authentication system. In case of watermark

embedding system, it is installed in the server as application

software that any authorized user, who has access to server,

can generate watermarked image. The distribution can use

any kind of network transmission such as FTP, e-mail etc.

Once image is distributed to externally, client can access to

authentication web page to get verification of image [8].

Min Wu and Bede Liu, June, 2003, proposed a new

method to embed data in binary images, including scanned

text, figures, and signatures. The method manipulates

“flippable” pixels to enforce specific blockbased relationship

in order to embed a significant amount of data without

causing noticeable artifacts. Shuffling is applied before

embedding to equalize the uneven embedding capacity from

region to region. The hidden data can be extracted without

using the original image, and can also be accurately

extracted after high quality printing and scanning with the

help of a few registration marks [9].

Debnath Bhattacharyya, Samir Kumar Bandyopadhyay

and Poulami Das, 2007, have conducted [10] an extensive

survey of the existing graphical password schemes and

proposed an alternate scheme. Entire work has divided into

three phases- a. sampling of users passwords, processing and

storage; b. security on transmission; and c. Recognition and

authentication.

III. OUR WORK

Number footnotes separately in superscripts. Place the

actual footnote at the bottom of the column in which it was

cited. Do not put footnotes in the reference list. Use letters

for table footnotes (see Table I). IEEE Transactions no

longer use a journal prefix before the volume number. For

example, use “IEEE Trans. Magn., vol. 25,” not “vol. MAG-

25.

Mainly, in this paper, we have focused on ‘Recognition of

Handwritten Signature’. Prior to discuss ‘Recognition of

Handwritten Signature’, it is important to get some idea of

‘Data Hiding and Extraction of Handwritten Signature’; our

earlier work.

Before Embedding process, in Figure-1, processing of the

image is must. Firstly, Draw the Signature on a device by

pen or by mouse on the screen panel. This drawn image is

captured and put into the processes of extracting Region Of

Interest (ROI), scaled (the ROI) into a specific size and

thinned into single pixel format [1].

Law of Independent Assortment is used to watermarking

the processed Handwritten Signature; double lined

protection is provided during transmission of Handwritten

Signature over network [2].

For Handwritten Signature Identification and

Authentication - a forward propagation technique is used to

authenticate of input image out of the available training

images [3]. Here we are providing another alternative of

Recognition Technique as follow:

The correlation is defined only if both of the standard

deviations are finite and both of them are nonzero. The

correlation is 1 in the case of an increasing linear

relationship, and some value in between (0 > r <= 1),

indicating the degree of linear dependence between the

values. The closer the coefficient is to 1, the stronger the

correlation between the Images.

The correlation coefficient ρX, Y between two random

variables x and y with expected values µX and µY and

standard deviations σX and σY is defined as:

ρX, Y = covariance(X, Y) / σX σY

= E (( X - µX ) (Y – µY )) / σX σY ….. (i)

where, E is the expected value operator.

µX = E(X), σX2 = E(X

2 ) − E

2(X) and same for Y

also, thus we can express,

(E(XY) – E(X) E(Y))

ρX,Y= ----------------------------------------------

((E(X2

) − E2(X))

1/2 (E(Y

2 ) − E

2(Y))

1/2)

…..(ii) We have a series of n number of 2D arrays generated from

corresponding training images, values are stored in the

arrays are 0s or 1s, size of each array is fixed, i.e., Size, S =

Width of Array x Height of Array. X is one of the training

arrays and Y is the array to be checked, measurements of X

and Y written as Xi and Yi where i = 1, 2, ...,S.

“Pearson product-moment correlation coefficient” or

“sample correlation coefficient” is used here to estimate the

correlation of X and Y. It is especially important if X and Y

are both normally distributed (possible if the images are

from same training set). The Pearson correlation coefficient

is then the best estimate of the correlation of X and Y. The

Correlation Coefficient is written (in this case) from

equation (i) and (ii):

(S∑XiYi - ∑Xi ∑Yi)

rX,Y= -------------------------------------------------

((S∑Xi2 – (∑Xi)

2)1/2

((S∑Yi2 – (∑Yi)

2)1/2

…..(iii)

rX, Y will be calculated using equation (iii) for each of the

n number of 2D arrays generated from corresponding

training images.

Pg 965

The correlation is 1 in the case of an increasing linear

relationship. If the values are independent then the

correlation is 0 (or negative or positive high value). Suppose

the random variable X is uniformly distributed on the

interval from >0 to 1, and Y = X2. Then Y is completely

determined by X, so that X and Y are dependent, but if their

correlation is zero; they are uncorrelated.

The correlation coefficient a concept from statistics is a

measure of how well trends in the predicted values follow

trends in past actual values. It is a measure of how well the

predicted values from a forecast model “fit” with the real-life

data.

The correlation coefficient is a number between 0 and 1.

If there is no relationship between the predicted values and

the actual values the correlation coefficient is 0 or very low

(the predicted values are no better than random numbers).

As the strength of the relationship between the predicted

values and actual values increases so does the correlation

coefficient. A perfect fit gives a coefficient of 1.0. Thus the

higher the correlation coefficient the better.

We have converted the Bi-Color images into 2D

corresponding arrays, where elements of the array are the

pixel values of Bi-Color images, taken as ‘0’ for white and

‘1’ for black.

Handwritten Signature Recognition Algorithm (HSRA):

Input : N-Training Image(s), 1-Test Image

Output : Test Image, FIT or UNFIT

Procedure HSRA()

{

1. Declare N number of 2D Training Arrays with size of

Training Image(s).

Declare a 2D Test Array with size of Test Image.

Declare a single dimensional ‘Correlation Coefficient

Array’ of size N.

Declare sum squares, TS1, TS2, TTS. Declare sum

elements, T1, T2.

2. for i = 0 to width of the Image(s)

3. for j = 0 to height of the Image(s)

4. Store corresponding Image[i, j]’s pixel value to

[i, j] location of corresponding 2D Array

(Stored values are either 0 or 1 depending on

the pixel value of the images, 1 for black and 0

for white).

5. end for

6. end for

7. Continue Steps-2 to Step-6 for N number of Training

Image(s) and Test Image.

8. for i = 0 to width of the any created 2D Array

9. for j = 0 to height of the any created 2D Array

10. Compute sum square, TS1 +=

Training array element x Training array

element

11. Compute sum square, TS2 +=

Test array element x Test array element

12. Compute sum square, TTS +=

Training array element x Test array element

13. Compute sum elements, T1 += Training array element

14. Compute sum elements, T2 += Test array element

15. end for

16. end for

17. Calculate r, correlation coefficient by the expression

using equation (iii), and store into correlation

coefficient array.

18. Continue Steps-8 to Step-17, N times (1 by 1) for N

number of Training Array(s) and Test Array each time

with the Training Array.

19. Check the correlation coefficient array for the value(s)

between 0.9999 to 1.0

20. if found then the Test Image is (FIT) matched with

any of the Training Images else (UNFIT) not matched.

}

IV. RESULT AND DISCUSSION

The stated Algorithm has got 2 distinct divisions, a.

conversion of Image to 2D Array; and b. Recognition. All

images are taken with same size including the Test Image.

This is done by our previous work(s), Extracting Area of

Interest, Scaling and Thinning [1]. Moreover all these

processes have done prior to store training images in the

storage area and data hiding [2, 10].

A. Complexity analysis of the stated algorithm

For conversion of Image to 2D Array:

Size of Image, S = Image width x Image height. Number

of Image(s) to convert, n. Thus the time complexity to

convert N number of images with size S each, is, N x S, for a

large problem set, this can be written as,

N x N = N2 ------------- (1)

Recognition:

This is necessary to access Elements of two 2D Arrays for

calculating Sum Square of elements and sum of the

elements, i.e., S+S = 2S = 2N ---------- (2)

Sum product of the elements, that is also,

S + S = 2S = 2N ---------- (3)

Calculating and storing of correlation coefficient, that is N

times, so, N ---------- (4)

Now, from equations (2), (3) and (4), we can state that, for

matching the Test Image with single Training Image,

2N + 2N + N = 5N ------------ (5)

And this checking has to be done with N number of

Training Images, that is,

5N x N = N2 (for a large Training Set) ----------- (6)

So, from equation (1) and (6), Time Complexity is 2N2.

B. Test Results

Testing is done here with 131 users (individuals)

Signatures, each user with 24 Handwritten Signatures and

10-trained forgery Signatures [11].

Table-1 shows the series of Correlation Coefficients,

returned by each of the Training Array for the given Test

Array Figure-1. Here, testing is done with 24 Training

Images set for a single user. Only one such instance is shown

here in Figure-1 out of 131. Perfect match found in Table-1

is with Signature-11 (one of the Training Image) and in this

Pg 966

Signature-1 Signature-2 Signature-3 Signature-4 Signature-22 Signature-23 Signature-24

Training Images converted to corresponding 2D Training Arrays (Training Set of same problem space)

Converted to 2D Array Test Image

(Signature-11 from Training Set)

[Draw the element-by-elemen

t Relation with each of the

figure-1

Pg 967

Test Array

training array, called Correlation Coefficient]

Table-1

Test Array generated from Test Image

(Here, it is taken as

Signature-11)

Training Arrays for

User1

Correlation Coefficient generated from

each Training Array with Test Array

Signature-1 0.2004229361600069

Signature-2 0.1790631326991368

Signature-3 0.1052254603432329

Signature-4 0.1942522684172455

Signature-5 0.1648025984549539

Signature-6 0.2710549123069337

Signature-7 0.2858090120330544

Signature-8 0.2270414224565152

Signature-9 0.2410276787612588

Signature-10 0.1849605626411834

Signature-11 1.0000000000000000

Signature-12 0.1855773367436578

Signature-13 0.2383045709100168

Signature-14 0.2396381537581523

Signature-15 0.1763162895592169

Signature-16 0.1614256952772022

Signature-17 0.1788460176153321

Signature-18 0.2141833381981659

Signature-19 0.2549800147305654

Signature-20 0.1863935765642522

Signature-21 0.2127480431132642

Signature-22 0.2261281705643858

Signature-23 0.2035685353062401

Signature-24 0.2116770968123705

>>>> Fit and Fitness Rate: 1.0 <<<<

Table-2

Test Array generated from Test Image

(forgery Signature)

Training Arrays for

User1

Correlation Coefficient generated from

each Training Array with Test Array

Signature-1 0.1603882402409401

Signature-2 0.1308927191867935

Signature-3 0.0216864692218872

Signature-4 0.1152753319031659

Signature-5 0.1145443439922423

Signature-6 0.1435363117501333

Signature-7 0.1788840115877254

Signature-8 0.1803741509777574

Signature-9 0.1187262870739589

Signature-10 0.1294898232917472

Signature-11 0.1903566207977627

Signature-12 0.1209446379722159

Signature-13 0.1758481630899941

Signature-14 0.1294655818378044

Signature-15 0.0812553839862523

Signature-16 0.1195819710595384

Signature-17 0.1810475033277922

Signature-18 0.1655539521357283

Signature-19 0.1833515998510241

Signature-20 0.1694563585575498

Signature-21 0.1628242070273894

Signature-22 0.1772467029199628

Signature-23 0.0918058808861437

Signature-24 0.1548684211509291

Forgery Signature >>>> UnFit <<<< of user1 figure-2

Pg 968

case Test Image is found “FIT”. Correlation Coefficient

returning 1.0 is the best match, however, value returning 0-1

depicts Test Signature is under same problem space, here,

under same training set.

Table-2 shows the series of Correlation Coefficients,

returned by each of the Training Array (Figure-1) for the

given Test Image (forgery Signature) of Figure-2, an

instance of a reverse case only shown here. However,

Correlation Coefficients returning here in between 0-1, but,

in any case nowhere nearer to 1.0 (exact match).

V. CONCLUSION

This is an extension work of Handwritten Signature

Recognition, that we have started a year back. Various

Watermarking and Data Hiding techniques we have already

proposed and published in different International Journals

and Conference Proceedings. Prior to these we have worked

on Morphological Image Processing focused on Handwritten

Signature Scaling, Thinning and extraction of area of interest

(Handwritten Signature Area within an Image). Thus a series

of work just going to be completed with this proposed

Recognition Scheme.

This Recognition scheme is based on extensive Statistical

Analysis, Theory of Correlation Coefficient and Standard

Deviation. Various test results are positively backing this

scheme. We hope our Study and Research definitely will be

in the spot light.

REFERENCES

[1] Debnath Bhattacharyya, Samir Kumar Bandyopadhyay and

Poulami Das, Handwritten Signature Varification System using

Morphological Image Analysis”, CATA-2007 International Conference, A publication of International Society for Computers

and their Applications, Honolulu, Hawaii, USA, March 28-30,

2007, pp. 112-117. [2] Debnath Bhattacharyya, Samir Kumar Bandyopadhyay and

Poulami Das, “Handwritten Signature Extraction from

Watermarked Images using Genetic Crossover”, MUE’07 IEEE CS Conference, Seoul, Korea, April 27-30, 2007, pp. 987-991.

[3] Debnath Bhattacharyya, Samir Kumar Bandyopadhyay and

Poulami Das, “A Flexible ANN System for Handwritten Signature Identification”, Proceedings of the International MultiConference of

Engineers and Computer Scientists 2007 Volume II, IMECS '07,

March 21 - 23, 2007, Hong Kong, Lecture Notes in Engineering and Computer Science, pp. 1883-1887, Newswood Limited, 2007.

[4] Debnath Bhattacharyya, Samir Kumar Bandyopadhyay and

Deepsikha Chaudhury, “Handwritten Signature Authentication Scheme using Integrated Statistical Analysis of Bi-Color Images”,

IEEE ICCSA 2007 Conference, Kuala Lumpur, Malaysia, August

26-29, 2007. [5] Berend-Jan van der Zwaag, Handwritten Digit Recognition : A

Neural Network Demo, Euregio Computational Intelligence Center

, Dept. of Electrical Engineering, University of Twente, Enschede, the Netherlands.

[6] F. Bartolini, A. Tefas, M. Barni and I. Pitas, “Image Authentication

Techniques for Surveillance Applications”, IEEE Proceedings, Vol. 89, No. 10, October 2001.

[7] Rehab H. Alwan, Fadhil J. Kadhim, and Ahmad T. Al-Taani, “Data

Embedding Based on Better Use of Bits in Image Pixels”, International Journal of Signal Processing Vol 2, No. 2, 2005.

[8] Yusuk Lim, Changsheng Xu and David Dagan Feng, “Web based Image Authentication Using Invisible Fragile Watermark”, 2001,

Pan-Sydney Area Workshop on Visual Information Processing

(VIP2001), Sydney, Australia. [9] Min Wu, Member, IEEE, and Bede Liu, Fellow, IEEE, “Data

Hiding in Binary Image for Authentication and Annotation”, IEEE Trans. Image Processing, vol. 12, pp. 696–705, June 2003.

[10] Debnath Bhattacharyya, Samir Kumar Bandyopadhyay and

Poulami Das, “User Authentication by Secured Graphical Password Implementation”, IEEE Electro-Information Technology (EIT’07),

Marriott O'Hare Chicago, IL, USA, May 17-20, 2007, pp. 32-41.

[11] Handwriting Databases: http://www.gpds.ulpgc.es/

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