online signature system

Acknowledgement

I would like to say a big thanks to all of those who have helped me in my research

work to achieve my goals, specially to my supervisor Mr Jameel Qadri who have

helped me a lot to understand the topic and provided me every possible assistance

whenever I needed it, and also to my friends and colleagues without their help it

would have been very difficult for me to carry out this research.

Table of Contents1. INTRODUCTION:-.................................................................................................................... 4

1.1 TOOLS USED:-...............................................................................................................................61.2 ORGANIZATION OF REPORT:-...........................................................................................................61.3 LITERATURE REVIEW:-.....................................................................................................................7

1.3.1 Analysis from literature Review in the context of OSV Model..........................................91.4 METHODOLOGY & SOFTWARE LIFE CYCLE:-......................................................................................13

1.4.1 Methodology:-...............................................................................................................131.4.2 Software Life Cycle Approach:-......................................................................................14

2. PROBLEM STATEMENT:-........................................................................................................16

2.1 DELIVERABLES AND DEVELOPMENT REQUIREMENTS:-.........................................................................172.1.1 Deliverables:-.................................................................................................................17

3. FUNCTIONAL REQUIREMENTS:-.............................................................................................19

3.1 DATA ACQUISITION:-....................................................................................................................193.2 SIGNATURE PREPROCESSING:-........................................................................................................193.3 RE-SAMPLING:-...........................................................................................................................193.4 FEATURE EXTRACTION:-................................................................................................................203.5 STROKE EXTRACTION USING THE DTW APPROACH:-...........................................................................203.6 VERIFICATION:-...........................................................................................................................213.7 NON-FUNCTIONAL REQUIREMENTS:-...............................................................................................21

3.7.1 Usability:-.......................................................................................................................213.7.2 Reliability:-.....................................................................................................................213.7.3 Performance:-................................................................................................................22

4. SYSTEM ARCHITECTURE:-......................................................................................................24

4.1 DATA ACQUISITION......................................................................................................................244.2 SYSTEM DESIGN:-........................................................................................................................25

4.2.1 Data Acquisition.............................................................................................................254.2.2 Online Signature Database............................................................................................264.2.3 Signature Preprocessing................................................................................................274.2.4 Re-Sampling...................................................................................................................304.2.5 Feature Extraction.........................................................................................................364.2.6 Stroke Extraction using the DTW Approach...................................................................384.2.7 Verification....................................................................................................................40

4.3 MAJOR DESIGN GOALS & CONSTRAINTS:-........................................................................................424.3.1 Design Goals:-................................................................................................................424.3.2 Constraints:-..................................................................................................................43

5. VERIFICATION AND VALIDATION...........................................................................................45

5.1 USABILITY TESTING.......................................................................................................................455.2 INTERGRATION............................................................................................................................455.3 SYSTEM TESTING..........................................................................................................................465.4 HARDWARE CONFIGURATION FOR TESTING.......................................................................................46

6. CONCLUSION:-...................................................................................................................... 48

7. BIBLOGRAPHY:..................................................................................................................... 49

Online Signature Verification Model 2

CHAPTER 1CHAPTER 1

INTRODUCTIONINTRODUCTION


1. Introduction:-

It is no longer a mere science fiction to automatically verify someone’s

identity by his biometrics e.g. faces, iris, DNA, voice or fingerprint but rather

it has become a daily routine authentication procedure in many places.

Biometrics is the utilization of physiological characteristics (face, iris, and

fingerprint) or behavioral traits (signature, voice) for identity verification of an

individual [1]. As it is impossible to steal copy or guess biometrics, biometric

authentication is being widely accepted. Biometric authentication systems are

a more trustable alternative to password based security systems. Furthermore,

forgetting one’s password is possible and one can even lose his keys, however

forgetting and losing is even not an issue for biometric properties.

To make a biometric authentication application, one must choose a proper

biometric that suits the application. The following criteria are important while

looking for a proper biometric:

uniqueness of the biometric

whether the biometric is hard to be copied or stolen

acceptability of the biometric by the public

Cost to employ that particular biometric data.

Like other biometrics e.g. fingerprint, eyes or face, signature is also a

biometric, but it is a behavioral biometric, unlike fingerprint, eyes or face

which are physiological biometrics. Although as it is nearly impossible to

forge iris patterns or fingerprints and using this biometrics may make security

authentication more reliable, while one’s signature may change over time and

it is also not impossible to forge the signatures, however signatures are widely

accepted by the public. Signature verification systems meet the needs of

certain lower-security authentication areas. Signature verification is becoming

increasingly popular for applications ranging from access control to restricted

areas to fraud prevention in financial transactions [2].


A signature can be defined as a unique identity of a person. No two signatures

can be identical, unless one of them is a forgery or a copy of the other. Also no

two signatures will be exactly identical no matter how hard one tries to copy

the signature.

Online signature verification is based on two approaches, functional approach

and parametric approach. In the functional approach, complete signals (x (t) y

(t), v (t), etc.) directly or indirectly make up the feature set. The two signals,

one from a genuine signature and the other from a forgery, are then compared

point-to-point. However in the parametric approach, only the parameters

abstracted from the complete signals are compared. Though the parametric

approach enjoys the advantages of algorithmic simplicity and computation

speed, but the task of selecting the right set of parameters is not trivial. The

comparison based on the complete signals generally yields better results [3].

I have chosen functional approach for research to develop this system. In

online (dynamic) signature verification system, signatures are captured by

pressure-sensitive tablets. These tablets are capable of extracting dynamic

properties of a signature in addition to its shape. Features like the number and

order of the strokes, the overall speed of the signature, the pen pressure at each

point etc. are called the dynamic features of a signature. Dynamic features

make the signature more unique and more difficult to forge. It is possible that

a skilled forger may duplicate the look of a signature but it is very difficult to

forge the dynamic properties like velocity, pressure, timing related to the

signature. Therefore, dynamic signature verification poses a great challenge to

the possibility of fraud and makes the authentication process highly trustable.

OSV can be applied in PDAs (Personal Digital Assistants) and laptops before

accessing the system. It can be used to authenticate computer users for

accessing sensitive data or programs. Internationally some banks have adopted

the signature verification system. Basically it can be applied in areas where

authentication of individuals is necessary for accessing physical devices or

buildings etc.


1.1 Tools Used:-

Ideally the developer should use following tools to develop this system

MATLAB 7 or higher (for the mathematical functions)

Wacom Graphire 2 Tablet ( for taking user input)

MovAlyzer Software (MovAlyzeR is a software for handwriting).

1.2 Organization of Report:-

In this chapter we have presented a brief introduction of our project work,

history of OSV, different algorithmic techniques available and the techniques

that we have used in our system.

Chapter 2 provides an overview of the problem statement and the outcome

that will be delivered by this research project.

Chapter 3 provides us with the detail of functional and non functional

requirements required for this system.

Chapter 4 explains the architecture and design of system. It explains all the

phases of the system.

Chapter 5 presents the pseudo codes of the techniques which can be used in

this system.


1.3 Literature Review:-

In the literature review we explain the techniques that can be used in the

process of signature verification. Introduction about the techniques is also

given to help understand them.

To calculate distance between two points a wide variety of techniques and

algorithms are introduced. Euclidean Distance is one such distance measuring

technique. In mathematics the Euclidean distance or Euclidean metric is

defined as the simple "ordinary" distance calculated between two points. It is

known as the distance that one would measure with a ruler, which can be

proven by repeated application of the Pythagorean Theorem.

DEuclid =

Manhattan Distance is another technique used for calculating distance

between two points. Manhattan Distance is defined to be the distance

calculated between two points measured along axes at right angles. More

formally, we can define the Manhattan distance between two points in an

Euclidean space with fixed Cartesian coordinate system as the sum of the

lengths of the projections of the line segment between the points onto the

coordinate axes [4].

For example, in the plane, the Manhattan distance between the point P1 with

coordinates (x1, y1) and the point P2 at (x2, y2) is

| x1 – x2 | + | y1 – y2 |

Manhattan distance depends on the choice on the rotation of the coordinate

system, but does not depend on the translation of the coordinate system or its

reflection with respect to a coordinate axis [4].


http://en.wikipedia.org/wiki/Reflection_(mathematics)

http://en.wikipedia.org/wiki/Translation_(geometry)

http://en.wikipedia.org/wiki/Rotation

http://en.wikipedia.org/wiki/Plane_(mathematics)

http://en.wikipedia.org/wiki/Coordinate_axes

http://en.wikipedia.org/wiki/Line_segment

http://en.wikipedia.org/wiki/Cartesian_coordinate_system

http://en.wikipedia.org/wiki/Euclidean_space

Another technique is the Mahalanobis distance. It is based on correlations

between variables by which different patterns can be identified and analyzed.

It is a useful way of determining similarity of an unknown sample set to a

known one. It differs from Euclidean distance in that it takes into account the

correlations of the data set and is scale-invariant, i.e. not dependent on the

scale of measurements [5]. Mahalanobis distance can also be defined as

dissimilarity measure between two random vectors and of the same

distribution with the covariance matrix Σ.

Dynamic Time Warping is yet another technique that is used to match two

series. It is a method that allows finding an optimal match between two given

sequences (i.e. time series). The time series don’t have to be of equal lengths.

The sequences are "warped" non-linearly to match each other. DTW is a very

robust and elastic technique.

Different interpolation techniques are also in use in the science and

mathematics world. Of the many, a few are explained below.

Linear Interpolation is a simple technique used to estimate unknown values

that lie between known values. Linear Interpolation is used to predict

unknown values between any two known values whose scale is known. The

rate of change is assumed to be constant. Linear interpolation creates new

values at equal distances along a line between two known values. Linear

interpolation is a process employed in mathematics, and numerous

applications including computer graphics. Linear interpolation is often used to

rigid evenly-spaced data, such as longitude / latitude gridded data, to a higher

or lower resolution [6].

Generally, linear interpolation takes two data points, say (xa, ya) and (xb, yb),

and the interpolant is given by:


http://en.wikipedia.org/wiki/Probability_distribution

http://en.wikipedia.org/wiki/Random_vector

http://en.wikipedia.org/wiki/Euclidean

http://en.wikipedia.org/w/index.php?title=Sample_set&action=edit

http://en.wikipedia.org/wiki/Correlation

at the point (x,y) [7].

Bilinear Interpolation Techniques is an extension of linear interpolation for

interpolating functions of two variables. The key idea is to perform linear

interpolation first in one direction, and then in the other direction [8]. Bilinear

interpolation is a mathematical method which interpolates a new cell's value

within a 2 x 2 neighborhood of cells. This technique is often used in digital

image processing to resample raster satellite images. The value of a pixel is

calculated using values of the four nearest pixels that surround the pixel i.e.

the neighboring pixels; this process is repeated to re-sample the entire image.

Cubic Spline Interpolation is another technique of interpolation used today.

Splines are drafting aids used to draw smooth curves through a set of points.

Weights are attached at the points to be connected and flexible strip is shaped

around the weights. Splines can be made to fit even the most random of data,

making numerical analysis possible even when the actual function is not

known [9].

A cubic spline is a piecewise cubic polynomial such that the function, its

derivative and its second derivative are continuous at the interpolation nodes.

The natural cubic spline has zero second derivatives at the endpoints. It is the

smoothest of all possible interpolating curves in the sense that it minimizes the

integral of the square of the second derivative.

1.3.1 Analysis from literature Review in the context of OSV Model

The methadology that should be used by the developer implies resampling the

signatures with the help of cubic spline interpolation technique. The signatures

are then warped using DTW and after that verification of the input signature

with the template signatures is done with the help of Mahalanobis Distance

technique.


http://www.geo.ed.ac.uk/agidexe/term?103

http://www.geo.ed.ac.uk/agidexe/term?103

Cubic Spline Interpolation Technique is a very efficient technique to resample

data points. Cubic spline is used to draw smooth curves through a number of

points. The goal of cubic spline interpolation is to get an interpolation formula

that is smooth in the first derivative, and continuous in the second derivative,

both within an interval and at its boundaries [10].

Figure 1.1 Cubic spline drawn through five points

The results produced by cubic spline are the smoothest results of all the

interpolation methods.

Splines are highly useful tools for data analysis.

The method of cubic spline preserves monotonicity and the shape of the data.

Over fitting effects are reduced by cubic spline method.

Cubic spline interpolation technique is useful for modeling yield curves,

forward curves, and other term structures.

Dynamic Time Wrapping (DTW) is a technique that finds the optimal

alignment between two time series if one time series may be “warped” non-

linearly by stretching or shrinking it along its time axis. The warped time

series are used to find corresponding regions between them or to determine the

similarity between the two time series. DTW is a non-linear (elastic)

alignment that produces a more intuitive similarity measure, allowing similar

shapes to match even if they are out of phase in the time axis. Other distance


http://www.riskglossary.com/articles/term_structure.htm

http://www.riskglossary.com/articles/forward.htm

http://www.riskglossary.com/articles/fixed_income_term_structure.htm

based techniques like Euclidean and Manhattan do point to point matching

between two time series produce a poor similarity score.

Given two sequences X = (x1, x2,…, xn) and Y =(y1, y2,…, ym), the distance

DTW(X,Y) is similar to the edit distance. To calculate DTW distance D(X, Y),

we can first construct an n-by-m matrix. Then, we find a path in the matrix

which starts from cell (1,1) to cell (n, m) so that the average cumulative cost

along the path is minimized. If the path passes cell (i, j), then the cell (i, j)

contributes cost (xi, yj) to the cumulative cost. The cost function cost (xi, yj)

can be defined flexibly depending on application, for instance, cost (xi, yj) =

(xi, yj) ^ 2. This path can be determined using dynamic programming, because

the following recursive equation holds [11]:

Figure1.2 DTW between test and reference series

DTW is a very robust technique used for measuring time series similarity.

In speech recognition, DTW is used to determine if same spoken phrase is

represented by two wave forms.

DTW has also been found useful in many other disciplines including gesture

recognition, robotics, speech recognition, manufacturing, bioinformatics,

chemistry and medicine.


DTW is commonly used in data mining as a distance measure between time

series.

Figure 1.3 Euclidean Distance: Sequences are alligned one to one

Figure 1.4 Warped time axis: Non linear allignments are possible

DTW is much better than Euclidean distance for classification, clustering,

query by content etc.

Continuity and monotonicity of warping is guaranteed by DTW.

Mahalanobis Distance Technique is a distance measure introduced by P. C.

Mahalanobis in 1936. It is based on correlations between variables by which

different patterns can be identified and analyzed. It is a very useful way of

determining the "similarity" of a set of values from an "unknown: sample to a

set of values measured from a collection of "known" samples [12].


http://en.wikipedia.org/wiki/Correlation

http://en.wikipedia.org/wiki/1936

http://en.wikipedia.org/wiki/P._C._Mahalanobis

http://en.wikipedia.org/wiki/P._C._Mahalanobis

http://en.wikipedia.org/wiki/Distance

This method has been applied successfully for spectral discrimination in a

number of cases. One of the main reasons the Mahalanobis distance method is

used is that it is very sensitive to inter-variable changes in the training data. In

addition, since the Mahalanobis distance is measured in terms of standard

deviations from the mean of the training samples, the reported matching

values give a statistical measure of how well the spectrum of the unknown

sample matches (or does not match) the original training spectra [13].

In Mahalanobis, the distances are calculated in units of standard deviation

from the group mean. Therefore, the calculated circumscribing ellipse formed

around the cluster actually defines the one standard deviation boundary of that

group. This allows the analyst to assign a statistical probability to that

measurement [13].

Mahalanobis has been extensively used as a distance metric in Machine

Learning and Computer Vision applications.

1.4 Methodology & Software Life cycle:-

1.4.1 Methodology:-

The methodology applied in this OSV uses Cubic Spline Interpolation

technique to resample the signatures. After resampling velocity feature is

extracted from all the signatures and strokes are extracted on the basis of

velocity with the help of DTW approach. The verification process is carried

out by Mahalanobis Distance technique that compares two signatures and

verifies the signature as genuine or forgery.

1.4.2 Software Life Cycle Approach:-


Incremental Life Cycle Approach is used in this OSV model. In an

Incremental development, the system is developed in different stages, and

each stage consists of requirements, design, development, and test phases.

New functionality is added in each stage. This type of development allows the

user to see a functional product very quickly and also allows impacting what

changes are included in subsequent releases.

More flexible – inexpensive to change scope and requirements.

Easier to test and debug during a smaller iteration.

Risk Management – risk management is made easy because risky pieces

can be identified and handled during its iteration.

Each iteration is an easily managed milestone.

As development is done in small incremental steps i.e. requirements,

design, implementation and test, so it can also handle a very complex

project with incomplete initial understanding of requirements.

Figure 1.5 Incremental Life Cycle Model


CHAPTER 2

PROBLEM DEFINITION

2. Problem Statement:-


It is a challenge to any large modern organization to find a reliable means of

personal identification system. Signature is a behavioral biometric and it is a

behavioral characteristic that is learnt and acquired over a period of time rather

than a physiological characteristic. It has become a fundamental task in

today’s world to verify people’s identity in a fast, easy to use and user-friendly

way. Signature verification is a commonly accepted way to verify people’s

identity.

The problem of

Affects

The impact

A successful solution would be

The problem of verifying people’s identity

by their signatures...

The process of signature verification in a

reliable and efficient manner.

It helps organizations like banks to ensure

authorized and authentic access to their

systems or applications.

An efficient system that verifies people’s

identity in a fast, easy to use and user-

friendly way.

Table 2.1 Problem Statement


2.1 Deliverables and Development Requirements:-

2.1.1 Deliverables:-

In an online signature verification system, the first step is to enroll the users by

getting their signature samples (reference signatures). These reference

signatures should be stored in a database. Then, when a user claims to be a

particular individual, he/she presents a test signature to the system. This test

signature is verified with respect to the reference signatures of the database.

The dissimilarity value achieved, and is checked again against a certain

threshold. If the dissimilarity is above the threshold, the user is rejected,

otherwise accepted and authenticated. For judging the similarity between the

series some similarity measures are applied e.g. DTW, Mahalanobis Distance

Technique.

Development Requirements:-

Table 2.2 Development Requirements for MATLAB

MATLAB 7 or higher

Wacom Graphire 2 Tablet

MovAlyzer Software


CHAPTER 3

REQUIREMENT ANALYSIS


3. Functional Requirements:-

3.1 Data Acquisition:-

The system can take input from users by the help of a graphic tablet. This

input would be stored in the data base against each individual to be used later

on. For this type of system recommended hardware is Wacom graphics tablet.

The pen takes samples on interaction with the graphics tablet.

3.2 Signature Preprocessing:-

In the preprocessing module, the signatures are first resized. Then the

maximum correlation of the input signature is found out with the reference

signature. The maximum correlation value helps in finding out the angle at

which the original signature should be rotated to. We will not rotate the

resized input signature; instead the original input signature is rotated at the

desired angel. After the signature is rotated, it will be normalized as well. The

preprocessing makes the matching of the signatures easy as it makes the

angles of all the database signatures almost equal and all the signatures are

normalized.

3.3 Re-Sampling:-

The process of re-sampling is carried out to increase the number of samples of

the signature. As the wacom signature capturing device is designed to capture

samples at the rate of 100 samples per second. By the help of our re-sampling

module, we change this rate to 300 samples per second by including samples


in the signature at a distance of every 1/300 of a second. Re-sampling process

is done is by the help of cubic spline interpolation. Cubic spline makes the

signal continuous. This process also helps while extracting the velocity feature

from the signature.

3.4 Feature Extraction:-

Feature extraction is that requirement of the project on the basis of which we

would be able to proceed further. In feature extraction, we extract that feature

from our signature on the basis of which two signatures are going to be

compared. Velocity feature is extracted from the signatures. Every individual

has its own speed of writing of his/her signature. A forger might copy the

shape of an individual’s signature but it would be very difficult for him to

copy the speed of the person. Cubic spline interpolation helps us in extracting

the velocity feature from the signature as velocity is the first derivative so we

use the first derivative equation of cubic spline interpolation. Strokes are

calculated on the basis on velocity.

3.5 Stroke Extraction using the DTW approach:-

DTW is used to establish correspondences between the velocities of two

signatures. DTW is able to match two series of unequal lengths. To match two

series of unequal lengths, the series are warped together. This warping lets us

match the two series with greater efficiency. DTW is a very efficient

technique to find out the similarity between two series.

3.6 Verification:-

Verification is done by the help of Mahalanobis Distance verification

technique. Mahalanobis is a distance measure introduced in 1936.

Mahalanobis is able to identify and analyze different patterns. It determines


the similarity of one set with another. The system calculates the Mahalanobis

distance for every signature which is stored in the database with respect to a

mean signature and declares whether the results are genuine or forged.

3.7 Non-Functional Requirements:-

3.7.1 Usability:-

The usability of the software depends upon the following factor

The user should be trained properly.

The user must be familiar with the software, its functionality and all related

components.

The user must know how to interact with the software via its hardware and

software interface.

The system must be robust yet flexible enough to cater for different signatures

of the same person in different states of mind as the signature can be a little

different then.

3.7.2 Reliability:-

There is always variation in genuine signatures of a writer. The system’s

reliability depends on the fact that the system should be flexible enough to

handle small variations in the genuine signatures of the writer and the system

should be robust enough to identify even the skilled forgeries.

3.7.3 Performance:-

The system can show performance degradation if the following factors are not

met.


Since the user initiates the verification process, the time taken to perform the

signature should also be taken in account as the writing speed varies from

person to person.

System speed must be fast enough to cater for larger databases and to perform

verification tasks efficiently (e.g. preprocessing etc).

Memory should be large enough to cater for larger databases. Greater memory

size will result in faster speed while performing operations.

The prime factor however is the security. Its assurance depends upon the

verification algorithms applied that take into account the dynamic features and

that how well they can distinguish these features in a skilled forgery and a

genuine signature.


CHAPTER 4

ARCHITECTURE & DESIGN


SignatureStroke

Database

SignaturePreprocessing

Re-sampling

FeatureExtraction

Calculate dissimilarityAnd check genuineness

Test Stroke

Input testSignature

SignaturePreprocessing

FeatureExtraction

Accept or Reject theSignature

4. System Architecture:-

4.1 Data Acquisition

Figure 4.1 Architectural Design of the system


4.2 System Design:-

This section gives a more detailed and illustrated account of the steps involved

in this systems development. To help tie the somewhat complicated sequence

of operations together, we then give a summary of how each step is focused at

a particular aspect of the model. Finally we describe how a new candidate

signature is compared to the model signature.

4.2.1 Data Acquisition

Signatures are captured by the help of a capturing device. We have used a

graphics tablet from Wacom as capturing device. More precisely it is the

Intuos A6 model with USB (Universal Serial Bus) interface. It provides 100

samples per second containing values for pressure and the four degrees of

freedom: X and Y coordinates, pen azimuth and inclination for every sample [14]. Our pen captures samples only during the interaction of the pen tip with

the tablet. Pressure coordinate is also recorded at the same sample along with

the spatial coordinates. The signature information is digitized and stored in a

file as a matrix.

Figure 4.2 Wacom Graphics Tablet


Table 4.1 Specification of Wacom Graphire

Figure 4.3 MovAlyzer Software for acquiring data from tablet

4.2.2 Online Signature Database

Signatures in the database are stored as true and skilled forged signatures. The

forgeries in the database are skilled forgeries, as the impostor tries several

times to copy the genuine signature of the user before a close match is finally

acquired and stored in the database.


4.2.3 Signature Preprocessing

Every time we sign, we do it in a different way. The angle of the signature

may be changed by us while signing or the there may come a little variation in

our speed while signing. To get a representation of the signature independent

from these factors we have to take into account speed variation, different sizes

or rotations or different places within the tablet.

The preprocessing module resizes all the signatures according

to a reference signature of the database so that the resulting

signature has the same length or number of samples.

After resizing our signature to same number of samples, the signature is made

rotation invariant. The signer may sign in different angles while signing on the

digital tablet with respect to his position. Rotation invariance is carried out to

align the signature according to the reference signature. The more similar the

signatures are; the easier it is to compare them. Before making the system

rotation invariant, it is necessary to determine the angle to which the signature

has to be rotated. This process is done by Correlation. Correlation compares

the input signature with the reference signature and the highest correlation

value indicates maximum similarity which helps us in determining the angle at

which the signature is to be rotated.


Figure 4.4 Before Rotation

Figure 4.5 After Rotation

Figure 4.3 shows angle of signature before rotation

Figure 4.4 shows angle of signature justified after rotation


After rotation the preprocessing module makes size normalization.

Normalization is carried out to make the scale of the two signatures equal

which would help in comparing the signatures. Normalized signatures give a

better similarity score while the signatures that are different in shape and size

give a poor similarity score. In this system where the writer may have to sign

on tablet, the size of the signatures may vary so signature size normalization

may be required. Signatures can have different sizes depending upon the area

provided to sign. Normalization is done with respect to width, height or both.

Figure 4.6 Before Normalization


Figure 4.7 After normalization

Figure 4.6 shows the scale of the signature before normalization

Figure 4.7 shows the change in scale of signature after normalization

4.2.4 Re-Sampling

Re-sampling means to recalculate samples in a file at a different rate than the

file was originally recorded. Every time a person signs, the acquired number

of samples will be somehow different. Therefore, the points in the signature

are re-sampled to make the size of the files equal. To compare two signatures

with respect to their shape and in order to extract more reliable shape features,

they must be re-sampled. Digitizing tablets take samples at a constant rate, and

accordingly, the sampling rate provides a uniform time unit. The re-sampling

process creates equidistant spacing between each point, where the spacing

distance can be defined by the user. Cubic Spline Interpolation technique is

used to resample the signatures. The graphic tablet, which should be used,

provides 100 samples per second. Internationally it is recommended that

samples must be taken at 300 samples per second. So with the help of cubic

spline technique we will resample our signatures to 300 samples per second.


Cubic spline is used to draw smooth curves through a number of points.

Splines are known as piece-wise defined functions whose individual curves

meet at the points. Cubic spline is used to make the function continuous. This

continuity later helps us in finding out the velocity feature of the signature.

General form of the n-1 cubic equations:

for i=1, 2, … , n-1

Where a, b, c and d are the weights or coefficients attached with the spline in

order to draw a smoother curve. Coefficients on the cubic polynomials are

used to interpolate the data.

The first and second derivatives of these n - 1 equation’s are fundamental to

this process, and they are

[24]

for i=1, 2, … , n-1

The first derivative equation of cubic spline would be used to calculate

velocity feature of the signature.

We will define the distance between consecutive x-values to be h.

h=x2 – x1= …= xn – xn-1

These equations can be much simplified by substituting Mi for si’’ ( xi ) and

expressing the above equations in terms of Mi. This makes the determination

of the coefficients a, b, c, and d a much easier task. The substitutions of M and

h into the derivations lead to the equations of our coefficients.


[24]

These systems can be handled more conveniently by putting them into matrix

form as follows.

[24]

Cubic Spline is of three types.

1. Natural Spline

2. Parabolic Runout Spline

3. Cubic Runout Spline


In Natural Spline the ends of the spline curve extend beyond the boundaries of

the data and become linear. Second derivative is zero at the end points in

natural spline [15].

Natural spline results in a curve degrading to a line at the end points.

Matrix Equation for Natural Spline

[24]

In Parabolic Runout Spline, the spline becomes a parabolic curve over the first

and last intervals. The parabolic spline imposes the condition that the second

derivative at the endpoints, M1 and Mn, be equal to M2 and Mn-1 respectively [15].


The result of this condition is the curve becomes a parabolic curve at the

endpoint. Parabolic spline is useful for periodic and exponential data.

Matrix Equation for Parabolic Runout Spline

[24]

Cubic Run-out Spline has the most extreme endpoint behavior. It causes the

spline to reduce to a single cubic curve extending beyond the endpoints. It

assigns M1 to be 2M2 - M3 and Mn to be 2Mn-1 – Mn-2 [15].

Matrix Equation for Cubic Runout Spline


[24]

Figure 4.8 Before resampling


Figure 4.9 After resampling

Figure 4.8 shows the original samples of signature

Figure 4.9 shows the resampled points in the signature after cubic

spline

4.2.5 Feature Extraction

In case of OSV, in addition to the trajectory co-ordinates of the signature, the

digital tablet is also capable of capturing the behavioral characteristics of the

signature like pressure at pen tip, acceleration and pen-tilt. Using these

characteristics more than 40 features have been used for signature verification

in various application areas.

Features can be classified into two types: global and local. Global features are

features that refer to a signature as a whole; for example signing speed,

signature bounding box, number of strokes in the signature, signing flow etc.

Local features correspond to a specific sample point along the trajectory.

Some of the commonly extracted local features are the x and y offsets relative


to the first point on the signature trajectory, x and y coordinate differences

between two consecutive points, curvature differences between two

consecutive points, critical points of the signature trajectory [16].

It is relatively easier to only extract and use global features for verification as

it requires less computational resources than local features. However, global

features alone are not discriminative.

Table 4.2 Global Features for signature verification

In the purposed system we will experiment with the velocity feature of the

sample points on the signature trajectory.

Cubic spline interpolation has two continuous derivatives, the first of which is

used in computing the velocity of the signature.

Using the first derivative of the cubic spline technique to find the velocity of

the signature.

After calculating the velocity, we have to truncate those values in the velocity

matrix that are below 15%. So we can find a threshold value accordingly. We

will also experiment other truncation limits as well but 15% is preferred as in

this case data loss is minimum and strokes can also be easily extracted. By the

help of the threshold value achieved, we truncate the below 15% values from


the signature’s x, y and z vectors. On the basis of velocity we extract strokes

from the signature.

Figure 4.10 Velocity Before

Figure 4.11 Velocity after

Figure 4.10 shows the velocity signal of the signature

Figure 4.11 shows the velocity signal of the signature after truncating

values below 15%


4.2.6 Stroke Extraction using the DTW Approach

There is always variation in genuine signatures of a writer. Signatures having

different lengths imply feature vectors of different lengths. Therefore doing

the simple element wise comparison of signatures will not provide us with

good similarity score. Algorithms like Dynamic Time Warping are used for

the comparison of two signatures based on their feature vector representations.

These algorithms take care of the cross-over alignments between the points

and variation within genuine signatures [17]. The DTW algorithm gives the

dissimilarity score of the two signatures which is also known as the distance

between the two signatures. Strokes are calculated with the help of DTW from

the signature.

DTW is widely used in similarity measure of sequences because of its

elasticity and robustness. Two sequences having similar shape but are not

strictly aligned along the time axis cannot be matched using the traditional

one-one mapping techniques.

After the strokes are encoded, we need to align the two encoded strings to

determine a measure of similarity between them. Considering these sequences

as time series, DTW is applied on them that align the series such that the

distance is minimized by “warping” the axis of one or more strings.

The DTW algorithm proceeds in two stages. First to construct an n x m

distance matrix is created, one signature is placed across the top of the matrix

and the other signature is placed across the left side of the matrix. In the

second stage, we find a shortest path alignment between opposite corners of

the matrix.


Figure 4.12 DTW Between two time series

The distance for every point in one signature to every point in the other

signature is represented in this matrix. Then a path in the matrix is found

which starts from cell (1, 1) to cell (n, m). An ideal alignment between points

in the signatures is implied by the shortest path found through the matrix. As

DTW does not map elements by one-one mapping rather it does the one-many

and many-one mapping, so the path followed by DTW may goes several cells

horizontally along X or vertically along Y. This shows the flexibility and

strength of DTW. The distance of this path determines the similarity of two

signatures. The rule goes as; “the shorter this distance, the more similar two

signatures are, and for ditto identical signatures this distance will be zero” [18].

Dynamic programming is used to calculate the shortest path recursively. The

shortest path from a given cell is simply the distance in the current cell along

with the smallest distance of a neighboring cell [18]. After calculating the

velocity, we can use DTW the velocities of two signatures i.e. the reference

and test signature. Strokes have already been calculated for the reference

signature.


4.2.7 Verification

To verify whether the writer is a true user or an impostor we calculate the

similarity between its signature and the trained model by Mahalanobis

Distance Technique. This technique was developed in 1936 by P.C.

Mahalanobis. This is a very efficient technique to compare two data sets and it

gives a very accurate similarity score. Mahalanobis distance technique

measures the distance of points to a center taking into account the variability

and correlation of the data [23].

Following equation is used to calculate Mahalanobis Distance. μ represents the

mean vector while Σ is the covariance matrix. A mean is calculated from

genuine signatures of the individual that are stored in the database.

x represents the signature vector. Covariance matrix is calculated for the

signature with respect to its mean. In DTW, we have found the strokes of

genuine and forgery signatures with respect to a reference signature. We can

find the Mahalanobis distance of these signature strokes with respect to the

mean signature calculated.

After this we have to find the Mahalanobis distances of all the signatures in

the training database. We take average of these distances to find a threshold

value that would confirm a test signature as genuine and forgery. The test

signature also passes through all the OSV phases and finally reach verification

phase. Here its Mahalanobis distance value is calculated, it the value is above

the threshold the signature is declared as a forgery else it is a genuine

signature of the individual.


Mahalanobis distance removes several of the limitations of the Euclidean distance.

1. Scaling of the coordinate axes is automatically catered for.

2. It corrects for correlation between the different features [22].

3. It can provide both curved and linear decision boundaries.

Figure 4.14 Classification of genuine and forgeries using Mahalanobis

Figure 4.14 shows the threshold dotted line that separates genuine and forged

signatures. The test signature plotted above the dotted line is declared as forgery

or if it is below the dotted line, the signature is declared as genuine.

4.3 Major Design Goals & Constraints:-


http://www.cs.princeton.edu/courses/archive/fall05/cos436/Duda/PR_lims/PR_lims.htm

4.3.1 Design Goals:-

An online signature database is to be created that stores all the genuine and

forged signatures of an individual.

4.3.2 Constraints:-

System speed must be fast enough to handle large databases.

Memory must be large enough to support the database and the system

functionality.


CHAPTER 5

TESTING & EVALUATION


5. Verification and Validation

In this project the proposed system should be provided with a test signature of

an individual. The signature passes through all the phases of the development

and a mahalanobis distance value is calculated for that test signature. Now this

mahalanobis value is checked against the database and on the basis of the

result achieved the signature is verified to be genuine or declared as forgery.

5.1 Usability Testing

OSV is a system that can be applied in many organizations that need user

verification before access to their systems like security zonesin, banks, can be

used for ATM (Automated Teller Machine) verification. Internationally some

banks have adopted the system of OSV using different models barclay’s

PinsEntry is an example of that. The features that this software should extract

from the signature and the verification techniques that we discussed make it a

very reliable software for verifying identity of some individual.

5.2 Intergration

All the modules the system work in accordance with each other so if there is a

problem in design on one no other module will run as well so they all need to


be perfect. When combined together the system should take input from the

user. Apply preprocesing on it, then resample it. Extract velocity feature from

the signature and find out the strokes with the help of DTW technique. Then

verification is applied on the test signature which declares it as genuine or

forgery.

5.3 System Testing

In system testing, when a user supplies a test signature to the system claiming

to be a particular individual, the system verifies that test signature with the

template signature stored in database for that individual. If the signature is a

genuine signature, the system declares it as a genuine and if an imposter is

trying to access the application with the signature of the individual, the system

will recognize that the signature is not true and declare it as forgery.

5.4 Hardware Configuration for Testing

Wacom Graphire Tablet and Stylus are needed to capture the signature of the

individual to verify his/her identity.


CHAPTER 6

CONCLUSION


6. Conclusion:-

In this research paper we have studied a proposed system to prevent identity

fraud, tough this system is not widely used, however its used at some very

secure places, the proposed system has its pros and cons like every system, the

pros of the proposed system are that it can help stop identity fraud but not

entirely stop it , The biggest con of it is that banks or other online merchants

have to start collecting data i.e. signatures from their customers in electronic

form and have to provide them with a special device which costs money hence

increasing the initial and maintenance costs, what’s recommended is that such

a system should be produced which will have the customer’s pins entry system

e.g. Barclays and also have a small finger print reader which will be issued to

a specific customer and will have that customer’s finger print stored in it , but

this limits the use of that device to one specific person hence making it less

portable, but through mobile communication it can be connected to a central

server containing the finger prints hence increasing its portability and

increased security of biometrics.


7. Biblography:

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Muralidharan and Dr. Subbarao Wunnava, Ph.D, P.E.

Second LACCEI International Latin American and Caribbean

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Hansheng Lei, State University of New York at Buffalo, Venu

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By Alisher Kholmatov and Berrin Yanikoglu Oct. 2004

[17] Signature Verification: A Popular Biometric technology By Neelima

Muralidharan and Dr. Subbarao Wunnava, Ph.D, P.E.

Second LACCEI International Latin American and Caribbean

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[18] Dynamic Signature Verification using Local and Global Features

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online signature system

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