IMPLEMENTATION AND ANALYSIS OF A HANDWRITTEN

SIGNATURE VERIFICATION TECHNIQUE

Alan McCabe

Fern Computer Services, Pty Ltd.

Belfast, Ireland

Jarrod Trevathan

School of Maths, Physics and Information Technology

James Cook University

Keywords:

Biometric security, authentication, dynamic features, string comparison, extrema avoidence.

Abstract:

There is considerable interest in authentication based on handwritten signature veriﬁcation because it is su-

perior to many other biometric authentication techniques such as ﬁnger prints or retinal patterns, which are

reliable but much more intrusive. The paper details a number of experiments using a signature verﬁcation

technique which is unlike any other reported in literature. Speciﬁcally, characters are used to represent various

features of a signature image allowing the use of existing and proven string distance metrics to determine

distances between signatures. Extensive testing shows that our proposed system is comparable with, and in

many aspects better than the highest quality signature verﬁcation techniques presented in literature.

1 INTRODUCTION

Biometric security systems such as ﬁnger prints and

retinal scanning are increasingly being used as a

means of authenticating an individual’s identity. De-

spite the reliability of these systems, they are some-

what intrusive and are often met with resistance by

those being authenticated. A more natural and ac-

ceptable authentication method is to verify an indi-

vidual’s handwritten signature. This involves captur-

ing the signature via a graphics tablet and compar-

ing this with a reference ﬁle. The process involved

is essentially the same as a credit card transaction,

however, the procedure is automated and the ultimate

veriﬁcation decision is made by a computer program

rather than relying on human judgment. (See (Mc-

Cabe, 2000; Trevathan and McCabe, 2005).)

This paper presents a Handwritten Signature Veri-

ﬁcation (HSV) system which extends an approach de-

scribed by (Gupta and Joyce, 1997a). Their approach

involves abstracting the signature data into a character

string representing the more discriminating signature

features. This approach’s difﬁculty lies in determin-

ing the type of features to capture, how to extract them

from the signature data, and how to incorporate the

extracted features into the character string.

This paper aims to improve the performance of the

techniques developed by (Gupta and Joyce, 1997a)

by combining shape and dynamics of the signature

in a number of different ways using a single-stage ap-

proach. The proposed HSV system’s goals include:

1. Uses no more than ﬁve reference signatures.

2. Does not have unrealistic resource requirements.

3. Thoroughly tested.

4. Can store reference signature information on a

credit card or a smart card.

This paper is organised as follows: Section 2 pro-

vides background relating to the approach used by our

HSV system. Section 3 presents the methodology be-

hind the proposed HSV system, along with a descrip-

tion of various novel approaches taken to deal with

problems encountered. It also evaluates the HSV sys-

tem’s performance and its limitations. Section 4 pro-

vides some concluding remarks.

2 BACKGROUND

This section describes speciﬁc approaches towards

solving the HSV problem and the motivation for our

proposed HSV system.

HSV involves the following ﬁve phases: data ac-

quisition, preprocessing, feature extraction, compari-

son process, and performance evaluation. During the

McCabe A. and Trevathan J. (2007).

IMPLEMENTATION AND ANALYSIS OF A HANDWRITTEN SIGNATURE VERIFICATION TECHNIQUE.

In Proceedings of the Second International Conference on Security and Cryptography, pages 48-58

DOI: 10.5220/0002121500480058

 SciTePress

ﬁrst three phases most methods would generate a ref-

erence signature (or a set of reference signatures) for

each individual. This requires a number of user sig-

natures to be captured at enrollment/registration time

and processed. In the discussion that follows, it is

assumed that there is only one reference signature.

When a user claims to be a particular individual, they

present a test signature, which is compared with the

reference signature for that individual. The differ-

ence between the two is then computed using a dis-

tance measure. If the distance is above a predeﬁned

threshold value, then the test signature is rejected as a

forgery, otherwise it is authenticated.

The following notion for performance evaluation

is used throughout this paper:

• r: the threshold value. (The threshold is r times

the standard deviations plus the reference mean.)

• F-accept: number of forgeries accepted as gen-

uine.

• G-reject: number of genuine signatures rejected

as forgeries.

• FAR: false acceptance rate expressed as a percent-

age.

• FRR: false rejection rate expressed as a percent-

age.

• ER: total error rate (FAR + FRR).

Performance evaluation of the proposed technique

is very important and normally researchers use a set

of genuine signatures and forgery attempts collected

by them (or by someone else), and determine the

FRR and FAR for the technique given the signature

database. Obtaining good FAR estimates is very dif-

ﬁcult since real-world successful forgeries are impos-

sible to obtain. Performance evaluations rely on two

types of forged signatures. A forgery may be skilled,

if it is produced by a person other than the individ-

ual whose signature is being forged when the forger

has had access to one or more genuine signatures for

viewing and/or practice. A forgery is called zero effort

or random when either another person’s genuine sig-

nature is used as a forgery, or the forger has no access

to the genuine signature and is either only given the

name of the person whose signature is to be forged, or

just asked to sign any signature without even knowing

the name. Tests on random forgeries generally lead to

a much smaller FAR than on skilled forgeries.

There are quite a large number of other systems

which deal with HSV. However, almost all of them

exhibit several shortcomings. This work’s main prior-

ity is to avoid these shortcomings and produce a sys-

tem which not only performs well, but is suitable for

real world applications. Four such pitfalls include:

Use of Too Many Reference Signatures – there is

a direct correlation between the number of reference

signatures and the quality of the reference created us-

ing those signatures. It is very important not to as-

sume the existence of too many reference signatures,

as it may not always be possible to obtain them.

Failure to Combine Static and Dynamic Features

– a signature is made up of features which are both

static (i.e., shape related such as the length of long

strokes) and dynamic (i.e., motion related such as the

velocity and pin tip acceleration at various stages).

Unrealistic Resource Requirements – although per-

forming huge amounts of preprocessing and calcula-

tions may result in high levels of reliability, it is im-

portant that the signature veriﬁer is fast. It is not ac-

ceptable for a system user to have to wait a few min-

utes every time they desire to verify a signature.

Insufﬁcient Testing – although most authors report

error rates in the form of both FAR and FRR, the level

of testing style varies greatly throughout literature,

making comparisons between different systems difﬁ-

cult. A realistic testing level must involve a high num-

ber of tests for false rejection (genuine signatures be-

ing rejected as forgeries) and false acceptance (forg-

eries, which should be high in both quality and num-

ber, being accepted as genuine signatures). In addi-

tion, it is not realistic to remove signatures from test-

ing simply on the basis that they do not work well

with the desired system, nor is it realistic to non-

randomly choose signatures to be used as a reference,

testing or otherwise. Finally, only one attempt should

be allowed for a user signature to be veriﬁed – many

systems allow a user three attempts to verify a signa-

ture and this is generally not acceptable.

There are three main categories which HSV sys-

tems can fall into: point-to-point comparison, feature

values comparison, and capturing signature shape.

Point-to-Point Comparison compares a test signa-

ture with a reference signature by comparing different

parts of the signature separately and combining these

comparisons to achieve an overall similarity measure.

A number of investigations suggest that point-to-point

techniques can lead to good results but the techniques

suffer from difﬁculties due to variations in the gen-

uine signatures of each individual. In order to make

more effective comparisons, a system must perform

some type of alignment of the test and reference sig-

natures in an attempt to “line-up” the corresponding

parts of the signatures. This alignment may in turn

create problems of its own, since forgeries will un-

dergo alignment as well as genuine signatures.

IMPLEMENTATION AND ANALYSIS OF A HANDWRITTEN SIGNATURE VERIFICATION TECHNIQUE

Figure 1: The valley/peak characters associated with the let-

ter ‘S’.

It appears that highly reliable HSV systems are

unlikely to be based on such techniques. Some low

error rates have been reported, but the testing proce-

dure performed on these systems were quite inade-

quate. The best results so far for well tested systems

seem to give total error rates of just over 15%. Also,

the systems have not been tested for zero-effort FAR.

Feature Values Comparison is relevant to this pa-

per, because many features are captured implicitly in

the representation. For example, the number of turn-

ing points, the pen-up time and the total time taken

to sign. There are two important issues within this

type of approach. Firstly, it is necessary to decide on

the number and type of features to capture, and sec-

ondly it is important to choose an appropriate means

of comparing those feature values.

Most HSV techniques are based on statistical fea-

tures capturing mainly dynamic details of the signa-

ture. The feature-based techniques work remarkably

well without having to store the entire signature, but

there is a limit to the performance level which can

be obtained. Most HSV proposals have error rates of

more than 10% and 15%. These systems have not

been tested for a zero-effort FAR.

Capturing Signature Shape - Most static HSV is

based on capturing the shape or some aspects of the

signature’s shape. Dynamic HSV involves capturing

details relating to signature dynamics (e.g., pen tip ve-

locity, acceleration, etc.). This category essentially is

a combination of static and dynamic HSV in that it

uses dynamic information and signature shape.

The (Gupta and Joyce, 1997a) technique assumes

that the signature is captured using a device capable

of obtaining the (x,y) coordinate pairs several times

per second (usually of the order of 200 samples per

second). The x and y data is then extracted into sepa-

rate vectors (known as proﬁles). The veriﬁcation tech-

nique can be explained using the following symbols:

A for a peak of the x proﬁle B for a valley of the x proﬁle

C for a peak of the y proﬁle D for a valley of the y proﬁle

A signature may now be processed to identify all

the peaks/valleys in the x and y proﬁles, and each of

the proﬁles may then be represented by a string of

symbols representing the peaks/valleys. The x pro-

ﬁle was then represented by a string ABABABAB...

and the y-valley proﬁle by a string like CDCDCD-

CDC... with each peak and valley in the two proﬁles

having a time associated with it (which was not dis-

played in this simple representation). The peak and

valley times may then be used to interleave the x and y

proﬁle representations so that the signature shape was

represented by a string like DACBADBC. This simple

example indicates that the signature’s x and y proﬁles

together had only nine peaks and valleys (typically

there might be 50 or more) that were x-peak followed

by y-peak, then an x-valley, etc. Another way to look

at this representation was to view it as a description

of the pen motion, i.e., from the initial position (x-

peak) the pen ﬁrst moved northwest to reach a y-peak

then southwest to reach an x-valley and then turned

around and moved southeast to reach an x-peak and

y-valley and so on. DACBADBC therefore represents

a pen motion something similar to the letter S writ-

ten from the top to bottom (see Figure 1). The rep-

resentation would be reversed if the letter S was writ-

ten from the bottom to the top. The representation

does not capture the curvature or the size of the curves

that make the letter S and therefore DACBADBC was

a representation for many curves that look somewhat

similar and thus the representation provides consider-

able ﬂexibility and tolerates considerable variation in

the way the pen moves. The representation captures

the shape and the direction of pen movement during

signature writing. Given the ﬂexible representation,

similar representation should always be obtained for

a person’s signatures in spite of minor variations in

the genuine signatures.

A small number of systems have been built us-

ing techniques for capturing signature shape in a way

that is quite different than the approach used in the

point-to-point comparisons. Most shape systems suf-

fer from poor performance when skilled forgeries are

tested, since skilled forgers are often able to repro-

duce the shape of the signature quite well. Simple

techniques which capture shape and then compare it

therefore are unlikely to produce high performance

for skilled forgeries. This is in contrast to the per-

formance of the dynamic feature-based techniques

which perform very well when skilled forgeries are

tested, since the dynamics of skilled forgeries are of-

ten very different than that of the genuine signatures.

3 IMPLEMENTATION

This section discusses the basic methodology, design,

implementation and performance evaluation of our

HSV system.

SECRYPT 2007 - International Conference on Security and Cryptography

The major HSV software components are as follows:

1. Input component: responsible for reading in the

signature data from signature ﬁles to the program.

2. Preprocessor: detects the genuine valleys/peaks

in the signature data read in during input and in-

dexes them according to their position in the sig-

nature.

3. String generator: takes the ordered set of valleys

and peaks as well as their positions and produces

a character string representing the signature data.

4. String comparison: uses the character strings to

compare two signatures and determines whether a

signature is to be accepted or rejected.

5. Report generator: collates the accepted/rejected

signatures and obtains error rates for false accep-

tance and false rejection. A detailed report for

each individual in the database, as well as for the

database as a whole is then written to an output

ﬁle.

The performance evaluation of our proposed HSV

system uses the same database employed by (Gupta

and Joyce, 1997b). The database contains a total of

1229 signatures taken from 59 users. There are 904

genuine signatures, each user providing usually 15

genuine signatures. There are also 325 highly skilled

forgeries, about ﬁve for each user. Further details of

the database can be found in (Nelson et al, 1994). In

most experiments ﬁve signatures were used for each

reference leaving 904 - (5× 59) = 609 genuine signa-

tures for computing FRRs.

Experimental Protocol

An experimental protocol similar to that described

in (Gupta and Joyce, 1997b) was used. The protocol

remained constant throughout the experimentation.

To create a reference signature, the ﬁrst ﬁve sig-

natures for each user were taken from the database

and transformed into strings using the technique be-

ing evaluated. The ﬁve strings were then compared

with each other using a string distance algorithm and

the ten distances were obtained. The reference mean

and the reference standard deviation of the distances

were computed. These ﬁve signatures, for each user,

are not used again as test signatures.

The remaining genuine/forged signatures for that

user are tested against the ﬁve reference signatures.

This is done by determining the distance between the

test signature string and each of the reference strings,

and ﬁnding the minimum of these distances. If this

minimum distance (known as the test distance) is

smaller than the threshold distance, the test signature

is accepted, otherwise it is rejected.

Various values of threshold were used in perfor-

mance evaluation; the threshold being the sum of the

reference mean and r times the reference standard de-

viation. The value of r depends on the type of applica-

tion that the HSV system is to be used for. If security

(low FAR) is the major concern, then a small value for

r will be used. Alternately, if a low FRR is the major

concern, then a larger threshold is used.

Comparing Two Strings

The importance of selecting and implementing

an appropriate algorithm for ﬁnding the distance be-

tween the two strings should not be underestimated,

since performance relies on the string distance al-

gorithm to determine accurately the distance be-

tween signatures’ string representations. The Wagner-

Fischer (WF) string distance algorithm (Wagner and

Fischer, 1974) best suited our purpose.

The WF dynamic-programming method is based

upon successively evaluating the distance between

longer and longer preﬁxes of the two strings until the

ﬁnal result is obtained. The partial results are com-

puted iteratively and are entered into an (m + 1) ×

(n + 1) array (where m and n are the lengths of the

two strings being compared), leading to O(mn) time

and space complexities.

The algorithm involves calculating the cost of

transforming one string into another in an iterative

fashion. For example, the cost of transforming one

string into an empty string to another empty string

is obviously zero, the cost of transforming from one

empty string with a single character is one. More gen-

erally, if the cost of transforming x(1, i) into y(1, j −

1) is known, then the cost of transforming x(1,i) into

y(1, j) may be obtained by adding the cost of insert-

ing y

. Similarly, if the cost of transforming x(1,i− 1)

into y(1, j − 1) is known, then the cost of transform-

ing x(1, i) into y(1, j) may be obtained by adding the

cost of replacing x

with y

. The primary advantage

of the WF algorithm for use in this application is that

the string AB can be transformed into the string BA at

a cost of only one. It is possible to use the iterative

nature of this algorithm to create a matrix where the

elements contain the cost of transforming from one

substring to another.

For example, suppose there are two character

strings ABCDA and BADCA, then the WF matrix

looks like:

A B C D A

0 1 2 3 4 5

B 1 1 1 2 3 4

A 2 1 2 2 3 3

D 3 2 2 3 2 3

C 4 3 3 2 3 3

A 5 4 4 3 3 3

IMPLEMENTATION AND ANALYSIS OF A HANDWRITTEN SIGNATURE VERIFICATION TECHNIQUE

The overall distance between the two strings

ABCDA and BADCA is 3.

Valley and Peak Detection Algorithm

A simple valley and peak detection algorithm

would involve detecting a valley (and similarly

a peak), if there was a ‘down’ motion, followed

possibly by some number of ‘ﬂats’ (possibly zero),

followed by an ‘up’ motion. For example, suppose

the following data existed in the y direction:

...,102,101,101,101,102,104,105,...

at times ...,t,t + 1,t +2,t + 3,t +4,t +5,t + 6, ...

The data represents a valley at 101 at times t + 1

(or t + 2 or t + 3). However, problems occur when

the graphics tablet used produces a set of values like

...,102,101,102,101,102,... which appear due to the

hardware used and due to “false” pixels. False pixels

occur when the line representing the pen’s tip goes

through the middle of the Cartesian grid represent-

ing the pixels of the signature capturing hardware (see

Figure 2). If the written line goes exactly in between

two pixels, then it is possible that the device will read

the position as being sometimes on the left pixel and

sometimes on the right. The pixel chosen by the de-

vice may be inﬂuenced by the way the signer is hold-

ing the pen, the pen’s tilt or the pressure being applied

by the user. So the data (say in the y direction) may

look something like this:

...,104,102,101,100,101,100,101,102,104,...

Using the simple valley and peak detection algo-

rithm, the above data returns a valley, followed by a

peak, followed by another valley. Does this data have

three turning points or does it have only a single val-

ley? Now suppose the data looked like this:

...,100,100,100,99,100,100,100,...

The simplest approach to removing the false turn-

Figure 2: Example of how false turning points can occur

using naive valley/peak detection algorithms.

ing points involved removing valleys and peaks which

had a depth or height less than some threshold. The

valley depth (and similarly a peak) was measured in

pixels and was calculated as the difference between

the height of the valley and the height of the smallest

of the immediately neighbouring peaks. Four experi-

ments were conducted using this method for removal

of valleys and peaks, which made use of the qual-

ity control technique. Valleys (and similarly peaks)

were removed if a valley’s depth was below a cer-

tain threshold value (measured in pixels). The four

different experiments used four different thresholds –

none, two, three and four. The optimal overall error

rate as well as the breakdown into FAR and FRR are

presented for each of these thresholds in Table 1. As

can be seen from this table, simple removal of small

valleys and peaks clearly has a detrimental effect on

veriﬁcation accuracy. The only conclusion that can be

drawn then is that valleys and peaks which have only

a very small depth or height are important character-

istics of the signing style.

Even though small valleys and peaks hold impor-

tant detail relating to the signature’s characteristic,

something still needs to be done to remove “false”

turning points. To do this, a different approach was

adopted in which, put simply, at least two “down”

events had to be followed by two “up” events for a val-

ley to be detected. This was slightly different in that

instead of considering the size of the valleys/peaks,

the relative positions of the pen are being considered.

That is, if the pen tip moves in a downward direc-

tion on two samples (without being interrupted by an

“up”), then this is thought to be the start of a gen-

uine valley. If the pen tip then moves back up for two

samples (without being interrupted by a “down”), the

genuine valley is completed and a valley is stored.

See (McCabe and Trevathan, 2007) for a complete

discussion of valley and peak detection algorithms de-

veloped in conjunction with this research.

Performance of the Gupta and Joyce System

Table 1: How removal of small valleys and peaks effects

error rate.

Threshold FAR FRR Overall

None 4.0% 3.1% 7.1%

2 8.3% 9.4% 17.7%

3 9.2% 10.3% 19.6%

4 10.2% 9.2% 19.3%

SECRYPT 2007 - International Conference on Security and Cryptography

Table 2: Initial results using the characters A, B, C, D, F.

r F-accept G-reject FAR FRR ER

0.0 45/325 86/609 13.8% 14.1% 27.9%

0.5 69/325 41/609 21.2% 6.7% 27.9%

1.0 107/325 22/609 32.9% 3.6% 36.5%

1.5 154/325 12/609 47.4% 2.0% 49.4%

2.0 188/325 6/609 57.8% 1.0% 58.8%

The (Gupta and Joyce, 1997a) technique was im-

plemented following the experimental procedure de-

scribed in their paper and the results presented in Ta-

ble 2 were obtained. The 27.9% overall error rate was

high because the technique was not capturing enough

detail to discriminate well between signatures (only

the ordering of turning points and the position and du-

ration of pen-ups were captured). Table 2 shows that

the FAR was the major problem, as it was too easy

for a forger to produce the correct ordering of turning

points, even though the actual signature may not be a

very accurate forgery.

Utilising Distance and Direction Characters

Capturing the optimal level of signature detail is

important to the overall success of the signature veriﬁ-

cation. Capturing too much detail leads to a high FRR

since each genuine signature needs to be very similar

to the reference signature(s), while capturing too lit-

tle detail leads to a high FAR because it is easy for the

forgeries to meet the minimal requirements. Table 1

shows that the FAR is high even for low threshold

values. This suggests that the technique is capturing

the shape well since most skilled forgeries reproduce

the signature shape well. Furthermore, the technique

is not capturing enough details other than the shape

which could have reduced the skilled forgeries’ FAR.

Thus a modiﬁcation of the technique that capture fur-

ther signature details should improve performance.

Previously, only the ordering of the valleys and

peaks in a signature were being captured and this ap-

proach allowed the skilled forgers to get the string

representation similar to the genuine signatures, even

though the forged signature was not an exception-

ally good forgery. It was therefore decided to include

more detail about the signature shape by including in-

formation about the stroke distances in the representa-

tion, which forces a forger (and genuine signer) to get

not only the ordering of the valleys and peaks correct,

but also the spacing between them. Additionally, the

location and duration of “pen-up” occurrences were

added to the signature representation.

How would the stroke distance between the turn-

ing point characters be represented? The distance it-

self may be computed in two different ways. It may be

computed by ﬁnding the distance between the coordi-

Table 3: Error rates using the characters A, B, C, D, P, I,

J, K, L... and using the time interval as the distance metric

(distance intervals based on global characteristics).

r F-accept G-reject FAR FRR ER

0.0 48/325 134/609 14.8% 22.0% 36.8%

0.5 55/325 109/609 16.9% 17.9% 34.8%

1.0 60/325 95/609 18.5% 15.6% 34.1%

1.5 71/325 67/609 21.8% 11.0% 32.8%

2.0 77/325 52/609 23.7% 8.5% 32.2%

Table 4: Error rates using the characters A, B, C, D, P, I,

J, K, L... and using the path length as the distance metric

(based on global characteristics).

r F-accept G-reject FAR FRR ER

0.0 51/325 135/609 15.7% 22.2% 37.9%

0.5 57/325 110/609 17.5% 18.1% 35.6%

1.0 60/325 96/609 18.5% 15.8% 34.3%

1.5 74/325 69/609 22.8% 11.3% 34.1%

2.0 81/325 55/609 24.9% 9.0% 33.9%

nates of the two successive valleys/peaks. It may also

be found distance in terms of the number of samples

between successive valleys/peaks. Effectively then,

the second alternative is determining the time lapsed

between the turning point characters. A vector repre-

senting all of the distance values between the turning

points of the signature image may then be obtained.

Using this approach, whatever distance technique

is used, it is necessary to compute distance between

vectors that are often of different sizes which is a dif-

ﬁcult problem. One approach for comparing two vec-

tors was to simply drop the smallest integers from the

larger vector until the two lengths are the same. For

example, suppose the following two vectors represent

the distances between the turning point characters in

two instances of a signature:

1 18 6 28 31 2 16

16 4 32 29 16

If the smallest numbers from the longer vector are re-

moved, the result is:

18 6 28 31 16

16 4 32 29 16

This idea has some merit, but difﬁculties can arise if

the process leads to poor alignment of the vectors,

therefore the approach was not investigated further.

Instead, it was decided to map the integers to charac-

ters and include the distance information in the string

representation itself.

To map the integers to characters, it was decided

to ﬁrst divide the distances into four classes. If the dis-

tance fell in the smallest quarter of the distances, the

character I was inserted into the string, next higher

quarter distance were represented by a J, and simi-

IMPLEMENTATION AND ANALYSIS OF A HANDWRITTEN SIGNATURE VERIFICATION TECHNIQUE

Table 5: Error rates using the characters A, B, C, D, P, I,

J, K, L... and using the time interval as the distance metric

(distance classes set automatically).

r F-accept G-reject FAR FRR ER

0.0 23/325 100/609 7.1% 16.4% 23.5%

0.5 33/325 59/609 10.2% 9.7% 19.8%

1.0 46/325 35/609 14.2% 5.7% 19.9%

1.5 64/325 26/609 19.7% 4.3% 24.0%

2.0 79/325 13/609 24.3% 2.1% 26.4%

larly the next higher distances were represented by K

and L. A pen-up character P was also included in the

string whenever the pen tip was not in contact with

the writing tablet. Pen-up time was divided into small

and large, where small pen-ups were represented by

a single P and large pen-ups represented as PP. The

limits for each of the four distance classes were mutu-

ally calculated using the distance values for all users

in the database. These limits were found by building

a frequency vector for the distance values, and then

dividing the distance values into four equal groups

based on their magnitude, and assigning a symbol to

each group. The limits for the distance classes were

then used globally on the signature database to ex-

plore this approach’s merit. The initial limits for the

four classes for time and path length distances, and

for pen-up occurrences were:

Time: 0 − 7; 8− 15; 16− 24; > 24

Path Length: 0− 25; 26− 60; 61− 120; > 120

Pen-Up: < 8; > 8

String representations of signatures were gener-

ated using the distance characters and the turning

point characters. Performance evaluation of the tech-

nique using the time interval and the path length as

the distance metric resulted in overall error rates of

32.2% and 33.9% respectively (see Table 3 and Ta-

ble 4).

The above classes used in developing representa-

tions for the distance and the pen-up time were based

on heuristics. Since the distances and the pen-up

times tend to be quite different for different individu-

als, it was decided to select the classes based on typi-

cal distance values for each individual. To do this, ﬁve

reference signatures for each individual were used,

and all of the distance values in between turning point

characters were obtained. These distance values were

divided into four equal groups according to their mag-

nitude and each group assigned a symbol. The small

and large pen-up time intervals were also found in

a similar fashion by dividing the pen-up time sizes

into two equal groups according to magnitude. The

performance was evaluated using the individualised

intervals. The results obtained were an 19.8% over-

Table 6: Error rates using the characters A, B, C, D, P, I,

J, K, L... and using the path length as the distance metric

(distance classes set automatically).

r F-accept G-reject FAR FRR ER

0.0 25/325 102/609 7.7% 16.7% 24.4%

0.5 36/325 58/609 11.1% 9.5% 20.6%

1.0 48/325 37/609 14.8% 6.1% 20.9%

1.5 66/325 27/609 20.3% 4.4% 24.7%

2.0 81/325 13/609 24.9% 2.1% 27.0%

all error rate using the time interval as the distance

metric and 20.6% using the path length. Table 5 and

Table 6 show that the best results are obtained when

the threshold value is 0.5. Although these results are

much better than those in Table 3, the FAR is still

high. From the results presented thus far, the time in-

terval seems to be the superior distance metric of the

two. Therefore we only concentrate on the time inter-

val as the distance metric from this point on.

The results show that the FAR was still dominat-

ing the overall error rate indicating that shape was still

the determining factor in the technique, since includ-

ing the distance only improved the shape representa-

tion, but did not include any motion or dynamic in-

formation. One type of information that can be easily

derived is the direction of pen motion at each moment.

It was decided to incorporate details of the direction

of the pen tip in between the valley and peak charac-

ters. To include pen tip direction, the motion direc-

tion was classiﬁed into four classes, corresponding to

quadrants on a Cartesian grid. The character to in-

clude between the turning points α, and the turning

point β, can then be found by positioning α at the ori-

gin and determining which quadrant β lies in.

Both the direction and the distance were included

in the signature representation by using one symbol

to represent both. To do this, for example, quadrant

one and distance class one is represented by the char-

acter E, quadrant two and the distance class one is the

character F and so on, until there was a unique charac-

ter for each of the sixteen direction/distance combina-

tions. Table 7 presents the results of evaluating these

two techniques. The results are much better with the

minimum total error at 9.2%.

An extension of the distance/direction approach

involved attaching more weight to longer strokes.

This was done by inserting not only the character ap-

propriate for each stroke, but also the distance char-

acteristic is considered, and the four distance classes

(in order) are represented by the characters W, X, Y

and Z. If the distance between two valleys/peaks falls

into the second largest class Y, then the three char-

acters WXY would be inserted in between the val-

ley/peak characters. This approach was considered

SECRYPT 2007 - International Conference on Security and Cryptography

Table 7: Error rates using the characters A, B, C, D, P, E, F,

G, H (direction components used).

r F-accept G-reject FAR FRR ER

0.0 3/325 98/609 0.9% 16.1% 17.0%

0.5 12/325 43/609 3.7% 7.1% 10.8%

1.0 25/325 26/609 7.7% 4.3% 12.0%

1.5 45/325 19/609 13.8% 3.1% 17.0%

2.0 60/325 9/609 18.5% 1.5% 19.9%

2.5 82/325 5/609 25.2% 0.8% 26.1%

3.0 96/325 4/609 29.5% 0.7% 30.2%

Table 8: Error rates using the characters A, B, C, D, P, I, F,

G, H, I, J, K, L (captures ordering, distance and direction).

r F-accept G-reject FAR FRR ER

0.0 1/325 97/609 0.3% 15.9% 16.2%

0.5 6/325 45/609 1.8% 7.4% 9.2%

1.0 15/325 29/609 4.6% 4.8% 9.4%

1.5 30/325 19/609 9.2% 3.1% 12.3%

2.0 47/325 11/609 14.5% 1.8% 16.3%

2.5 68/325 6/609 20.9% 1.0% 21.9%

3.0 76/325 4/609 23.4% 0.7% 24.1%

to have some advantage as (Dimauro et al, 1994)

note that longer strokes are generally more difﬁcult to

forge. Accumulating the characters allows a level of

variability for a genuine signer who only gets a long

stroke slightly wrong. For example, suppose a ref-

erence signature contains the sequence WXYZ. In this

situation, if the user formed the long stroke such that it

was slightly shorter, the test signature would contain

the sequence WXY, so the mismatch would be quite

small. Table 8 presents the results for the cumulative

technique giving a best-case 9.2% overall error rate.

Representing Stroke Length

The approaches implemented thus far had in-

volved increasing the level of detail which is captured

by the signature representation. Table 8 shows that in-

cluding more detail in the signature representation has

improved the overall error rate signiﬁcantly by lower-

ing the FAR, but the FRR has increased as expected.

Table 9: Error rates obtained using the ‘cumulative’ tech-

nique.

r F-accept G-reject FAR FRR ER

0.0 1/325 96/609 0.3% 15.8% 16.1%

0.5 9/325 46/609 2.8% 7.5% 10.3%

1.0 15/325 30/609 4.6% 4.9% 9.5%

1.5 33/325 19/609 10.1% 3.1% 13.2%

2.0 46/325 12/609 14.2% 1.9% 16.1%

2.5 64/325 7/609 19.7% 1.1% 20.8%

3.0 77/325 4/609 23.4% 0.7% 24.1%

To improve the error rates further, it is necessary to

study the representation and improve it if possible. It

should be noted that including the direction informa-

tion in the signature representation is not necessary

since the direction of pen motion is implied by the

peak-valley representation. For example, if a x-peak

is followed by a y-valley, then the direction of pen

motion between the two must be southwest.

Therefore it was decided to reﬁne the signature

representation yet again. Two changes were intro-

duced, ﬁrstly the direction information was removed

since the direction is implicit in the peak-valley repre-

sentation as noted above. Also, the representation of

the distance between each successive turning points

was changed. Using single characters to represent

different distance magnitudes was perhaps leading to

problems since the signatures of each individual have

variations, and if the two corresponding stroke dis-

tances were somewhat different they could well be

represented by different symbols leading to a mis-

match when the signature representations are com-

pared. Therefore a new representation was developed

which retains the valley and peak characters, but in-

stead of using a single character to represent each dis-

tance (or direction or both), multiple identical char-

acters are used to represent it. The number of char-

acters used is proportional to the magnitude of the

distance. The strength of this representation is that

if two corresponding stroke distances are somewhat

different in two signatures, the corresponding repre-

sentation would not be very different, it might only

differ by a single character in a string of characters

that represent those two corresponding distances. Let

the distance be represented by a number of T char-

acters in between the turning point characters. Using

multiple characters also captures pen tip velocity to an

extent, as the number of T characters in between the

segment will be less if the pen is being moved quickly.

It is possible to insert a T character for each signa-

ture sample point, but this can result in strings well

over one thousand characters in length. This not

only results in string matching requiring signiﬁcant

resources, but leads to an ineffective signature repre-

sentation since the representation mostly consists of

the T characters, and the ﬁfty or sixty turning point

characters do not have a signiﬁcant inﬂuence on the

results of signature comparisons. It is essential that

the number of T characters included to represent the

stroke distances is not much more than the number of

turning point characters. One approach is to insert a T

character for every n signature sample points (or time

units) where n perhaps has a range of 100 to 300).

The characters which are now included are the four

turning point characters A, B, C, D, the pen-up char-

IMPLEMENTATION AND ANALYSIS OF A HANDWRITTEN SIGNATURE VERIFICATION TECHNIQUE

Table 10: Error rates using the characters A, B, C, D, P, T.

r F-accept G-reject FAR FRR ER

0.0 0/325 117/609 0.0% 19.2% 19.2%

1.0 9/325 40/609 2.7% 6.5% 9.2%

2.0 17/325 19/609 5.2% 3.1% 8.3%

3.0 24/325 13/609 7.4% 2.1% 9.5%

4.0 36/325 7/609 11.0% 1.2% 13.2%

acter P, and a new character T representing the time

spacing between the turning point characters.

The signature representation now essentially rep-

resents a signature as a description similar to the fol-

lowing: “The pen moved northwest for 100 ms then

southwest for 150 ms then southeast for 75 ms... etc.”

This appears to be a ﬂexible representation which still

captures a signiﬁcant level of detail.

The results in this section were obtained by insert-

ing a T character for every n time units. This places

a large emphasis on correct spacing of turning points,

but at the same time the direction information is rep-

resented in the ordering of the turning points them-

selves. The representation also captures pen tip ve-

locity to an extent, as the number of T characters in

between a segment will be less if the pen is being

moved quickly. Six sets of results were obtained cor-

responding to different values of n ranging from n= 2

to n = 8. However, only the results which were most

attractive (those which used an n value of four) are

presented (Table 10). The total error rate is now 8.3%

(at a threshold of 2.0) compared to 9.2% in Table 8.

Controlling Reference Signature Quality

A HSV system’s reliability depends on the quality

of the reference signatures. It is assumed that these

signatures provide an accurate indication of how a

person’s signatures vary. A HSV system is going to

have difﬁculties if the sample signatures are very sim-

ilar, i.e., they show less variation than the person’s

signatures actually do. The system will suffer from a

high FRR but will have a low FAR. Also, if the sam-

ple signatures show more variation than is normal for

the person, then the system will lead to higher FAR

but lower FRR. If possible, a HSV system should try

to protect itself from such problems.

Heuristics have been developed to check the ref-

erence signature quality, and to determine if the level

of variability in the reference signatures is unusually

high or low, and correcting it if it is. The variability

of the reference signatures can be judged by the ratio

of the standard deviation to the mean of the distances

between reference signatures. If this ratio is too small,

then the reference signatures are unusually similar. If

the ratio is large, the reference signatures are unusu-

ally different. It was decided to place a lower limit of

1.75 on this ratio and if the ratio was found to be be-

low 1.75, it was assumed that the reference signatures

were too similar, and the reference standard deviation

was adjusted up to 1.75 times the reference mean. In

experimentation a limit of 1.5 was also considered,

but the limit of 1.75 produced superior results. Im-

posing the lower limit on the ratio should reduce the

FRR although it might increase the FAR somewhat.

The decision on reference signatures being too

different was not based on the ratio of the standard

deviation to the mean of the distances between the ref-

erence signatures. Instead, the ratio of the mean to the

distances between the reference signature representa-

tions to the average length of that person’s signature

representations was examined. If this ratio was large,

then it was assumed that the reference signatures had

too much variation. It was decided to impose an upper

limit of 0.25 on this ratio. If the ratio was greater than

0.25, then the reference mean was reduced to 0.25

times the average length of the reference signatures’

representations. Values of 0.2 and 0.225 were also

considered in experimentation, but performance eval-

uation indicated that the 0.25 limit was superior. This

approach would be expected to reduce the FAR while

still allowing genuine signers a large degree of vari-

ability so as not to signiﬁcantly raise the FRR.

Modifying the last technique that used multiple

characters to represent distance and imposing the

above upper bound and lower limits on the two ra-

tios, the technique was tested again and the detailed

results are presented in Table 11. A minimum 4.1%

total error rate is obtained which is a very signiﬁcant

improvement on the results without the limits. The

technique is now quite reliable with a 1.8% FRR and

a 2.3% FRR. Smaller FAR or FRR is possible, but

the total error rates are then higher than the minimum

4.1% total error rate.

It is possible to investigate other modiﬁcations of

the techniques that have been investigated. In a practi-

cal system, it may be sufﬁcient to just print a warning

when a user provides the reference signatures if the

variability of the signatures is unusually high or low.

There is then the option of requesting a new set of ref-

erence signatures.

Path Length and Elapsed Time

A slightly different extension to the earlier tech-

nique that used only distance characters involved us-

ing both the path length and the elapsed time in

the signature representation. The approach’s purpose

was to incorporate both the physical spacing and the

elapsed time in between turning points, thereby cap-

turing a notion of pen tip velocity. These features

were incorporated by inserting the appropriate num-

ber of T characters ﬁrstly, and then inserting a number

SECRYPT 2007 - International Conference on Security and Cryptography

Table 11: Error rates obtained after adjustment of variation.

r F-accept G-reject FAR FRR ER

0.0 0/325 141/609 0.0% 23.2% 23.2%

0.5 0/325 69/609 0.0% 11.3% 11.3%

1.0 3/325 27/609 0.9% 4.4% 5.4%

1.5 6/325 14/609 1.8% 2.3% 4.1%

2.0 8/325 13/609 2.5% 2.1% 4.6%

2.5 23/325 11/609 7.1% 1.8% 8.9%

3.0 37/325 8/609 11.4% 1.3% 12.7%

Table 12: Error rates using path length and elapsed time.

r F-accept G-reject FAR FRR ER

0.0 0/325 140/609 0.0% 23.0% 23.0%

0.5 1/325 72/609 0.3% 11.8% 12.1%

1.0 4/325 29/609 1.2% 4.7% 5.9%

1.5 6/325 15/609 1.8% 2.5% 4.3%

2.0 8/325 14/609 2.4% 2.3% 4.7%

2.5 23/325 12/609 7.1% 2.9% 9.1%

3.0 39/325 9/609 12.0% 1.5% 13.5%

of S characters (one S for every m pixels). Table 12

presents the results using this technique where the op-

timal uses a value of thirty for m and one T for every

four time units. The error rates produced using this

technique were slightly higher than those found in Ta-

ble 11, including an optimal 4.3% overall error rate.

Zero Effort FAR

Tests were performed using other users’ genuine

signatures as zero-effort forgeries. This test’s purpose

was to determine how effective the HSV system was

if the forger had no knowledge of the genuine user’s

signing style, and just signed his or her own signature.

The FAR for such a test should be much smaller than

for skilled forgeries, and ideally should be close to

zero, although it is known that for some feature-based

techniques the zero-effort FAR is not low. The total

number of zero-effort forgeries was 71282, since for

each signature in the database, every signature for ev-

ery other user is a zero-effort forgery. The optimal re-

sult for zero-effort forgeries will always be at r = 0.0

since the FRR is not a problem. At this threshold the

overall zero-effort FAR is 0.0%. However, it is more

realistic to use the same global threshold that was op-

timal for the skilled FAR tests in Table 11. When this

threshold (r = 1.5) was used, the zero-effort FAR is

1.4%, which was quite low.

Fewer Reference Signatures

The experiments performed so far have involved

the use of ﬁve reference signatures in order to estab-

lish the normal variability level for a particular user.

Additional experiments were undertaken to explore

the possibility of using fewer reference signatures,

perhaps three or even just one. When only a single

reference signature was used, no value for variability

could be obtained, so the reference mean was set to

0.25 times the length of the reference signature char-

acter string and the reference standard deviation was

set to 1.75 times the reference mean. The overall

error rates using three and one reference signatures

remained quite low at 8.4% and 12.8% respectively.

Few techniques in literature report results this accu-

rate when such a limited reference set is used.

Individual Thresholds

The results reported in this paper have been ob-

tained using the same threshold for all users in each

test. The results would improve signiﬁcantly if op-

timal threshold values were used for each individ-

ual. Many studies reported in literature use individ-

ual thresholds, although none of them reports how

an individual threshold can be computed given only

the reference signatures. Generally, all studies using

individual thresholds arrive at locally optimal thresh-

olds by using the threshold for the lowest error rate for

each user individually, and then summing these error

rates to determine the overall error rate. If this ap-

proach is used the total error rate reduces from 4.1%

to 1.3%, which consists of a 1.3% FRR and 0% FAR.

The total number of misclassiﬁed signatures being

just eight. Additionally, only four users contribute

to this misclassiﬁcation, meaning that 55 users (i.e.,

93% of the 59 users) would have a 0% overall error

rate if locally optimal thresholds were used. Clearly,

this shows the technique is highly reliable.

4 CONCLUSIONS

The results presented in this paper show that the pro-

posed HSV system is comparable to the highest qual-

ity signature veriﬁers presented in literature. The fea-

tures which have led to this success include:

The use of a string to represent the signature – this

allows existing string matching algorithms to be used

to determine distances between signatures. Further-

more, this makes the signature veriﬁer quite tolerant

to variations in genuine signatures. For example, in

the signature database there was one individual who

sometimes signed using his middle initial, while other

times signed without his middle initial. When these

signatures are represented as strings, the only real dif-

ference are the characters in the middle of the signa-

ture. The signature veriﬁer handles the situation well,

reporting a 20% FRR and a 0% FAR using the global

optimum threshold. Few other HSV systems perform

this well in such an extreme case.

IMPLEMENTATION AND ANALYSIS OF A HANDWRITTEN SIGNATURE VERIFICATION TECHNIQUE

Reference signature quality checking – This is un-

common in literature. It determines if the reference

signature variability is too high/low, and if so, adjust-

ing the reference mean and standard deviation.

Use of a small number of reference signatures –

Using ﬁve reference signatures led to a 4.1% overall

error rate. Results using three and even one reference

signature were also quite attractive (as low as 8.7%

using three and 12.5% using just one) when compared

to similar experiments in literature.

The overall results used a single globally optimal

threshold value (i.e., the threshold value was the same

for each user). By choosing a locally optimal thresh-

old for each individual the total error rate drops to just

1.3% FRR and 0% FAR.

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SECRYPT 2007 - International Conference on Security and Cryptography