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VARIABILITY OF HANDWRITING BIOMECHANICS: AFOCUS ON GRIP KINETICS DURING SIGNATURE

WRITING

by

Bassma Ghali

A thesis submitted in conformity with the requirementsfor the degree of Doctor of Philosophy

Graduate Department of Institute of Biomaterials and BiomedicalEngineering

University of Toronto

c⃝ Copyright 2013 by Bassma Ghali

Abstract

VARIABILITY OF HANDWRITING BIOMECHANICS: A FOCUS ON GRIP

KINETICS DURING SIGNATURE WRITING

Bassma Ghali

Doctor of Philosophy

Graduate Department of Institute of Biomaterials and Biomedical Engineering

University of Toronto

2013

Grip kinetics are emerging as an important measure in clinical assessments of hand-

writing pathologies and fine motor rehabilitation as well as in biometric and forensic

applications. The signature verification literature in particular has extensively examined

the spatiotemporal, kinematic, and axial pressure characteristics of handwriting, but has

minimally considered grip kinetics. Therefore, the focus of this thesis was to investi-

gate the variability of grip kinetics in adults during signature writing. To address this

goal, a database of authentic and well-practiced bogus signatures were collected with an

instrumented pen that recorded the forces applied to its barrel. Four different analyti-

cal studies were conceived. The first study investigated the intra- and inter-participant

variability of grip kinetic topography on the pen barrel based on authentic signatures

written over 10 days. The main findings were that participants possessed unique grip

force topographies even when the same grasp pattern was employed and that participants

could be discriminated from each other with an average error rate of 1.2% on the basis

of their grip force topographies. The second study examined the stability of different

grip kinetic features over an extended period of a few months. The analyses revealed

that intra-participant variation was generally much smaller than inter-participant varia-

tions even in the long term. In the third study, grip kinetics associated with authentic

and well-practiced bogus signatures were compared. Differences in grip kinetic features

ii

between authentic and bogus signatures were only observed in a few participants. The

kinetics of bogus signatures were not necessarily more variable. The variation of grip

kinetic profiles between participants writing the same bogus signature was evaluated in

the fourth study and an average error rate of 5.8% was achieved when verifying signa-

tures with kinetic profile-based features. Collectively, the findings of this thesis serve to

inform future applications of grip kinetic measures in biometric, clinical and industrial

applications.

iii

Dedication

To my beloved husband,

Nawar Mahfooth,

who has been and will always be a great husband,

a best friend, and an excellent supporter.

Thank you for being there for me in every step, good or bad, happy or sad.

Thank you for being the reason behind this whole great experience.

iv

Acknowledgements

I would like to express my deepest appreciation to all those who provided me their

support to obtain my Ph.D. degree.

A special gratitude I give to my supervisor, Dr. Tom Chau, who provided guidance,

expertise, and encouragement throughout the past four years. He is always a great

inspiration for the hard work, dedication and kindness.

I also appreciate the guidance given by my supervisory committee members, Dr.

Heather Carnahan and Dr. Dimitrios Hatzinakos, and my examiners, Dr. Kei Masani

and Dr. Jae Kun Shim. Their comments and suggestions were very valuable in the

progress and completion of my thesis.

I also want to acknowledge the Natural Sciences and Engineering Research Council

of Canada (NSERC) and Dr. Tom Chau for providing the financial support through out

the years it took to get my Ph.D. degree.

Furthermore, I would also like to acknowledge with much appreciation the crucial role

of the staff of the PRISM lab, Ka Lun Tam, Pierre Duez, Siva Rajaratnam and Tasnim

Kamani. They were always happy to help and answered any question I had. Sincere

gratitude also goes to the members of the PRISM lab for making the lab a great place

and for their continuous support especially during the data collection. I would also like to

thank all the participants for their time, without them this thesis could not be possible.

Last but not least, many thanks go to my husband and my family for their love and

support through out the years and a special thanks goes to my dearest son, John, for

being a great baby during pregnancy and during his first few months until i finished this

thesis. I love you and i will always be there for you.

v

Contents

1 Introduction 1

1.1 Handwriting Biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Grip kinetics in clinical assessments and rehabilitation studies . . 2

1.1.2 Grip kinetics in biometric and forensics studies . . . . . . . . . . . 5

1.2 Biometric Authentication . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.1 Overview of handwritten signature verification . . . . . . . . . . . 10

1.2.2 Signature verification features . . . . . . . . . . . . . . . . . . . . 13

1.2.3 Signature verification algorithms and databases . . . . . . . . . . 15

1.2.4 Recent patents and commercial signature verification systems . . 17

1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.4 Objectives and Research Questions . . . . . . . . . . . . . . . . . . . . . 19

1.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 Variability of Grip Kinetics During Adult Signature Writing 24

2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2.1 Clinical assessments . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2.2 Rehabilitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2.3 Biometrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2.4 Forensics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

vi

2.2.5 Ergonomics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.1 Ethics statement . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.2 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.3 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.4 Calibration set-up and procedure . . . . . . . . . . . . . . . . . . 29

2.3.5 Data collection protocol . . . . . . . . . . . . . . . . . . . . . . . 31

2.3.6 Data preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.3.7 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.4.1 Spatiotemporal features . . . . . . . . . . . . . . . . . . . . . . . 38

2.4.2 Grip shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.4.3 Topographical analysis of grip shape variability . . . . . . . . . . 38

2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.5.1 Grip shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.5.2 Within-participant variation of grip kinetics . . . . . . . . . . . . 44

2.5.3 Between-participant variation of grip kinetics . . . . . . . . . . . 46

2.5.4 Possible applications . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3 Long Term Stability of Handwriting Grip Kinetics in Adults 50

3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2.1 Clinical studies of grip kinetics . . . . . . . . . . . . . . . . . . . 52

3.2.2 Grip kinetics in biometrics, forensics and sport . . . . . . . . . . . 53

3.2.3 Variability of grip kinetics . . . . . . . . . . . . . . . . . . . . . . 53

3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

vii

3.3.1 Ethics statement . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.3.2 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.3.3 Data collection set-up . . . . . . . . . . . . . . . . . . . . . . . . 55


3.3.5 Data preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.3.6 Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.3.7 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.4.1 Intra-participant statistical analysis . . . . . . . . . . . . . . . . . 62

3.4.2 Inter-participant discrimination analysis . . . . . . . . . . . . . . 64

3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.5.1 Intra-participant variation of grip kinetics . . . . . . . . . . . . . 67

3.5.2 Inter-participant grip kinetic variation . . . . . . . . . . . . . . . 69

3.6 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4 A Comparison of Handwriting Grip Kinetics Associated with Authentic

and Well-Practiced Bogus Signatures 71

4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.3.1 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73


4.3.3 Experimental protocol . . . . . . . . . . . . . . . . . . . . . . . . 74

4.3.4 Data pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . 76


4.3.6 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

viii

4.6 Conflict of interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83


5 Grip Kinetic Profile Variability in Adult Signature Writing 84

5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.3.1 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88



5.3.4 Data pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . 90


5.3.6 Pattern classification . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101


6 Conclusions 102

6.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.3 Resulting Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

References 108

Appendix A 121

A.1 Overview of handwriting grip shapes . . . . . . . . . . . . . . . . . . . . 121

A.2 Definition of kinematics and kinetics . . . . . . . . . . . . . . . . . . . . 122

ix

A.3 Introduction to some analytical methods . . . . . . . . . . . . . . . . . . 123

A.3.1 Box plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

A.3.2 Linear discriminant analysis . . . . . . . . . . . . . . . . . . . . . 123

x

List of Tables

2.1 Temporal, spatial and speed information of the authentic signa-

tures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.2 Grip shape of each participant and associated observations . . . 40

2.3 Error rates in the classification of full grip shape images . . . . . 43

3.1 The effect of training set composition . . . . . . . . . . . . . . . . . 67

xi

List of Figures

1.1 Block diagram showing the topic and the data set used in each

of the main chapters of the thesis. . . . . . . . . . . . . . . . . . . . 23

2.1 Data Collection instrumentation setup. Participants wrote with the

instrumented writing utensil on a digitizing LCD display. The data acqui-

sition box and the computer transmitted and saved the data respectively. 29

2.2 The calibration setup. Each sensor in the force sensor array was cali-

brated using this setup through loading and unloading of the sensors. . . 30

2.3 A signature example and the associated grip force signals. The

top graph shows the position signals of a signature sample annotated at 1

second increments, and the middle and bottom graphs show the associated

raw and processed grip force signals respectively. For clarity, only the non-

zero force traces are shown in the latter. In bottom two graphs, each line

represents the readout of a different grip sensor. Note that this sample is

not an authentic signature; it is a sample of a well-practiced signature. . 35

2.4 Mean grip shape images of the 20 participants. Each grip shape

image represents the grip force distribution on the 4 by 8 force sensor array

with the black points being the ones with the highest force. . . . . . . . . 41

xii

2.5 Box plots of the intra- (left panel A) and inter-participant (right

panel B) NCC values for all 20 participants. Each box represents the

distribution of NCC values for one participant, while ‘+’ symbols denote

outliers (values beyond 1.5 interquartile ranges from the median). . . . . 42

2.6 Separability of intra- and inter-participant NCC values. Separa-

bility measured by Fisher’s ratio (top graph) and classification error rates

by LDA, KNN and NN classifiers (bottom three graphs respectively). The

dashed line represents the average value of each method. . . . . . . . . . 43

3.1 Data collection instrumentation set-up. A close up of the instru-

mented pen is shown, highlighting the section of the force sensor array of

interest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.2 Box plots of the three grip force features based on phase 1 and

phase 2 data. For each participant, the first box represents the phase

1 feature distribution while the second box is the phase 2 distribution of

the same feature. NCC= normalized correlation coefficient; TAF= total

average force; TFIQR= total force interquartile range. . . . . . . . . . . 63

3.3 Heat maps showing percentage of participants exhibiting signif-

icant kinetic differences between phases 1 and 2. The left subplot

presents the results for the “all signatures” case while the right subplot

presents the results based on the first 5 signatures. Each heat map shows

the percentage of participants exhibiting a significant difference for each

grip force feature (horizontal axis NCC= normalized correlation coeffi-

cient; TAF= total average force; TFIQR= total force interquartile range)

using each statistical test (vertical axis RS=Wilcoxon rank-sum test; KS=

Kolmogorov-Simrnov test; AB= Ansari-Bradley test). . . . . . . . . . . 64

xiii

3.4 Feature distributions for phase 1 (left) and phase 2 (right) sig-

natures. Data from participant 13 are shown. Circles denote feature

vectors from authentic signatures from participant 13. X’s denote feature

vectors from other participants. The dark diagonal line is the separating

plane determined by linear discriminant analysis. (TFIQR= total force in-

terquartile range; TAF= total average force; NCC= normalized correlation

coefficient) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.5 Misclassification rates for phases 1 and 2. Asterisks indicate that

the participant has a significant difference between phase 1 and phase 2

MCRs. The dashed lines show the average MCRs across all 18 participants. 66

4.1 Data collection instrumentation set-up. . . . . . . . . . . . . . . . 75

4.2 A sample of the bogus signature. . . . . . . . . . . . . . . . . . . . 75

4.3 Different representations of the grip force signals associated with

a bogus signature shown in Figure 4.2. ‘A’: a functional represen-

tation of the grip force signals on each sensor; ‘B’: a topographical rep-

resentation of the grip force signals, each square represents a sensor and

its value is the normalized average force applied on that sensor; ‘C’: the

functional representation of the total grip force profile over the course of

a signature, which is the sum of the signals shown in ‘A’. . . . . . . . . . 80

xiv

4.4 Heat maps depicting the percentage of participants for whom

significant kinetic differences arose between signatures. Authen-

tic and well-practiced bogus signatures comparison of feature medians is

shown on the left graph and feature spread is shown on the right graph.

Dark coloring denotes low percentages. Features are specified on the ver-

tical axis while the nature of the difference between authentic (A) and

well-practiced bogus (B) signatures appears on the horizontal axis. Each

numerical overlay corresponds to the percentage of participants showing

the specified difference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.1 Data collection instrumentation setup. . . . . . . . . . . . . . . . . 89

5.2 The bogus signature. Each participant practiced this signature for two

weeks prior to the data collection to develop familiarity with the signature. 90

5.3 A signature sample, its grip force signals and total grip force

profile. Top: a signature sample and the associated timing of selected

points; Middle: the pre-processed grip force signals of the 32 force sensors;

Bottom: the total grip force signal over the course of a signature, which

is the sum of the signals shown in the middle figure. . . . . . . . . . . . 91

5.4 Example of total force signals for one participant before (left

graph) and after (center graph) registration. To facilitate visu-

alization, only a subset of total force signals is shown. Pre- and post-

registration mean total force profiles for the given participant appear in

the rightmost graph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.5 Examples of mean total force signals. The solid line shows the overall

mean total grip force signal based on all participants while each dotted line

exemplifies the mean total grip force signal of a participant. . . . . . . . 94

xv

5.6 The means (bars) and standard deviations (error bars) of the

MCRs of the different classifiers with full (unshaded bars) and

reduced feature sets (shaded bars). . . . . . . . . . . . . . . . . . . 97

5.7 Performance of the LDA classifier for each participant. The per-

centage of false positives (FP) and false negatives (FN) are shown for

each participant. The average values across participants are shown as the

dotted lines with their values on the right side of the figure. . . . . . . . 98

5.8 The number of samples and the average MCR obtained when

changing the percentage of data considered. . . . . . . . . . . . . . 98

A.1 Photos taken during the data collection of the three most typical

grip shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

A.2 An example of a box plot and its interpretation. . . . . . . . . . . 124

xvi

List of Abbreviations

AB Ansari-Bradley test

CDF Cumulative Distribution Function

CV Coefficient of Variation

EER Equal Error Rate

FAR False Acceptance Rate

FN False Negatives

FNR False Negative Rate

FP False Positives

FPR False Positive Rate

FRR False Rejection Rate

GF Grip Force

GMM Gaussian Mixture Models

HMM Hidden Markov Models

KNN K Nearest Neighbors

KS Kolmogorov-Smirnov test

xvii

LDA Linear Discriminant Analysis

MCR Misclassification Rate

NCC Normalized Cross-Correlation

NN Neural Networks

PCA Principal Component Analysis

PDA Personal Digital Assistant

RBF Radial Bases Function

RMSE Root Mean Square Error

RS Wilcoxon Rank-Sum test

SVM Support Vector Machine

TAF Total Average Force

TER Total Error Rate

TFIQR Interquartile Range

TGF Total Grip Force

TGFIQR Total Force Interquartile Range

TGFmax Maximum Total Grip Force

TUF Total Unnormalized Force

WC Writer’s Cramp

WSFS Weighted Sequential Feature Selection

xviii

Chapter 1

Introduction

1.1 Handwriting Biomechanics

Handwriting is a fine motor skill that is shaped by varied instruction on letter formation

integrated with personal choice reflecting the interaction between personality, social,

and cultural influences (Wing, Watts, & Sharma, 1991). It is also considered a well-

trained motor skill that entails the integration and coordination of multiple abilities and

muscular systems (Stelmach & Teulings, 1983; van Galen, 1991; Ramsay, 2000; Falk,

Tam, Schwellnus, & Chau, 2010; Van Drempt, McCluskey, & Lannin, 2011). Handwriting

involves a complex biomechanical system that requires the coordination of dozens of

muscles to hold the pen and generate the handwriting movements that result in the

written script. The complexity of these biomechanical and cognitive systems introduces

variations between individuals as well as variation within an individual (Ramsay, 2000).

These facts make handwriting a highly automated and personalized motor skill (Jasper,

Haußler, Baur, Marquardt, & Hermsdorfer, 2009).

Handwriting grip is the arrangement of the fingers and thumb around the barrel of

a writing instrument for the production of written output. Recent advances in instru-

mented writing utensils (Chau, Ji, Tam, & Schwellnus, 2006; Hooke, Park, & Shim,

1

Chapter 1. 2

2008; Baur, Furholzer, Marquardt, & Hermsdorfer, 2009) have enabled the measurement

of handwriting grip kinetics, i.e., the forces exerted by the fingers and thumb on the bar-

rel of the writing implement during handwriting. Handwriting grip kinetics are emerging

as an important quantitative measure in the clinical and rehabilitation domains, and

may also have relevance in biometrics, forensics, and ergonomics as detailed in the next

section.

1.1.1 Grip kinetics in clinical assessments and rehabilitation

studies

Recent clinical handwriting studies have expanded from pen-tip kinematics to pen-hand

kinetics that include the forces at the pen-hand contact points (Falk et al., 2010; Falk,

Tam, Schwellnus, & Chau, 2011; Kushki, Schwellnus, Ilyas, & Chau, 2011; Shim et al.,

2010; Hermsdorfer, Marquardt, Schneider, Furholzer, & Baur, 2011). The rationale is

that there exists unique kinetic relationships that may define individual handwriting

(Hooke et al., 2008) since the pen grasp is a kinetically redundant system in which

different grip force combinations can generate similar kinematic profiles (Latash, Danion,

Scholz, Zatsiorsky, & Schoner, 2003; Shim et al., 2010).

Hooke et al. (2008) developed a kinetic pen that records grip forces and torques on

four points for handwriting research. Their pen determines finger joint torques from

inverse dynamics and the authors contend that this information may help in the diag-

noses, quantification and treatment of movement as well as psychological disorders that

are manifested in handwriting. This pen was used by Shim et al. (2010) to examine

the grip force synergies used during circle drawing. It was found that the strength of

these synergies was dependent on the phase and direction of circle drawing as well as

on the force component considered (radial, tangential, normal components), which had

implications on how the central nervous system prioritizes the hand-pen contact force

synergies for this task.

Chapter 1. 3

The characteristics of handwriting grip kinetics in patients with writer’s cramp (WC)

and the use of these kinetics for diagnoses and treatment of WC have been investi-

gated in many studies (Baur, Furholzer, Jasper, Marquardt, & Hermsdorfer, 2009; Baur,

Furholzer, Marquardt, & Hermsdorfer, 2009; Schneider et al., 2010; Hermsdorfer et al.,

2011). In a sample of patients with WC, Schneider et al. (2010) discovered a significant el-

evation of grip forces above the levels of healthy participants only for those with dystonic

WC. This condition suggested that grip kinetics may uniquely provide clinical subtype

differentiation. Likewise, Hermsdorfer et al. (2011) reported that exaggerated forces in

patients with WC occurred more frequently than abnormal kinematics, concluding that

grip force is an important descriptor of individual impairment characteristics that are

independent of writing kinematics. In addition to the clinical characterization of hand-

writing function, grip forces have been found to play a role in both treatment and outcome

measurement. Baur, Furholzer, Marquardt, and Hermsdorfer (2009) developed a novel

intervention for patients with writer’s cramp, using auditory grip force feedback, namely,

a continuous low frequency tone whose pitch increased with escalating grip force. Signif-

icant reduction in writing pressures and pain were noted over seven treatment sessions.

Deploying grip force as an outcome measure, Baur, Furholzer, Jasper, et al. (2009) found

that both a modified pen grip and handwriting training (motor exercises) decreased grip

force in patients with writer’s cramp and in a sample of asymptomatic controls.

Another kinetic pen that quantifies grip activity during handwriting was developed

by Chau et al. (2006). This system records grip forces exerted on the writing utensil

using strips of pressure sensors mounted on the barrel. This arrangement allows for

any number of fingers to grip the pen without restricting finger position. The system

also records normal forces and other kinematic and temporal parameters. This novel

instrument has been used for quantitative studies of handwriting difficulties in pediatric

populations (e.g., cerebral palsy (Chau et al., 2006)). Correlations between normal and

grip forces have been identified and certain grip force parameters have discriminated

Chapter 1. 4

between writers with and without handwriting difficulties (Falk et al., 2011; Kushki

et al., 2011). Falk et al. (2010) used this instrumented pen to measure the grip force

variability in children’s handwriting and found that grip force dynamics play a key role

in determining handwriting quality and stroke characteristics. Grip force features, along

with other temporal and spatial handwriting measures, have been found to correlate

with standard subjective quality measures that supported the evaluation of handwriting

proficiency through objective computer-based handwriting assessment tools (Falk et al.,

2011). Such an objective assessment tool can complement the conventional subjective

quality scores. Also, changes in grip forces applied on a pen barrel over the duration of

a 10 minute writing task have been examined in Kushki et al. (2011) and it was found

that grip forces increased over time as a compensation by the motor system to alleviate

physical fatigue. Schwellnus et al. (2013) examined the difference in writing forces (axial

and grip forces) among four different pencil grasps in children in grade four during a 10

minutes copy task. It was found that kinetic differences existed when the grasps were

categorized according to the thumb position. Specifically, it was found that the adducted

grasps exhibited higher mean grip and axial forces.

The importance of considering the kinetic information between the hand and the pen

in handwriting studies has also motivated a recent study by Hsu et al. (2013) to design

a force acquisition pen with physical properties similar to a regular pen. This pen can

record the forces applied on the pen in three adjustable contact spots, which limits the

accommodated grip patterns to dynamic tripod and lateral tripod grasps. The study

confirmed the validity and reliability of the recorded forces and explored the variability

of the forces applied by the three digits. The study reported that the force applied by the

middle finger was more variable than the force applied by the thumb and index fingers

because of the supportive role that the middle finger plays in these two grip patterns.

However, the study reported that this variation was within an acceptable range since

handwriting forces are expected to have some variability.

Chapter 1. 5

Grip forces have also been studied in contexts other than handwriting. Kutz, Wolfel,

Timmann, and Kolb (2007) developed a method capable of measuring the temporal and

spatial distribution of grip forces while holding a slipping object in a hand. This was

performed by using a special grip rod covered with a film of pressure sensors and a force

change detection algorithm that isolated the pressure and position of individual fingers.

This system enabled the study of the grip of any number of fingers without restricting

finger position. Kutz, Wolfel, Timmann, and Kolb (2009) used a similar system for

the quantification of torque while increasing grip forces during a task similar to picking

a raspberry. It was found that healthy subjects were able to minimize torque despite

increasing grip forces while cerebellar patients increased torque disproportionately with

increasing grip forces.

1.1.2 Grip kinetics in biometric and forensics studies

Handgrip force patterns have demonstrated value as a biometric measure for gun control

applications. Various pattern recognition approaches have been applied to distinguish

users by the way they grip the firearm (Yampolskiy & Govindaraju, 2008; Veldhuis,

Bazen, Kauffman, & Hartel, 2004; Shang & Veldhuis, 2008a, 2008b, 2008c). For these

smart gun applications, pressure sensors are embedded into the gun’s grip. The grip

pattern contains useful information for identity verification. The input to the verifica-

tion algorithms is an image with pixel values representing the pressure distribution on

the sensors. A likelihood ratio classifier, assuming Gaussian probability densities, was

employed for the verification algorithm (Veldhuis et al., 2004) and it generated an equal

error rate (EER) of 1.8%. Shang and Veldhuis (2008a) suggested the use of different

sessions’ data, image registration, and classifier fusion to reduce the effect of grip pattern

variation between sessions and improve the verification accuracy.

The biometric value of the pressure applied by fingers has also been examined in stud-

ies that use keystrokes dynamics for personal authentication. A review article in this field

Chapter 1. 6

showed that, in addition to considering the time to type, the latency between keystrokes,

and many other features, few studies have considered the keystroke pressure applied by

the fingers on the keys and found it to be a valuable discriminative feature (Karnan,

Akila, & Krishnaraj, 2011). Salami, Eltahir, and Ali (2011) and Sulong, Wahyudi, and

Siddiqi (2009) proposed the use of a keyboard embedded with force sensors that measure

the force applied on the keyboard along with the time latency between keystrokes to

authenticate the user while typing. Using a keystroke pattern that was generated based

on these features and multiple classifiers, it was found that combining the pressure with

the latency achieved better performance than that achievable by considering each fea-

ture alone. Saevanee and Bhattarakosol (2009) studied the effectiveness of three features,

that is hold-time, inter-key and finger pressure, for the authentication of touch pad users

and found that finger pressure provides the most discriminative information. Based on

a database of 10 participants writing their cell phone numbers on a notebook touch pad

30 times and a probabilistic neural network classification method, the finger pressure of

the participants achieved an EER of 1%.

Recently, a number of studies examined the use of grip kinetics for handwriting and

person recognition (Bashir & Kempf, 2009, 2012). Bashir and Kempf (2009) used a bio-

metric smart pen that recorded the grip forces using a grip pressure sensor (piezoelectric

foil wrapped around the case of the pen) along with other signals. When each signal was

considered separately, the best performance for person authentication was obtained with

the grip force signal and refill pressures. Bashir and Kempf (2012) used an advanced

biometric pen system that includes a WACOM tablet and an enhanced WACOM pen,

which measures the grip pressure of fingers holding the pen using a piezoelctric film foil

that is wrapped around the pen near the gripping area. Using a dynamic time warping

based classification, the performance of private and public PIN recognition using separate

or fused (x, y, and grip force) signals was evaluated. The study found that considering

the grip pressure data in addition to the x-y position data improved the performance of

Chapter 1. 7

the recognition system by about 1%, which demonstrates the importance of integrating

the grip pressure in such recognition systems.

Grip forces have also been investigated in a number of sports including tennis, cricket,

baseball, and golf to evaluate their effect on a resulting shot’s distance and accuracy

(Komi, Roberts, & Rothberg, 2008). Multiple studies have measured the grip forces

associated with golf swings (E. Schmidt, Roberts, & Rothberg, 2006; Komi, Roberts,

& Rothberg, 2007; Komi et al., 2008). A matrix of thin-film force sensors on the golf

grip or a number of force sensors attached to golf gloves were used to measure the forces

applied by the golfer’s hands on the golf grip. By comparing the total grip force traces

that were generated during multiple shots of twenty golfers of varying ability using a

cross-correlation technique, it was revealed that despite some similar trends between the

golfers, each player had repeatable grip force patterns that were quite distinct from those

of other players.

An early study by Herrick and Otto (1961) researched the point and barrel pressure

patterns in the handwriting of 60 writers from three different educational levels. A grip

pressure transducer pen and a table with a pressure sensing platen were used in this study

to examine the relationship between point and barrel pressures, the pressure patterns

of different digits and the pressure patterns between individuals with different levels

of familiarity with handwriting. A significant between-participant variation in finger

pressure patterns during handwriting was observed because of the personalized nature of

this activity. In addition, this study on grip forces associated with handwriting suggested

that the inter-finger absolute pressures widely vary by individual participants and that,

in most cases, the barrel and pen point pressures are correlated. A correlation was also

observed between the magnitude and the variability of the barrel pressure applied by each

finger. This makes the barrel pressure and its variability an important distinguishing

characteristic of individual handwriting (Chau et al., 2006).

Forensic document examiners also rely on different written product features to detect

Chapter 1. 8

a forgery in a document as it is believed that each person’s writing is unique to that

individual with some intra-participant variability (Girard, 2007; Koppenhaver, 2007).

The handwriting features that are usually examined include the spacing and style as well

as the shapes of letters and strokes (Girard, 2007), in addition to the paper indentation

caused by the pen tip’s normal force (Furukawa, 2011). Koppenhaver (2007) suggested

that the type of grip pressure in combination with the pressure pattern can also carry

unique features for writer identification and forgery detection since they usually occur

automatically without the writer’s awareness. Given the relationship between axial (pen

tip force on the writing surface along the length of the pen) and grip forces, knowledge

of the former from an analysis of paper indentations (Furukawa, 2011) may shed light

on the pen grip of the writer and possibly the presence of musculoskeletal pathologies of

the writer.

1.2 Biometric Authentication

Biometrics as a discipline is concerned with the automatic recognition of an individual by

using certain physiological or behavioral characteristics associated with the person (Jain,

Ross, & Prabhakar, 2004; Impedovo, Pirlo, & Plamondon, 2012). Biometric systems

address some of the problems with traditional authentication systems such as the user

forgetting or giving away a password in the case of knowledge-based systems and stolen

or lost ID cards in case the of token-based systems (Jain & Ross, 2004). To restrict

access to secure systems, biometric systems rely on person-based characteristics that

are always with or can be generated by an individual. These characteristics can be

physiological such as finger print, hand geometry, palm print, retinal scan, or iris and

facial features. Biometric characteristics can also be behavioral as they are based on

skills, style, preference, knowledge, motor skills and strategies used by different people to

accomplish different tasks (Yampolskiy & Govindaraju, 2008). There are many examples

Chapter 1. 9

of behavioral biometrics. However, the most developed include keystroke dynamics, gait

profiles, and handwritten signatures (Yampolskiy & Govindaraju, 2008).

All biometric characteristics should be: universal (each person should have the char-

acteristic); distinctive (sufficiently different between any two people); permanent (suffi-

ciently invariant with time); and collectable (easily obtainable) (Jain et al., 2004; Yam-

polskiy & Govindaraju, 2008). In addition, for the biometric systems to be practical,

they should meet the required performance in terms of speed, accuracy, and available

resources. A biometric should also be acceptable to potential users and robust against

fraudulent attacks.

Biometric systems can be used for two purposes: verification (confirming the identity

of the person) and identification (determining the identity of the person). In both cases,

the biometric system is a pattern recognition system that obtains the biometric data from

the user (sensor module), extracts the required features (feature extraction module) and

compares these features to a template set in a database to calculate a similarity measure

(matcher module) (Jain et al., 2004). Since biometric characteristics are almost never

identical, the similarity measure is compared to a predefined threshold to determine the

outcome of the system. Also, each biometric system requires a database module that

stores the users’ biometric templates and an enrollment module that is used to add new

users to the database.

Biometric systems generally have two main performance measures (Jain et al., 2004;

Impedovo & Pirlo, 2008). The first is the false acceptance rate (FAR) or equivalent

the false positive rate (FPR), which reflects how often the system incorrectly provides

a positive match for a false user. The second is the false rejection rate (FRR) or false

negative rate (FNR), which measures the system’s tendency to mismatch a valid user.

Another performance measure is the EER which is the error rate of the system when

FAR is equal to FRR. Total error rate (TER), estimated as a weighted sum of FAR and

FRR, is also a common performance measure.

Chapter 1. 10

The rest of this section focuses on the handwritten signature as a biometric for veri-

fication purposes.

1.2.1 Overview of handwritten signature verification

The most developed behavioral biometrics are the ones that rely on learned motor skills

(Yampolskiy & Govindaraju, 2008). The handwritten signature is a behavioral biometric

that has been accepted in government, as well as legal and commercial applications for

verification purposes. It is traditionally accepted world-wide and does not require any

invasive measurements, which makes it very easy to obtain from the user (Plamondon

& Srihari, 2000; Impedovo, Pirlo, & Plamondon, 2012). However, signatures change

with time and forgers can easily fool verification systems that only consider the image

of the signature (Jain et al., 2004; Rashidi, Fallah, & Towhidkhan, 2012). Emotional

and physical conditions can also affect accuracy of the handwritten signature. Therefore,

signature verification is still an open challenge and there is a lot of on-going research in

this area (Impedovo, Pirlo, & Plamondon, 2012).

In general, signature verification has been achieved in one of two ways: off-line and

on-line. The first is a static approach, often known as image-based verification because an

image of the signature is captured after the user signs, and the similarity measure reflects

differences between this image and those stored in the database. For example, Kalera,

Srihari, and Xu (2004) employed a combination of Gradient, Structural and Concavity

features derived from the signature image for verification and identification purposes.

This combination of global, statistical and geometrical features of the signature achieved

accuracies of 78% for verification and 93% for identification. A recent study reported that

the best available off-line signature verifiers achieve error rates of 9%-10% when tested

with a public database and skilled forgeries (Kovari & Charaf, 2013). Kovari and Charaf

(2013) proposed a probabilistic model for off-line signature verification that can analyze

each verification step to predict and improve the accuracy of such off-line systems.

Chapter 1. 11

The second and more reliable approach is dynamic on-line verification in which many

time-varying measurements are captured while the signature is being produced with a

pressure sensitive pen and a digitizing tablet. With this approach, the imposter must

reproduce more than just the static image of the signature, but some personal gesture

associated with the signature, which is usually more difficult to imitate (Garcia-Salicetti

et al., 2009). The exact nature of the recognition algorithm depends largely on the data

collected (Yampolskiy & Govindaraju, 2008). Some of these dynamic systems collect

kinematic data such as position, velocity, acceleration and pen-tilt signals for verifica-

tion purposes. For example, Bovino, Impedovo, Pirlo, and Sarcinella (2003) proposed a

multi-expert system for dynamic signature verification based on a stroke-oriented signa-

ture description which included position, velocity, and acceleration signals. A Euclidean

distance classifier was employed in a two-tiered decision scheme. The first was to com-

bine decisions from different representations of each stroke and the second was to combine

authenticity decisions of each stroke. To test the system, a database of 750 authentic

signatures from 15 individuals and 750 skilled forgeries from 15 other individuals was

employed and an EER of 0.4% was achieved.

Other dynamic systems have employed combined kinematic-kinetic data including, in

particular, the pressure at the tip of the pen (normal/axial forces). An example of this

approach was employed by participants in the 2004 Signature Verification Competition

who used position, timing, pen orientation and pen-to-paper pressure for verification

(Yeung et al., 2004). The different systems were tested with a database of 100 sets of

signatures, each set containing 20 genuine signatures and 20 skilled forgeries. The best

system achieved an EER of 2.9% by employing dynamic time warping to compare the ref-

erence and test signatures and a linear classifier in conjunction with principal component

analysis (PCA) to classify each signature (Kholmatov & Yanikoglu, 2004). In Fierrez,

Ortega-Garcia, Ramos, and Gonzalez-Rodriguez (2007), a list of features was extracted

from pen position, timing and pressure for use in a hidden Markov model classifier. The

Chapter 1. 12

system was tested with a subcorpus of the MCYT bimodal biometric database (Ortega-

Garcia et al., 2003) comprising over 7,000 signatures from 145 participants and achieved

an EER of 0.74% and 0.05% for skilled and random forgeries, respectively. Rashidi et

al. (2012) used 44 time signals based on position, velocity, pressure, and pen angles. By

applying a discrete cosine transform and a forward feature selection algorithm on two

signatures databases, a parzen window classifier achieved EERs of 2.04% with SVC2004

database and 1.49% with SUSIG database, which are lower than EERs of other systems

in the literature using the same databases.

Impedovo, Pirlo, and Plamondon (2012) lists a number of the international compe-

titions that have been performed in the last few years for on-line and off-line signature

verification systems. Houmani et al. (2012) compared three of these competitions and

reported the results of the BioSecure Signature Evaluation Campaign (BSEC2009) in

which the performance of 12 signature verification systems was evaluated. This compe-

tition evaluated the effect of the acquisition conditions and the signatures’ information

content on the performance using a database that included 382 people who wrote signa-

tures on a digitizing tablet and a personal digital assistant (PDA). It was found that the

best system achieved an EER of 2.2% for skilled forgeries and 0.51% for random forgeries

with the signatures written on a digitizing tablet as well as an EER of 4.97% for skilled

forgeries and 0.55% for random forgeries with the signatures written on the PDA. The

results of the more recent BioSecure Signature Evaluation Campaign (ESRA’2011) are

reported by Houmani et al. (2011). The main aim of this competition was to evaluate the

performance of 13 systems on skilled forgeries of different quality using only coordinate

time functions first (task 1) and using coordinates with axial pressure and pen incli-

nation second (task 2). It is worth noting that the genuine signatures considered were

from one session since the competition did not deal with the time variability issue. The

main observations of this competition include the finding that the best system with poor

quality forgeries was not the same as the system with the good quality forgeries and that

Chapter 1. 13

the gap in performance between these two categories of forgeries increased when the pen

inclination signals were considered. The results of another recent signature verification

competition (SigComp2011) are reported by Liwicki et al. (2011). In this competition, 12

systems were evaluated using datasets of on-line and off-line with two scripts (Dutch and

Chinese). In addition to evaluating the systems based on their accuracy, the likelihood

ratio was evaluated, which is a measure used by forensic handwriting examiners (FHEs)

to assess the value of the evidence. For on-line verification, the best system achieved

an accuracy of 93% with the Chinese signatures and 96% with the Dutch signatures.

Interestingly, most systems performed better with the Dutch signatures.

More comprehensive reviews of signature verification can be found in Impedovo and

Pirlo (2008), Garcia-Salicetti et al. (2009) and Plamondon and Srihari (2000).

1.2.2 Signature verification features

An extensive list of signal features have been used for signature verification. See for ex-

ample Impedovo and Pirlo (2008) and Rashidi et al. (2012) for a comprehensive listing.

These features can be classified as global or local features (Yampolskiy & Govindaraju,

2008; Kholmatov & Yanikoglu, 2004; Impedovo & Pirlo, 2008; Impedovo, Pirlo, & Pla-

mondon, 2012). Global features relate to the signature as a whole such as max/min

speed, signature bounding box, total number of strokes, and total time duration. Other

features are considered local because they correspond to a specific sample point along

the trajectory of the signature such as distance and curvature change between two points

on the signature trajectory and height-to-width ratio of a specific stroke.

On-line and off-line writer identification and signature verification studies have inves-

tigated the intra- and inter-participant variability of multiple handwriting characteristics

(Guest, 2004; Lei & Govindaraju, 2005; Guest, 2006; Bulacu, 2007; Impedovo & Pirlo,

2008; Ahmad, Shakil, & Anwar, 2008; Shakil, Ahmad, Anwar, & Balbed, 2008). For a

feature to be valuable for signature verification, the feature should have high consistency

Chapter 1. 14

within genuine signatures and high discrimination between genuine and forged signatures

(Lei & Govindaraju, 2005; Rashidi et al., 2012). Lei and Govindaraju (2005) examined

the consistency and discriminative power of multiple features commonly used in on-line

signature verification systems. This study found that pen-tip coordinates, speed and

angle with an x axis are among the most consistent features. Guest (2004, 2006) assessed

the stability of a number of static and dynamic features by evaluating the repeatability

of these features within a single session and between multiple sessions. Using the coeffi-

cient of variation as a measure for repeatability and based on signatures collected from

more than 250 participants signing at least 10 signatures in at least two sessions, these

studies found that many of the considered features maintained high repeatability both

within and between sessions given the different age groups analyzed. A number of other

studies have also indicated the importance of considering the stability of handwriting

in signature verification (Dimauro, Impedovo, Modugno, Pirlo, & Sarcinella, 2002; Pirlo

& Impedovo, 2010; Impedovo, Pirlo, Sarcinella, Stasolla, & Trullo, 2012). Shakil et al.

(2008) and Ahmad et al. (2008) examined the repeatability of handwritten signature

features by studying the effect of using different dynamic and static features on the per-

formance of a hidden Markov model (HMM)-based signature verification. These authors

used the SIGMA database along with ANOVA and EER-based analysis. While the first

study found that the dynamic features (speed, angle, pressure, and acceleration) had high

distinguishing capability between genuine and skilled forgeries compared to other static

features, the second study found that the pen pressure had the highest intra-subject

variability within and between sessions compared to the other dynamic features. The

BSEC2009 competition intended to evaluate the effect of time variability on the perfor-

mance of signature verification systems; however, Houmani et al. (2012) did not report

the results of this evaluation.

To characterize forgeries, some studies have compared different handwriting charac-

teristics associated with authentic and forged signatures. When kinematic and dynamic

Chapter 1. 15

features were compared between authentic samples of a model writer and simulations of 10

other participants, it was found that forgeries were associated with longer reaction times,

slower movement velocities, more dysfunctions and higher limb stiffness (G. Van Galen

& Van Gemmert, 1996). Van Den Heuvel, van Galen, Teulings, and van Gemmert (1998)

also found that a higher pen tip pressure was associated with handwriting that required

more processing demand such as forging a signature. A more recent study investigated

the differences and similarities of kinematic and kinetic characteristics between authentic

signatures and forgeries (Franke, 2009). In this study it was found that even though some

forgers experienced slower movements, multiple pen stops and higher axial forces, other

forgers were able to simulate the general velocity with no hesitations and with compara-

ble or even lower pen tip forces. The difference in handwriting measures between writing

a true versus a deceptive message has also been examined. It was found that false writing

was associated with a significantly higher mean axial pressure, stroke length and height

(Luria & Rosenblum, 2010). These differences were found because of the higher cognitive

load required to forge another person’s handwriting or write a deceptive message.

1.2.3 Signature verification algorithms and databases

Many different verification algorithms have been implemented in the literature. These

algorithms can be divided into two main classes of methods (Garcia-Salicetti et al., 2009;

Houmani et al., 2012):

• Distance-based: Repeated signatures from a specific person are saved in a database.

A test signature is compared to these reference signatures by means of a distance

measure. Example distance measures include dynamic time warping (elastic dis-

tance), Euclidean distance, Mahalanobis distance and adapted Levenshtein dis-

tance.

• Model-based: A statistical signature model is built using repeated signatures from

Chapter 1. 16

the same person. A test signature is then compared to this model yielding a likeli-

hood measure. Some of the commonly used models are HMM or Gaussian mixture

models (GMM).

Rashidi et al. (2012) also listed a number of algorithms that were used by different

research groups for signature verification such as support vector machine and neural

networks.

There are many on-line handwritten signature databases that are available and used

by researchers for testing different signature verification systems. Some of these databases

include: Philips; Biomet; SVC 2004 development set; MCYT; and Bioscure. These

databases differ from each other in many aspects including the size of the population,

sensor resolution, nature of skilled forgeries, stability of genuine signatures, presence or

absence of time variability, and the nature of time variability (Garcia-Salicetti et al.,

2009). All of these databases capture a set of signature characteristics including the x

and y coordinates, the pen pressure on the tablet and two pen orientation angles. The

most common type of forgery considered in these databases, and consequently reported

in verification papers, is skilled forgeries. The skilled forger is one who has had access

to a genuine signature for practice. In the Philips database these skilled forgeries are

known as ‘home-improved forgeries’. Another type of commonly considered forgery is

the random or zero-effort forgery. In this instance, the forger does not have any prior

information about the signature or even the name of the person whose signature is being

forged (Kholmatov & Yanikoglu, 2004; Namboodiri, Saini, Lu, & Jain, 2004). Other types

of forgeries appearing specifically in the Philips database include ‘over the shoulder’ and

‘professional’ falsifications. In the former, the forger learns the dynamic properties of the

genuine signature by observing the signing process, while with the latter the forgeries are

produced by individuals who have professional expertise in handwriting analysis (Garcia-

Salicetti et al., 2009).

Chapter 1. 17

1.2.4 Recent patents and commercial signature verification sys-

tems

Many patents have been issued and commercial systems developed for signature verifi-

cation purposes in the past few years. Some patents such as US patents 6873715 (2005)

and 6904416 (2006) describe manual verification systems that require a human expert

to compare two captured signatures. Other patents such as US patents 7415141 (2008)

and 7694143 (2010) focus on devices used to collect electronic signatures for signature

authentication purposes rather than on methods for signature verification. Even though

some patents discuss a general framework for signature verification, they do not report

quantitative measures of authentication performance. For example, US patent 7454042

(2008) proposes signature verification by speed equalization and a velocity transform fol-

lowed by characteristic extraction and difference vector estimation to determine whether

or not input and reference signatures are signed by the same person. Likewise, US patent

7529391 (2009) employs Hidden Markov Models and Gaussian Mixture Models for sig-

nature verification. Neither patent, however, provide any indication of the quantitative

performance of their respective methods.

Many signature verification systems have been developed commercially on the mar-

ket, including, for example, Topaz systems, Softpro, KeCrypt, xyzmo SigNificant and

Wondernet. All these systems enable customers to capture signatures digitally and sign

documents from around the world. Many of these companies add security by including

signature authentication solutions. However, these signature authentication solutions

rely only on image-recognition and kinematic-kinetic signals. Further, authentication

performance is often not reported.

Chapter 1. 18

1.3 Motivation

Based on the introduction given on handwriting biomechanics in Section 1.1, it is evident

that the handwriting grip kinetics play an important role in this well-learned motor skill.

It has been shown that a comprehensive understanding of the underlying biomechanical

processes utilized during handwriting is needed to accurately guide clinical interventions

as well as to develop improved assessments and retraining programs (Van Drempt et al.,

2011). It has been proved that such studies can offer help in the diagnoses, quantification,

and treatment of disorders connected to handwriting (Hooke et al., 2008). In addition,

the discussion, as found in Section 1.1, explored the connection between handwriting

grip kinetics and its biometric value for gun control and writer recognition applications.

Handwriting grip kinetics has also been used to discriminate between different writers in

clinical handwriting studies.

On the other hand, as described in Section 1.2, it is clear that a lot of work on

signature verification has been done as evidenced by the scientific literature, patents and

commercial systems. Most of the available research uses axial forces, kinematic features

(e.g., position, velocity, acceleration, inclination angle) and spatiotemporal features (e.g.,

stroke durations, stroke length, in-air time) for signature verification. Some of this work

has reported high rates of authentication under specific conditions but the performance

seems to decline in more realistic scenarios. However, the work on signature verification

has not yet taken into consideration the grip biomechanics and specifically the grip forces

applied on the pen’s barrel while writing a signature. Only recently, the study by Bashir

and Kempf (2012) reported the advancement of pin recognition performance when a grip

force signal was added to the classification. However, this study used a limited database

that included only 10 samples per person collected in a single session, which does not

incorporate the variability that can be generated over multiple sessions and multiple

days. In fact, a recent literature review of adult handwriting by Van Drempt et al.

(2011) showed that studies of adult pencil grasps are very limited in number. Further,

Chapter 1. 19

studies have typically not considered the grip biomechanics associated with pencil grasps.

Therefore, the biometric value of grip patterns and its associated kinetics has yet to be

explored in handwriting studies.

The study of handwriting grip kinetics and grasp patterns may uncover discriminatory

grip force features that can be used for handwriting personal verification systems and

forensic document examination. In fact, since pencil grasps, such as the three-digit grasp

often used in handwriting, are known to be kinetically redundant, different digit force and

torque combinations can produce identical kinematic profiles (Hooke et al., 2008). This

suggests that even if kinematic profiles can be imitated, the corresponding kinetic profiles

will likely be different. Also, the invariance of the individual relative forces produced by

the muscles employed during a learned motor program such as handwriting (R. Schmidt

& Lee, 2011) can contribute to the unique pattern of grip forces.

Collectively, the evidence presented in this chapter encourage the investigation of the

value of grip forces as a biometric measure for signature verification. It is hypothesized

that it is difficult to replicate the grip kinetic profiles associated with someone’s signature

and that individuals can generate authentic signatures with repeatable force profiles.

1.4 Objectives and Research Questions

The main objective of this thesis was to investigate the feasibility of using grip kinetics as

a biometric characteristic in signature verification system. Towards this main objective

and in light of the literature discussed above, the following secondary objectives were

examined to verify that grip forces fulfill the main requirements of a biometric measure

as mentioned in Section 1.2:

• Investigate the intra- and inter-subject variability of grip forces associated with

signatures written on different days and different times within the same day to

verify that these grip forces are distinctive and permanent.

Chapter 1. 20

• Identify discriminatory grip force features that are sufficiently invariant with time

but variant between any two people, such that these features can discriminate

between forged and authentic signatures.

• Estimate the size of data set required to model personal grip forces given the intra-

subject variation.

Based on the above objectives and considering different representations of grip forces,

the following four research questions were formulated and answered in the following four

chapters:

1. What is the extent of intra- and inter-subject variation in forces applied to the barrel

of the pen during signature writing in an adult population, with a particular focus

on the topographical representation of forces? This representation examined the

distribution of forces applied on the pen barrel which characterize the grip shape

utilized during writing. Image-based analysis of grip kinetics along with several

classification algorithms were used to gauge the level of accuracy of participant

discrimination based on grip shape kinetics. This question is explored in Chapter

2.

2. Does the variability in handwriting grip kinetics change over time? This question

focused on investigating the intra- and inter-participant variability of different grip

kinetic features based on data collected over a longer period of time (a few months).

This is crucial for the viability of using grip kinetics in signature verification sys-

tems, where performance must be maintained over longer periods. Statistical and

classification analyses were used to gauge long term variability in grip kinetics.

This question is explored in Chapter 3.

3. Do authentic and well-practiced signatures have different grip kinetics? This ques-

tion focused on comparing the magnitude and dispersion of grip kinetics between

Chapter 1. 21

repeated samples of a subject’s authentic signature and a well-practiced bogus sig-

nature written by the same subject. This study determined if there are differences

in grip kinetic features between authentic and well-practiced signatures and whether

these kinetics are associated with different levels of intra-subject variability. This

question is explored in Chapter 4.

4. What is the extent of intra- and inter-subject variation in forces applied to the

barrel of the pen during signature writing in an adult population, with a particu-

lar focus on the functional representation of forces? This representation examined

the profile (curve) of total forces applied to the pen barrel while writing a sig-

nature, thereby characterizing grip force dynamics during writing. Curve-based

analysis of grip kinetics along with several classification algorithms were used to

identify discriminatory grip kinetic features and gauge the level of accuracy of sig-

nature verification. This analysis was performed based on multiple repetitions of

a well-practiced signature since it requires all participants to be writing the same

signature. The effect of sample size was also examined in this study. This question

is explored in Chapter 5

Answering these questions required establishing a database of signatures with grip

force data since all available databases to date do not incorporate grip force information.

The data were collected in two phases: Phase 1 included authentic signatures as well as

well-practiced bogus signatures that were collected over 10 days; and Phase 2 included

authentic signatures that were collected over a longer period of time (a few months).

Further details regarding the data collection can be found in the chapters that follow.

1.5 Thesis Organization

Chapters 2 through 5 represent the main body of this thesis. Each chapter details a

distinct study that answers one of the research questions and addresses one or more of

Chapter 1. 22

the thesis’s objectives, as explained in section 1.4 above. Since the chapters analyze

different subsets of the same data set, the introduction and parts of the method section

of some chapters (data collection instrumentation and protocol) may contain repeated

information that the reader may wish to skip. Figure 1.1 shows a block diagram of

the main chapters of the thesis along with the topic and data set used in each of these

chapters. Further details on different grip shapes, kinematics versus kinetics, and some

analytical methods, such as box plot and linear discriminant analysis, are presented in

appendix A.

Each chapter is a verbatim excerpt of an independent manuscript that has been

published, accepted, or submitted for publication in a peer-reviewed journal. Permission

to reproduce articles in this thesis was obtained as necessary. The final chapter, Chapter

6, discusses the main conclusions and summarizes the major original contributions of this

thesis.

Chapter 1. 23

Chapter Topic Data

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Phase 1 Phase 2

Authentic

Authentic Authentic

Authentic

Bogus

Bogus

Variability of grip kinetic

topography during

signature writing

Long term stability of

handwriting grip kinetics

A comparison of grip

kinetics between authentic

and well-practiced

signatures

Variability of grip kinetic

profiles between adults

writing the same signature

Figure 1.1: Block diagram showing the topic and the data set used in each ofthe main chapters of the thesis.

Chapter 2

Variability of Grip Kinetics During

Adult Signature Writing

This chapter is a reproduction from the following journal article: Ghali, B., Anantha,

N. T., Chan, J., & Chau, T. (2013). Variability of grip kinetics during adult signature

writing. PLoS One, 8 (5), e63216.

The reader is advised to skip the introduction section of this chapter, since it contains

common information with Chapter 1.

2.1 Abstract

Grip kinetics and their variation are emerging as important considerations in the clinical

assessment of handwriting pathologies, fine motor rehabilitation, biometrics, forensics

and ergonomic pen design. This study evaluated the intra- and inter-participant vari-

ability of grip shape kinetics in adults during signature writing. Twenty (20) adult

participants wrote on a digitizing tablet using an instrumented pen that measured the

forces exerted on its barrel. Signature samples were collected over 10 days, 3 times a

day, to capture temporal variations in grip shape kinetics. A kinetic topography (i.e.,

grip shape image) was derived per signature by time-averaging the measured force at

24

Chapter 2. 25

each of 32 locations around the pen barrel. The normalized cross correlations (NCC) of

grip shape images were calculated within- and between-participants. Several classifica-

tion algorithms were implemented to gauge the error rate of participant discrimination

based on grip shape kinetics. Four different grip shapes emerged and several participants

made grip adjustments (change in grip shape or grip height) or rotated the pen dur-

ing writing. Nonetheless, intra-participant variation in grip kinetics was generally much

smaller than inter-participant force variations. Using the entire grip shape images as a

32-dimensional input feature vector, a K-nearest neighbor classifier achieved an error rate

of 1.2 ± 0.4% in discriminating among participants. These results indicate that writers

had unique grip shape kinetics that were repeatable over time but distinct from those of

other participants. The topographic analysis of grip kinetics may inform the development

of personalized interventions or customizable grips in clinical and industrial applications,

respectively.

2.2 Introduction

Handwriting grip is the arrangement of the fingers and thumb around the barrel of a writ-

ing instrument for the production of written output. Recent advances in instrumented

writing utensils (Chau et al., 2006; Hooke et al., 2008; Baur, Furholzer, Marquardt, &

Hermsdorfer, 2009) have enabled the measurement of handwriting grip kinetics, i.e., the

forces exerted by the fingers and thumb on the barrel of the writing implement dur-

ing handwriting. Handwriting grip kinetics are emerging as an important quantitative

measure in the clinical domain, but may also have relevance in biometrics, forensics and

ergonomics.

Chapter 2. 26

2.2.1 Clinical assessments

Recent clinical handwriting studies have expanded from pen tip kinematics to pen-

hand contact kinetics (Falk et al., 2010, 2011; Kushki et al., 2011; Shim et al., 2010;

Hermsdorfer et al., 2011). In a sample of patients with writer’s cramp (WC), Schneider

et al. (2010) discovered significant elevation of grip forces above the levels of healthy

participants only for those with dystonic WC, and thus suggested that grip kinetics may

uniquely provide clinical subtype differentiation. Likewise, Hermsdorfer et al. (2011)

reported that exaggerated forces in patients with WC occurred more frequently than

abnormal kinematics, concluding that grip force is an important descriptor of individual

impairment characteristics that are independent of writing kinematics. This finding cor-

roborates earlier conclusions by Fernandes and Chau (2008) that the dynamics of grip

force and pacing are independently regulated.

2.2.2 Rehabilitation

In addition to the clinical characterization of handwriting function, grip force has a

role in both treatment and outcome measurement. Baur, Furholzer, Marquardt, and

Hermsdorfer (2009) developed a novel intervention for patients with writer’s cramp, us-

ing auditory grip force feedback, namely, a continuous low frequency tone whose pitch

increased with escalating grip force. Significant reduction in writing pressures and pain

were noted over 7 sessions of treatment. Deploying grip force as an outcome measure,

Baur, Furholzer, Jasper, et al. (2009) found that both a modified pen grip and handwrit-

ing training (motor exercises) decreased grip force in patients with writer’s cramp and in

a sample of asymptomatic controls.

Chapter 2. 27

2.2.3 Biometrics

Online and offline writer identification and signature verification studies have investigated

the intra- and inter-participant variability of handwriting (Impedovo & Pirlo, 2008; Lei

& Govindaraju, 2005; Bulacu, 2007). However, these studies have focused exclusively

on normal forces, and kinematic (e.g., position, velocity, acceleration, inclination angle),

spatiotemporal (e.g., stroke durations, stroke length, in-air time) and image-based fea-

tures. The biometric value of grip patterns and its associated kinetics has yet to be

explored in handwriting studies. In gun control applications, for example, grip force pat-

terns have already proven valuable for biometric verification (Shang & Veldhuis, 2008a,

2008b, 2008c).

2.2.4 Forensics

Given the relationship between axial (pen tip force on the writing surface along the

length of the pen) and grip forces, knowledge of the former from an analysis of paper

indentations (Furukawa, 2011) may shed light on the pen grip of the writer and possibly

the presence of musculoskeletal pathologies of the writer.

2.2.5 Ergonomics

Grip forces may inform the design of new pens, such as in (Udo, Otani, Udo, & Yoshinaga,

2000), which proposed a pen with a flared silicon grip area as a means of reducing

muscle load (EMG activation) and upper limb pain during extended periods of continuous

writing.

Given the emerging importance of grip kinetics, in this study we systematically eval-

uated the intra- and inter-participant variability of grip shape and forces in an adult

population during signature writing.

Chapter 2. 28

2.3 Methods

2.3.1 Ethics statement

The protocol of the study was approved by the research ethics boards of Holland Bloorview

Kids Rehabilitation Hospital and the University of Toronto. Each participant provided

an informed written consent.

2.3.2 Participants

We recruited a convenient sample of 20 adult participants (8 males; 17 right-handed; age

27 ± 6 years) with no history of musculoskeletal injuries or neurological impairments.

Each participant completed a simple demographic questionnaire upon acceptance to par-

ticipate in the study. The questionnaire asked about gender, handedness, age, occupation,

education level, fathers education level, mothers education level and racial/ethnic group.

2.3.3 Instrumentation

Figure 2.1 depicts the study equipment, which consisted of an instrumented writing uten-

sil and a digitizing LCD display. The utensil was constructed by inserting the electronics

of a Wacom 6D Art Pen inside a cylindrical barrel machined out of Delrin. To capture

grip forces, an array of 64 Tekscan 9811 force sensors were first adhered to the pen barrel

using an adhesive (3M Super 77 Multipurpose Spray Adhesive) and then taped down

to mitigate sensor peeling. Note that in sensor calibration and data collection, only the

32 sensors closest to the apex of the pen were considered as the more distal sensors

were generally not activated during writing. Four such pens were manufactured for this

study. See (Chau et al., 2006) for further details about utensil construction. The writing

utensil was connected to a data collection computer via a custom-made data acquisition

box containing operational amplifier circuits that biased voltages to maximize the input

signal resolution, multiplexers and a 16 analog input data acquisition card. Grip forces

Chapter 2. 29

were sampled at 250Hz. The force sensor array was replaced multiple times during data

collection due to sensor wear and tear. The total pen weight was 24g. The pen had a di-

ameter of 1.3 cm and a height of 14 cm. The writing surface was an electronically inking

Wacom Cintiq 12WX digitizing LCD display, which collected axial force, pen tip position

and pen angles (rotation, altitude and azimuth) at a frequency of 105 Hz. The digitizing

display was connected to the data collection computer via VGA and USB cables.

Figure 2.1: Data Collection instrumentation setup. Participants wrote with theinstrumented writing utensil on a digitizing LCD display. The data acquisition box andthe computer transmitted and saved the data respectively.

2.3.4 Calibration set-up and procedure

Prior to data collection, the force sensors on the barrel of the writing utensils were

systematically calibrated. Figure 2.2 portrays the calibration setup, which included a

digital scale that measured the applied load, a fixed lower nest on which the pen rested,

a top nest that loaded the pen from above, and, a lead screw assembly that raised and

lowered the top nest via a rotary knob and moving bracket. To accelerate calibration,

the top nest was designed to simultaneously load a column of eight sensors at one time.

Specifically, the top nest was contoured to match the curvature of the pen’s barrel and

padded with a thin layer of vinyl (CON-TACT non-adhesive liner) to encourage uniform

Chapter 2. 30

distribution of force along the targeted section of the pen barrel. To avoid slippage of

the pen, the fixed bottom nest was similarly padded.

Figure 2.2: The calibration setup. Each sensor in the force sensor array was calibratedusing this setup through loading and unloading of the sensors.

The pen was placed on the bottom nest with the targeted column of sensors facing up.

The column of sensors was gradually loaded and unloaded by rotating the knob. The load

on an individual sensor ranged from 0 to 1100 grams. Force and digital scale readings were

synchronized and recorded directly to a computer via the custom-made data acquisition

box and a serial cable, respectively. From these data, loading and unloading curves were

derived offline. These calibration curves facilitated the translation of subsequent sensor

readings (in Volts) into physical units of force (Newtons).

Each time a pen was calibrated, the above loading and unloading procedure was

repeated 6 times, 3 with the pen tip pointing in one direction and 3 with the pen in the

Chapter 2. 31

opposite direction. Averaging calibration curves from these iterations helped to minimize

the effect of any differences due to misalignment between the top nest and sensor bank,

and any orientation-dependent load imbalance.

Throughout the data collection described below, the force sensors for each pen were

calibrated every 2 to 3 days to account for possible changes in sensor behavior over time,

especially a decrease in sensor sensitivity with usage.

2.3.5 Data collection protocol

All data collection took place in a laboratory within a university teaching hospital. Each

session adhered to the following steps:

1. Participants sat comfortably on a height-adjustable task chair, facing a typical

workbench. Participants wore a grounding strap on the non-dominant hand and

held the instrumented utensil with the dominant hand.

2. The force sensors were checked by a researcher through visual inspection of a

real-time colour display of individual sensor force values.

3. A custom software ‘wizard’ was launched and systematically guided participants

through each step of data collection.

4. The participant answered a status question on the tablet, namely,“Do you think

there is any emotional, mental or biomechanical factors that can affect your hand-

writing now? (E.g. angry, stressed, nervous, sick, muscle stiffness or fatigue). The

answer should be yes or no.”

5. The participant was asked to hold the distal end of the pen without contacting any

of the sensors on the pen for a 10 second period to collect baseline values of the 32

force sensors on the pen. These baseline values are used to calculate the pre-grip

values of each force sensor as explained in taring and calibration procedures below.

Chapter 2. 32

6. The participant held the pen naturally and provided 20 samples of a well-practiced

bogus signature that each participant practiced for two weeks prior to data collec-

tion. The participant signed on the tablet within a delineated area, which was

refreshed by an explicit button press after each signature.

7. Two digital photos, one a dorsal view and the other a palmar view of the hand

grip, were taken at the halfway point of the session.

8. The participant provided 20 samples of his/her own authentic signature.

9. Two digital photos (dorsal and palmar views) of the hand grip were taken at the

end of each session.

The above procedure was repeated three times a day (morning, afternoon, and evening),

on 10 different days according to participant availability. On average, data collection

was completed in 20.4 ± 3.6 days. The iterative collection was designed to capture grip

shape and kinetic variations over time. For each participant, 600 authentic signatures

and 600 well-practiced bogus signatures were obtained over a total of 30 sessions (3

sessions per day × 10 days). In this study, we only consider the 12000 (600 signatures

× 20 participants) authentic signatures. A researcher noted any writing mistakes during

data collection or any suspicious sensors during calibration, to inform subsequent data

screening.

2.3.6 Data preprocessing

Clean-up

Upon visual review of the collected data and cross-referencing with researcher notes, we

discarded 225 authentic signatures out of the 12,000 for one or more of the following rea-

sons: visible mistakes while writing the signature (e.g., scratched out text), an extended

pause in the midst of a signature, or an obvious force sensor malfunction (e.g., loss of

Chapter 2. 33

signal). Also, signature samples accidentally contaminated with extra lines or dots on

the tablet before or after the signature were salvaged by trimming the contaminant data

from the beginning or end of the signature sample as appropriate.

The force data were subjected to a sixth order Butterworth low-pass filter with a

cutoff frequency of 10 Hz, which was deemed to be the lowest frequency below which more

than 95% of the signal power resided. Signatures that exhibited visible low frequency

oscillations unrelated to handwriting (likely noise from nearby electronic devices) were

excluded from the subsequent analysis. The total number of samples that were excluded

at this stage was 735 authentic signatures. In total, 8% of the 12,000 authentic signatures

were excluded subsequent to data cleanup, leaving 11,040 signatures for analysis, with

an average of 552 samples per participant.

Taring and calibration

Since the force sensors were curved around the barrel of the pen, they had non-zero

readouts prior to the participant gripping the pen. These pre-grip values were estimated

using the 10 second baseline collected prior to any handwriting, on a per sensor, per

session basis. For each sensor, the mean pre-grip value was subtracted from all subsequent

grip force data in a given session. In this way, the readout of each sensor prior to the

participant gripping the pen was zero. Each sensor reading was then translated into units

of physical force (N) via a least-squares second order polynomial fit to the corresponding

shifted calibration data, as shown below:

F = (P1 + P2 ∗ S + P3 ∗ S2) ∗ g (2.1)

where F is the calibrated sensor reading in Newtons, P1, P2 and P3 are the polynomial

coefficients, S is the raw reading for a particular sensor, and g is the gravitational constant

(9.81 m/s2).

Chapter 2. 34

Figure 2.3 shows one signature sample and the associated raw and processed (trimmed,

filtered, shifted and calibrated) grip forces. Note that the signature shown in Figure 2.3

is a sample of the well-practiced rather than authentic signature. This sample was used

to illustrate the relation of the writing sample to the raw and processed grip force data.

To provide the reader with a sense of the spatial and temporal characteristics of the

authentic signatures considered in this study, a list of key spatiotemporal features is pre-

sented in the results section below. The time and pen tip position (x and y coordinates)

data collected by the LCD digitizing display were used to calculate duration, total path

length, height, width and average speed of each signature. Note that these data were

collected only when the writing instrument touched the digitizing display, which thus

provided the onset and offset of writing. The height of each signature was calculated

as the difference between the minimum and maximum position in the vertical direction.

The width was calculated similarly but in the horizontal direction. The manufacturer-

specified resolution of the digitizing display was used to convert the derived distances

from pixels to millimeters. No other preprocessing was applied to these data.

2.3.7 Data analysis

Grip shape identification

By reviewing the collected photos, the grip shape of each participant was classified ac-

cording to standard grip shape taxonomies (Selin, 2003; Dennis & Swinth, 2001; Burton

& Dancisak, 2000; Tseng, 1998). To establish inter-rater reliability, a random sample

of 20% of the photographs were examined by an independent occupational therapist not

associated with the study. Complete (100%) agreement was achieved.

Deriving grip shape

The time-average of forces applied to each sensor over the course of a signature was

computed. These average forces were arranged into a matrix corresponding to the spatial

Chapter 2. 35

0 1 2 3 4 50

2

4

Time (s)

Grip

forc

e (N

)

0 1 2 3 4 5

1

1.5

2

Time (s)

Vol

ts (

V)

100 150 200 250 300

20

40

0 s1 s 2 s

3 s 4 s 5 s

x (pixels)

y (p

ixel

s)

Figure 2.3: A signature example and the associated grip force signals. The topgraph shows the position signals of a signature sample annotated at 1 second increments,and the middle and bottom graphs show the associated raw and processed grip forcesignals respectively. For clarity, only the non-zero force traces are shown in the latter. Inbottom two graphs, each line represents the readout of a different grip sensor. Note thatthis sample is not an authentic signature; it is a sample of a well-practiced signature.

arrangement of sensors around the barrel. The resultant matrix was termed the grip

shape, given that a heat map of this matrix (i.e., grip shape image) reveals the spatial

distribution of forces around the barrel. Each signature thus had an associated grip

shape matrix (See Figure 2.4 for an example). Note that for a given grip shape matrix,

the forces were normalized to fall within [0, 1]. The distance, D, between two grip shape

matrices, M1 and M2, was computed as the Frobenius norm of their difference (Szabo,

Chapter 2. 36

2000), i.e.,

D =

√√√√ 32∑i=1

(M1i −M2i)2 (2.2)

where M1i and M2i are the ith entries of the respective grip shape matrices. For each

signature’s grip shape matrix, we further computed the mean of the distances to the

grip shape matrices of all other signatures by the same participant, and termed this the

discrepancy measure for that signature. Grip shape matrices with discrepancy measure

falling within the lowest 50% were then averaged across signatures to arrive at the mean

grip shape for each participant. In short, the mean grip shape for each participant was

an average of the signature-specific force distributions across signatures with the most

typical grip shape for that participant.

Grip shape variation

The intra- and inter-participant variability of the grip shape was studied in three different

ways.

1. Fisher’s ratio of 2-dimensional normalized cross-correlation (NCC) between two grip

shape images: Intra-participant differences were estimated by the NCC between a

participant’s mean grip shape and the grip shape images of all other signatures

of the same participant. Inter-participant differences were captured by the NCC

between the participant’s mean grip shape and the grip shape images of signatures

of all other participants. Fisher’s ratio (Duda, Hart, & Stork, 2001) was used to

quantify the separation between distributions of intra- and inter-participant NCC

values, namely,

Fisher’s ratio =(m1 −m2)

2

v1 + v2(2.3)

where m1 and m2 are the means, and v1 and v2 are the variances of the two

distributions.

Chapter 2. 37

2. Error rates of discriminating NCC values among writers: Three types of classifiers,

namely, linear discriminant analysis (LDA), K-nearest neighbor (KNN) and back-

propagation neural networks (NN), were invoked. For KNN, we considered K-values

of 1,3 and 5 while the NN had an architecture of 1-10-1 (input-hidden-output units).

In each case, one classifier was trained per participant to determine if a signature

belonged to that participant or not. For a given writing sample, the input to the ith

classifier (i = 1, . . . , 20) was a one-dimensional NCC value between the unknown

signature and mean grip shape of the ith participant. The one dimensional binary

output denoted the predicted membership of the unknown signature (1=belongs

to ith participant). For each participant-specific classifier, the training set included

intra-participant NCC values with a desired output of 1 and an equal number of

inter-participant NCC values with a desired output of zero. Inter-participant NCC

values were pseudo-randomly selected to ensure representation from all participants.

The misclassification rate was calculated for all these classifiers using 10-fold cross

validation.

3. Error rate of discriminating grip shape matrices among writers: We discriminated

among writers using the entire 32-element grip shape matrix as the input to mul-

ticlass LDA and KNN classifiers with a single output denoting the participant

number. A backpropagation multiclass NN classifier with an architecture of 32-

25-5 was also tested. In this case, the 5 digit output was a binary representation

of the participant number. Misclassification rate was estimated using 10-fold cross

validation for all these classifiers.

Pen rotation within- and between-sessions may have led to spatial misalignment of

grip shape images. To mitigate these rotational effects, the grip shape images of each par-

ticipant were aligned horizontally to the mean grip shape image of the same participant

using the horizontal offsets that maximized the NCC between the mean and individual

grip shape images. Here, horizontal refers to the circumferential axis. We then repeated

Chapter 2. 38

the grip shape variation analyses described above post-alignment.

2.4 Results

2.4.1 Spatiotemporal features

Table 2.1 summarizes the duration, total path length, height, width and average speed of

the authentic signatures across participants. Clearly, signatures ranged in duration, size

and speed. The duration of the signatures ranged from 1-6 seconds, depending on the

writing speed of the particular participant and the length of the individual’s signature. An

earlier study that collected signatures from 70 participants reported that the duration

ranged from 2-10 seconds (Herbst & Liu, 1977). According to the size taxonomy by

Araujo, Cavalcanti, and Carvalho Filho (2006), the size of the signatures collected herein

ranged from small to large. The values of average speed echo those reported by Franke

(2009), which were based on 55 writers writing their authentic signature 30 times.

2.4.2 Grip shapes

Table 2.2 lists the grip shape for each participant as determined via photo-review. Based

on the observed grip shape variation, the participants were categorized into four groups,

namely, (1) six who maintained a consistent grip shape throughout, (2) seven who ro-

tated the pen and/or altered grip height either within or between sessions, (3) four who

routinely changed grip shapes within and/or between sessions, and, (4) three who altered

their grip shape after the initial sessions.

2.4.3 Topographical analysis of grip shape variability

Figure 2.4 shows the mean grip shape for each of the 20 participants. The topographic

images represent the force distributions over the 8x4 force sensor array, with the bottom

Chapter 2. 39

Table 2.1: Temporal, spatial and speed information of the authentic signaturesDuration(sec)

Totalpathlength(mm)

Height(mm)

Width(mm)

Averagespeed(mm/sec)

Participant Mean SD Mean SD Mean SD Mean SD mean SD1 1.1 0.2 95 12 18 3 49 8 115 172 6.1 0.3 491 56 27 3 100 15 87 113 3.5 0.4 239 30 17 4 60 15 84 194 3.1 0.2 251 33 17 2 60 9 90 95 2.6 0.2 275 38 24 3 51 7 112 106 5.8 0.2 468 49 18 2 71 9 79 97 1.3 0.2 226 28 29 3 87 6 226 278 3.9 0.3 314 25 21 2 82 5 88 89 4.3 0.3 172 21 14 3 38 3 45 610 3.9 0.3 163 13 14 1 47 4 43 311 3.6 0.3 296 30 25 3 54 5 95 912 4.3 0.4 246 37 25 5 68 8 63 913 1.2 0.1 122 14 20 2 16 2 106 914 2.9 0.6 140 28 21 3 29 5 55 815 3.7 0.3 173 16 13 2 40 4 49 416 2.2 0.3 244 66 32 7 35 6 110 2017 2.3 0.3 87 9 12 1 26 3 38 518 1.3 0.2 139 28 17 3 35 9 111 1619 4.2 0.3 188 19 15 2 47 6 53 420 3.3 0.3 305 40 18 2 73 7 104 12Average 3.2 0.3 231.7 29.6 19.8 2.9 53.3 6.7 87.7 10.7

SD (standard deviation)

row of sensors being closest to the tip of the pen. The mean grip shape images appear to

be unique among participants even when participants were categorized by photo-review

as having the same, consistently employed grip shape (e.g., Participants 9, 10 and 19 all

have dynamic tripod grasps).

Notice that there are generally a 2 to 4 focal areas of peak force and a blurring of

lower forces elsewhere. Also note that most the force is concentrated near the apex of

the pen and that the forces are distributed horizontally, presumably to provide stability

to the utensil.

Chapter 2. 40

Table 2.2: Grip shape of each participant and associated observationsParticipant Grip shape Observations1 Quadrupod Rotated pen in some sessions2 Dynamic tripod Changed grip height and rotated pen slightly be-

tween sessions3 Dynamic tripod Rotated pen in most sessions4 Lateral tripod Occasionally started with a dynamic tripod grasp5 Dynamic tripod Rotated pen in some sessions6 Quadrupod / other Changed grip shape and grip height in most ses-

sions7 Static tripod Consistent grip shape8 Lateral tripod Consistently used quadrupod grasp for the first 3

sessions but varied grip shape in other sessions9 Dynamic tripod Consistent grip shape10 Dynamic tripod Consistent grip shape11 Quadrupod Changed grip shape to lateral quadrupod grasp

and rotated pen in some sessions12 Quadrupod (left) Rotated pen slightly13 Static tripod (Left) Consistent grip shape14 Dynamic tripod Changed grip shape in some sessions15 Lateral tripod Changed grip height between sessions16 Quadrupod (left) Changed grip after first session17 Dynamic tripod Rotated pen slightly18 Dynamic tripod Used different grip shape (quadrupod) for the first

three sessions19 Dynamic tripod Consistent grip shape20 Quadrupod Consistent grip shape

Box plots of the intra- and inter-participant NCC for all 20 participants are shown

in Figure 2.5. The plot on the left portrays the level of grip shape consistency within

each participant based on the distribution of grip forces. Note that median NCC values

are close to 1 and adorned with small boxes, suggesting high consistency of static grip

shape images for a given participant, over all 30 sessions. It is worthy to note that

some participants (4, 9, 10, 13, 17, 19, and 20) were more consistent than others (3,

6, 11, 15, and 18). In most cases, this finding resonates with the observations made in

Table 2.2 which is a descriptive characterization of the grip shape based on retrospective

photo review only (i.e., that some participants were consistent whereas others altered

Chapter 2. 41

Participant 1

2 4

2

4

6

8

Participant 2

2 4

2

4

6

8

Participant 3

2 4

2

4

6

8

Participant 4

2 4

2

4

6

8

Participant 5

2 4

2

4

6

8

Participant 6

2 4

2

4

6

8

Participant 7

2 4

2

4

6

8

Participant 8

2 4

2

4

6

8

Participant 9

2 4

2

4

6

8

Participant 10

2 4

2

4

6

8

Participant 11

2 4

2

4

6

8

Participant 12

2 4

2

4

6

8

Participant 13

2 4

2

4

6

8

Participant 14

2 4

2

4

6

8

Participant 15

2 4

2

4

6

8

Participant 16

2 4

2

4

6

8

Participant 17

2 4

2

4

6

8

Participant 18

2 4

2

4

6

8

Participant 19

2 4

2

4

6

8

Participant 20

2 4

2

4

6

8

0

0.5

1

Figure 2.4: Mean grip shape images of the 20 participants. Each grip shape imagerepresents the grip force distribution on the 4 by 8 force sensor array with the black pointsbeing the ones with the highest force.

their grip shapes from session to session). However, the observation of consistent grip

shape through static photographs does not preclude the possibility of high force variation,

which is the case for participant 18 who only changed grip shape in the first three sessions,

but exhibited high kinetic variability. Also, note that the intra-participant NCC values

shown in Figure 2.5 are post-horizontal alignment; therefore, some participants such as

participant 17, who rotated the pen as noted in Table 2.2, still surfaced as having a

consistent grip shape (i.e., high intra-participant NCC values).

The plot on the right side of Figure 2.5 indicates the amount of variation between

Chapter 2. 42

−0.2

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Participant

Intra−participant NCC with horizontal alignment

NC

C v

alu

e

−0.2

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Participant

Inter−participant NCC

NC

C v

alu

e

A B

Figure 2.5: Box plots of the intra- (left panel A) and inter-participant (rightpanel B) NCC values for all 20 participants. Each box represents the distributionof NCC values for one participant, while ‘+’ symbols denote outliers (values beyond 1.5interquartile ranges from the median).

participants. Note that the overall inter-participant NCC values are lower than the

intra-participant NCC values, indicating that the grip forces vary significantly between

participants but are consistent within a participant. Some participants (6, 7, and 8) have

very low inter-participant NCC values, suggesting that their kinetic grip shapes are very

different from those of other participants.

Figure 2.6 summarizes the Fisher’s ratio and the error rates associated with classifying

NCC values for each of the 20 participants. The results from the different methods agree

with each other; as expected, high Fisher’s ratio corresponds to low classification error

rate. However, using the inter-image NCC value as an input feature generally leads to

mediocre classification rates.

Table 2.3 summarizes the effect of grip shape image alignment on error rates associated

with classifying the entire grip shape matrix. For all three classifiers, the error rates only

decreased slightly after alignment, verifying our observations of circumferential offsets in

grip shape but suggesting that these within-participant differences are not large enough

Chapter 2. 43

2 4 6 8 10 12 14 16 18 200

53.1

2 4 6 8 10 12 14 16 18 200

2016.4

LDA

2 4 6 8 10 12 14 16 18 200

20 16.6

KNN

2 4 6 8 10 12 14 16 18 200

10

2014.3

Participant

% E

rro

r ra

teF

ish

er r

atio

Neural network

Figure 2.6: Separability of intra- and inter-participant NCC values. Separabilitymeasured by Fisher’s ratio (top graph) and classification error rates by LDA, KNN andNN classifiers (bottom three graphs respectively). The dashed line represents the averagevalue of each method.

to compromise image-based classification. Note however that the error rate for KNN grip

shape matrix classification is much lower than that of the LDA and NN classifiers and

generally much lower than that achievable with any classifier using NCC as input.

Table 2.3: Error rates in the classification of full grip shape imagesLDA KNN NN

Without grip shape alignment 24.2± 1.2 1.3± 0.3 13.6± 3.0With grip shape alignment 22.2± 1.3 1.2± 0.4 12.9± 1.1

Mean and standard deviation of error rates using LDA (linear discriminant analysis),KNN (K nearest neighbors) and NN (neural networks).

Particularly noteworthy is the fact that the intra-participant variability of some par-

ticipants (1, 3, 6, 7, 8, 11, 17 and 18) decreased after horizontal alignment of grip shape

images (slightly higher NCC values and fewer outliers). These were generally partici-

Chapter 2. 44

pants who were identified through photo review as having rotated the pen from session

to session. Also, note that the handedness of the participant (right or left) did not have

any particular effect on the grip shape variability.

2.5 Discussion

In this study, we studied the intra- and inter-participant variation in forces applied to

the barrel of the pen during signature writing in adults, with a particular focus on the

topographic distribution of forces. Kinetic data were collected on multiple days and at

multiple times within-day.

2.5.1 Grip shapes

Nearly half the participants deployed a dynamic tripod grasp, while the remainder

adopted quadrupod, lateral tripod or static tripod grasps. The predominance of grip

shapes other than the dynamic tripod has also been found in a pediatric population

(Schwellnus et al., 2012). In particular, 15% of participants adopted a lateral tripod

grasp in our sample, which is on par with the fraction of lateral tripod writers that

Bergmann (1990) reported among 447 adults (without any known pathologies). The

functional implications of grip shape on handwriting in adults is not well-documented at

this time (Van Drempt et al., 2011). However, Stevens (2009) did suggest that adults

with a lateral tripod grasp may fatigue more quickly than those who employ other grip

shapes in extended-duration writing tasks.

2.5.2 Within-participant variation of grip kinetics

The grip shape topographic maps and NCC results support the hypothesis that each

participant possesses unique grip shape kinetics that are repeatable within-participant

over time. This finding agrees with R. Schmidt and Lee (2011), who contend that the

Chapter 2. 45

relative force produced by muscles is an invariant feature of motor programs associated

with a unique pattern of activity. Signature writing can be considered an example of such

a learned motor program (Yanushkevich, Stoica, Shmerko, & Popel, 2005), rationalizing

the observed within-individual kinetic consistency.

Our finding also aligns with Greer and Lockman (1998) who examined the variation

of handwriting grip patterns with age, from childhood through to adulthood. They

observed a decrease in the variation of pen-surface positioning and the number of grips

that individuals use as they mature, and speculated that this emerging invariance may

be due to increasing automaticity and efficiency of handwriting as a manual motor skill.

However, it is important to note that Greer and Lockman (1998) only used a video-

based grip classification scheme which did not consider the biomechanics associated with

different pencil grip shapes. Finally, studies of grip forces associated with golf swings

have shown that each player deploys a repeatable grip force profile that is distinct from

that of other players (E. Schmidt et al., 2006; Komi et al., 2007, 2008). Our finding

corroborates the general conclusion of these studies that a high level of intra-participant

grip kinetic repeatability tends to accompany a well-learned manual motor activity.

Despite the general finding of personal consistency, there was a degree of intra-

participant variation. Hooke et al. (2008) and Shim et al. (2010) contend that pencil

grip shape is governed by a kinetically redundant system; different combinations of fin-

ger forces and torques can generate similar kinematic and spatiotemporal profiles. Indeed

multiple muscle groups, including those that move the fingers, wrist and forearm, are in-

volved in the generation of hand kinetics and thus, kinetic variation invariably exists

within individuals (Ramsay, 2000). Johnston, Bobich, and Santello (2010) found that

activation of both the extrinsic and intrinsic muscles of the hand is modulated by wrist

angle during a two digit grasp. Thus, even in dynamic grasps where pen motion comes

largely from finger articulation, forces may vary depending on the current wrist angle.

Studies have also shown that for the control of multi-joint movements such as handwrit-

Chapter 2. 46

ing, proprioception plays a critical role (Teasdale et al., 1993; Hepp-Reymond, Chakarov,

Schulte-Monting, Huethe, & Kristeva, 2009) and thus afferent inputs from the hand may

also lead to variations in kinetic output.

Two participants (Figure 2.5) exhibited an inflated level of within-individual kinetic

variability. Participant 6 had the lowest within-individual NCC. This can be explained

by the participant’s tendency to modify his grip height and to alternate between grip

shapes, specifically, extending or curling the index finger around the utensil. The partic-

ipant confessed that these were habitual strategies to compensate for fatigue. Likewise,

Participant 15 exhibited the widest variation of within-individual NCC. As noted in Table

2.2, this participant oscillated between various grip heights while writing. This obser-

vation also explains why horizontal alignment of the grip shape matrix did not reduce

the within-individual NCC variation. The lack of familiarity with the instrumented pen,

nervousness, or fatigue may have contributed to the use of multiple grip shapes while

writing. Summers and Catarro (2003) found that 28% of university students in their

study used more than one grip shape during a 2 hour exam.

2.5.3 Between-participant variation of grip kinetics

Four different types of grip shapes were identified through retrospective picture review.

However, an examination of the topographic distribution of the forces associated with

each grip shape indicated that the mean grip shape images were distinct between par-

ticipants even if two participants invoked the same grip shape. This kinetic uniqueness

may be attributed in part to the personalized coordination of muscles in executing a

complicated but well-trained motor skill such as handwriting and specifically signature

writing (Stelmach & Teulings, 1983). With a three digit grasp, Poston, Danna-Dos San-

tos, Jesunathadas, Hamm, and Santello (2010) posit that the distribution of neural drive

to multiple hand muscles may reflect anatomical or functional properties of hand mus-

cle groups, characteristics that are likely to vary among individuals and thus further

Chapter 2. 47

contribute to unique grip shape images.

It is worthy to mention that Participants 6, 7 and 8 had the lowest inter-participant

NCC, implying that their grip shape images were most unique among participants. In-

deed, Participant 6 adopted a unique combination of a quadrupod grasp and minor

variations thereof. Participant 7 preferred a tripod grasp but tended to hold the pen

distal to the apex (Figure 2.4). Participant 8 on the other hand, held the pen nearly

perpendicular to the tablet surface. These personal grip idiosyncrasies contributed to

the distinct grip shape images of these three participants.

Using the full grip shape matrix as the input to a KNN classifier yielded much more

compelling error rates (1.2± 0.4 after horizontal alignment). This finding suggests that

the boundaries among the individual grip shapes in 32-dimensional kinetic space are

nonlinear. The low error rate also indicates that the entire force distribution provides

a much more discriminatory feature set than that of a summary statistic (e.g., NCC).

Indeed, handwriting requires multi-digit synergies (Latash et al., 2003; Chau et al., 2006)

that involve both intrinsic and extrinsic hand muscles (Johnston et al., 2010). The full

grip shape matrix likely captures some of these interdigit coordination patterns that are

missed by a simple summary statistic.

Our inter-participant variability findings echo earlier indications of significant between-

participant variation in finger pressures during handwriting on the account of the per-

sonalized nature of this activity (Herrick & Otto, 1961). Further, Latash et al. (2003) re-

marked that natural handwriting depends critically on the stability of individual-specific

multi-digit synergies in which the fingers work as dependent force generators to stabilize

the pen. Hence, kinetic variation across individuals is not unexpected. Such variation

has also been noted with other motor skills such as golf swings (E. Schmidt et al., 2006;

Komi et al., 2007, 2008).

Chapter 2. 48

2.5.4 Possible applications

The topographic representation and analysis presented herein may lead to new applica-

tions of handwriting grip kinetics in rehabilitation, biometrics and ergonomics. Building

on the finding that certain handwriting disorders such as writers’ cramp are associated

with abnormal finger postures and highly individualized grip shapes (Hermsdorfer et al.,

2011), topographical kinetic analyses that evaluate the subject’s grip shape and the ex-

tent of its variability may add to the clinical characterization of these conditions. Also a

recent literature review on adults’ handwriting (Van Drempt et al., 2011) pointed out the

lack of handwriting research on healthy adults and the need for normative data. On these

fronts, the present study contributes to the definition of typical variation in grip kinetics

in adults, in the absence of handwriting pathologies. The uniqueness of grip kinetics may

further inform the development of personalized fine motor interventions. For example, the

prescription of different writing utensil adaptations (e.g., rubber or foam grips, indented

pencils, triangular pencils, ring clips) may depend on the individual grip shape of the

client. Kinetic topographies may also bear biometric value given that three dimensional

forces of the pen tip have demonstrated potential for signature verification (Wu, Shen,

& Yu, 2006) and that pen tip and grip forces are strongly correlated (Chau et al., 2006).

Kinetic grip topographies, particularly, interdigit force synergies (S. Lee, Kong, Lowe, &

Song, 2009) may also inform hand grip designs that maximize comfort and performance

for different hand sizes.

2.6 Conclusion

In this study, we introduced a topographic representation and image-based analysis of

grip kinetics associated with adult signature writing. We conclude that despite day-to-day

force variations within-individual, asymptomatic adult writers tend to exhibit a unique

kinetic grip shape when writing. Further, these individual-specific kinetic grip shapes are

Chapter 2. 49

algorithmically discernible from one another when the entire force distribution around

the pen barrel is considered. The topographic analysis of grip kinetics may inform the

development of personalized neuromotor interventions or customizable grips in clinical

and industrial applications, respectively.

2.7 Acknowledgements

The authors would also like to acknowledge Ka Lun Tam, Pierre Duez, Alex Posatskiy,

Laura Bell, Sarah Stoops, Dr. Heidi Schwellnus, Dr. Azadeh Kushki, and Dr. Khondaker

Manum for their support and the participants for their time.

Chapter 3

Long Term Stability of Handwriting

Grip Kinetics in Adults

This chapter is a reproduction from the following journal article: Ghali, B., Mamun, K.,

& Chau, T. Long term stability of handwriting grip kinetics in adults. (Under review).

The introduction section of this chapter and parts of the methods section (particularly

3.3.1, 3.3.2, and 3.3.3) contain common information with Chapter 1 and Chapter 2.

Therefore, the reader is advised to skip these parts of this chapter.

3.1 Abstract

While there is growing interest in clinical and industrial applications of handwriting grip

kinetics, the stability of these forces over time is not well-understood at present. In

this study, we investigated the short- and long-term intra- and inter-participant vari-

ability of grip kinetics associated with adult signature writing. Grip data were collected

from 20 adult participants using a digitizing tablet and an instrumented pen. The first

phase of data collection occurred over 10 separate days within a three week period. To

ascertain long-term variability, a second phase of data collection followed, one day per

month over several months. In both phases, data were collected three times a day. Af-

50

Chapter 3. 51

ter pre-processing and feature extraction, nonparametric statistical tests were used to

compare the within-participant grip force variation between the two phases. Participant

classification based on grip force features was used to determine the relative magnitude

of inter- versus intra-participant variability. The misclassification rate for the longitu-

dinal data was used as an indication of long term kinetic variation. Intra-participant

statistical analysis revealed significant changes in grip kinetic features between the two

phases for many participants. However, the misclassification rate, on average, remained

stable, despite different demarcations of training and testing data. This finding sug-

gests that while signature writing grip forces change over time, inter-participant kinetic

variation consistently exceeds within-participant force changes in the long-term. These

results bear implications on the collection, modeling and interpretation of grip kinetics

in clinical, biometric and forensic applications.

Keywords: grip kinetics, signature writing, long-term stability, inter-participant vari-

ability.

3.2 Introduction

Handwriting is a complicated, but well-trained, motor skill that involves the integration

and coordination of multiple physiological sensors (e.g., mechanoreceptors and vision)

and actuators (e.g., muscles) (Stelmach & Teulings, 1983; Falk et al., 2010; Van Drempt

et al., 2011). Many recent studies have focused on the kinetic aspects of handwriting

with an aim to better understand the relationship between the hand, the pen and the

written output. These studies have been enabled by the development of instrumented

writing utensils capable of measuring grip kinetics during handwriting (Chau et al., 2006;

Hooke et al., 2008; Baur, Furholzer, Marquardt, & Hermsdorfer, 2009).

Chapter 3. 52

3.2.1 Clinical studies of grip kinetics

Multiple clinical studies have reported the characterization of handwriting function using

grip kinetics (Hooke et al., 2008; Chau et al., 2006; Falk et al., 2010; Kushki et al., 2011;

Schwellnus et al., 2013). In Chau et al. (2006), an instrumented pen with force sensors

on the pen barrel provided new insights into the intimate coordination between pen tip

and barrel forces. The authors showed that grip force characteristics could discriminate

between pediatric writers with and without handwriting difficulties. In another pediatric

study, Falk et al. (2010) found that grip force dynamics play a key role in determining

handwriting quality and stroke characteristics. In an extended duration writing task,

Kushki et al. (2011) examined grip force changes in children over 10 minutes of writing

and found that grip forces increased over time, likely as a musculoskeletal compensation

strategy to maintain a stable grip in the face of muscle fatigue. Most recently, through

a biomechanical analysis of handwriting in 74 primary school children, Schwellnus et

al. (2013) contended that grip forces are generally similar across different grasps and

that kinetic variations due to thumb placement have no effect on speed and legibility

. Generally, in the above pediatric studies, the strong association between quantitative

handwriting measures (e.g., grip force and temporal-spatial parameters) and standard-

ized quality measures (e.g., speed and legibility) supports the quantitative evaluation

of handwriting through objective computer-based assessments (Falk et al., 2011). Grip

kinetics have also found their way into outcome measurement and treatment. In several

adult studies, elevated grip forces have been reported as being characteristic of writer’s

cramp (WC) while grip force-modulated auditory feedback along with a modified pen

grip and handwriting training has been an effective treatment for WC (Baur, Furholzer,

Marquardt, & Hermsdorfer, 2009; Baur, Furholzer, Jasper, et al., 2009; Schneider et al.,

2010; Hermsdorfer et al., 2011).

Chapter 3. 53

3.2.2 Grip kinetics in biometrics, forensics and sport

In addition to clinical applications, handwriting grip kinetics may play a role in bio-

metric and forensic applications. The available literature on handwriting and signa-

ture verification has focused on pen tip forces, kinematic, and spatiotemporal features

(Impedovo & Pirlo, 2008; Bulacu & Schomaker, 2007; Yeung et al., 2004). The intra- and

inter-participant variability of these features have been documented (Guest, 2004; Lei &

Govindaraju, 2005; Ahmad et al., 2008). However, the biometric value of handwriting

grip patterns and their associated kinetics remain largely unexplored (Bashir & Kempf,

2012). Grip force patterns have already proven to be a useful biometric in gun control

applications (Shang & Veldhuis, 2008a, 2008b). Forensic document examiners rely on

handwriting features, such as spacing, style, letter shape and stroke morphology, in ad-

dition to paper indentation caused by the pen tip (Furukawa, 2011) to detect forgery

(Girard, 2007; Koppenhaver, 2007). In Koppenhaver (2007), it is suggested that the

grip pressure pattern may also offer unique features for writer identification and forgery

detection. Grip forces have also been studied in a number of sports including tennis,

cricket, baseball, and golf to evaluate their effect on distance and accuracy (Komi et al.,

2008). In particular, in golf swings, each player produces a repeatable grip force profile

that is quite distinct from that of other players (E. Schmidt et al., 2006; Komi et al.,

2007, 2008).

3.2.3 Variability of grip kinetics

An early study on handwriting grip forces observed significant between-participant vari-

ability in finger pressure patterns and widely varying inter-finger absolute pressures

within-participants(Herrick & Otto, 1961). Grip forces are also likely to change as the

writer matures. Greer and Lockman (1998) noted an age-related decrease in the vari-

ation of pen-surface positioning and the number of grips that individuals use. It was

hypothesized that this decreasing variability of grip patterns might be due to increasing

Chapter 3. 54

stability and efficiency. From a motor control viewpoint, R. Schmidt and Lee (2011) sug-

gest that the relative force produced by muscles is an invariant feature of a generalized

motor program, such as that of signature writing (Yanushkevich et al., 2005), although

a unique pattern of activity results whenever the motor program is executed.

Aside from the studies mentioned above, little is known to date about the typi-

cal within-individual, functional variation of grip forces over time (Van Drempt et al.,

2011). From the clinical perspective, this knowledge is important in the identification

of pathological force patterns and in measuring treatment effects. From the biometric

and forensic perspectives, knowledge of the stability of within-subject grip forces would

inform algorithmic writer verification and identification.

In light of the above, we investigated the stability of multiple grip kinetic features

of signature writing in adults. We chose to focus on adult writers to sidestep the issue

of developmental grip changes. To mitigate kinetic variation due to skill acquisition,

we focussed on signature writing as it is generally a well-learned motor task. To ascer-

tain inter- and intra-participant kinetic variability, signature writing data were collected

several times a day, over multiple months.

3.3 Methods

3.3.1 Ethics statement

The study’s protocol was approved by the research ethics boards of Holland Bloorview

Kids Rehabilitation Hospital and the University of Toronto, both situated in Toronto,

Canada. Each participant read and signed a written consent form.

3.3.2 Participants

We recruited a sample of 20 adult participants from the students and staff population

of a local academic teaching hospital. The sample included 8 males and 17 right-handed

Chapter 3. 55

participants. The age of the participants ranged from 18 to 45 years with a mean of 27

± 6 years. Participants had no known history of musculoskeletal injuries or neurological

impairments that could affect their handwriting function. Each participant received a

study information sheet and completed a simple demographic questionnaire.

3.3.3 Data collection set-up

As illustrated in Figure 3.1, the instrumentation set-up consisted of five main parts:

an instrumented writing utensil, a digitizing LCD display (tablet), an interface box, a

computer, and a grounding strap. The instrumented utensil was constructed by placing

the electronics of a Wacom 6D Art Pen inside a cylindrical barrel that was covered with

an array of Tekscan 9811 force sensors. As highlighted in Figure 3.1, only the sensors

closest to the apex of the pen were considered during sensor calibration and data analysis.

A custom-made interface box connected the writing utensil’s force sensor array to the

data collection computer. Grip data were acquired at a frequency of 250 Hz. The writing

surface was an electronically inking Wacom Cintiq 12WX digitizing LCD display, which

collected axial force, pen tip position, pen tilt angles, as well as pen rotation angles at

a frequency of 105 Hz. Data collection from the digitizing display and grip force sensors

were synchronized and stored on the same data collection computer.

Four instrumented utensils were manufactured for this study and the force sensor

arrays were replaced multiple times during data collection due to sensor wear and tear.

In addition, the force sensors on the barrel of the writing utensils were systematically

calibrated every two to three days to account for possible changes in sensor behavior over

time (e.g., a decrease in sensor sensitivity with usage). Loading and unloading curves

for each sensor were used to translate subsequent sensor readings (Volts) into physical

units of force (Newtons) off-line. Further details regarding the calibration procedure and

the instrumentation set-up can be found in Ghali, Anantha, Chan, and Chau (2013) and

Chau et al. (2006).

Chapter 3. 56

Grounding

strap

Custom interface

box

Computer

Tablet

Instrumented

pen

Force sensor array

Figure 3.1: Data collection instrumentation set-up. A close up of the instrumentedpen is shown, highlighting the section of the force sensor array of interest.


Data collection involved two phases. In the first phase, each participant completed a

total of 30 sessions on 10 different days. On each day, there were three sessions (morn-

ing, afternoon, and evening). The duration of the first phase of data collection varied

according to participant availability but was, on average, completed in 20.4± 3.6 days.

At the beginning of each session, a customized software ‘wizard’ was launched to guide

participants through each step of data collection. In each session, the participant sat com-

fortably, wore the grounding strap (to minimize grip sensor noise) on the non-dominant

hand, held the instrumented utensil with the dominant hand naturally, answered a health

Chapter 3. 57

status question, wrote 20 samples of a well-practiced bogus signature on the tablet, and

finally wrote 20 samples of his/her own authentic signature consecutively. In addition, in

each session, the force sensors were checked by a researcher through visual inspection of

a real-time colour display of individual sensor force values. Prior to writing, a 10 second

no-load baseline value for each force sensor was obtained by holding the distal end of the

pen such that none of the sensors of interest were loaded. Two digital photos (dorsal and

palmar views) of the hand grip were taken at the mid and end points of each session. To

minimize force changes due to pen rotation between trials, participants were reminded

to orient the pen such that the visible marking on the barrel faced outward. Further,

participants were discouraged from rotating the pen during writing, and instructed not

to fix mistakes or pause while writing. The duration of each session was approximately

five minutes, on average.

The second phase involved the collection of writing samples over an extended period of

time (one day per month× three sessions per day). Due to limited participant availability,

only 18 of the 20 participants were involved in the study’s second phase. Twelve of these

participants completed 15 sessions over five months while the remaining six participants

completed nine sessions over three months. Only authentic signatures were collected in

phase two (20 signatures per session). Otherwise, the phase two sessions resembled those

of phase one.

All data collection took place in a laboratory within an academic teaching hospital

and a researcher noted any writing mistakes that occurred during data collection or

any potential sensor malfunction during calibration. In the first phase, 600 authentic

signatures and 600 well-practiced bogus signatures were obtained from each participant

over a total of 30 sessions (3 sessions per day × 10 days). In the second phase, 300

authentic signatures were obtained from each of the 12 participants who completed 15

sessions. An additional 180 authentic signatures were obtained from each of the remaining

six phase two participants over a total of nine sessions. In this study, we only consider

Chapter 3. 58

authentic signatures, i.e., 12,000 (600 signatures × 20 participants) from phase one and

4,680 (300 × 12 + 180 × 6) from phase two. The authentic signatures from phase one

were previously reported in a topographic kinetic analysis (Ghali, Anantha, et al., 2013).

3.3.5 Data preprocessing

Several preprocessing steps were performed in order to prepare the grip force data for the

subsequent analysis. These steps included exclusion of contaminated signature samples,

noise removal, and calibration, as detailed below.

1. Signature samples were excluded from analysis if they contained visible mistakes,

an extended pause, and/or an obvious force sensor malfunction while writing.

2. Signature samples accidentally contaminated with extra lines or dots before or after

the signature were recovered by trimming the contaminant data from the beginning

and/or end of the signature sample as appropriate.

3. High frequency noise was suppressed using a Butterworth low-pass filter with a

cut-off frequency of 10 Hz, which was deemed to be the frequency below which

more than 95% of the signal power resided.

4. Signature samples that exhibited visible low frequency noise were excluded.

5. The grip force data were shifted by a pre-grip value for each sensor that was es-

timated using the 10 second no-load baseline collected at the beginning of each

session. These non-zero pre-grip values were a result of the force sensors being

curved around the barrel of the pen.

6. Grip force values for each sensor reading in units of physical force (Newton) were

derived via a least-squares, second order, polynomial fit to the corresponding shifted

calibration data.

Chapter 3. 59

In total, the above steps resulted in the exclusion of 8% of the 12,000 phase one authentic

signatures and 4.5% of the 4,680 phase two authentic signatures from subsequent analysis.

3.3.6 Feature extraction

Three features were extracted from each authentic signature sample for the study of

handwriting grip force kinetics over time. These features included the normalized cor-

relation coefficient (NCC), total average force (TAF), and total force interquartile range

(TFIQR).

1. The NCC quantified the consistency of the grip shape image. The grip shape image

(GSs) for each signature s was calculated by computing the time-average of forces

applied to each sensor over the course of a signature and arranging these average

forces into a 8 × 4 matrix that corresponded to the spatial arrangement of sensors

around the barrel. The elements of the grip shape matrix were then normalized to

values between 0 and 1 yielding, GSsnorm. The mean grip shape matrix GSp

mean for

a given participant p was the element-by-element average of all grip shape matrices

corresponding to that participant’s phase 1 authentic signatures:

GSpmean =

1

Np

Sp∑s=1

GSsnorm (3.1)

where Np is the number of phase 1 authentic signatures by participant p. Finally,

we calculated the two-dimensional normalized correlation coefficient between the

normalized grip shape matrix of each signature GSsnorm and the mean grip shape

matrix of the given participant GSpmean as follows:

NCC (GSsnorm, GSp

mean) =cov(GSs

norm, GSpmean)

σGSsnorm

σGSpmean

(3.2)

where cov denotes the matrix covariance and σ denotes the standard deviation of

Chapter 3. 60

the elements within a given matrix.

2. The TAF summarized the magnitude of grip forces applied on the pen barrel and

was calculated for each signature by summing the unnormalized time-averaged

forces applied to each sensor over the course of the signature,

TAF =8∑

i=1

4∑j=1

GSs(i, j) (3.3)

3. The TFIQR represented the extent of total grip force variation over the course of a

signature. The total force signal (TF s) of each signature was calculated by adding

the forces applied to all sensors at each point in time t, namely,

TF s(t) =32∑i=1

Fi(t) (3.4)

where Fi(t) is the force applied on sensor i at time t. TFIQR of each signature s

was then calculated as the interquartile range of the values in the total force signal

TF s.

These kinetic features were selected for their ease of interpretation and previous use

in handwriting grip force studies such as in (Komi et al., 2008; Kushki et al., 2011; Chau

et al., 2006).

3.3.7 Data analysis

Within-participant kinetic variation

To investigate the within-subject variation of grip force kinetics over time, we compared

each participant’s grip force features between the two phases, with the individual sig-

nature as the unit of analysis. Three nonparametric statistical tests were invoked for

this purpose, given that the feature distributions were not normal. These tests assessed

Chapter 3. 61

potential differences in the location, shape, and spread of the feature distributions of

phases 1 and 2 (Sheskin, 2003). The equality of distributional medians across phases

1 and 2 was evaluated using a Wilcoxon rank-sum (RS) test. To detect differences in

the location and shape of the cumulative distribution functions (cdf) between the two

phases, the two-sample Kolmogorov-Simrnov (KS) test was deployed. Finally, to test the

equality of the dispersion of feature values from phase 1 to 2, the Ansari-Bradley (AB)

test was applied to the median-removed feature values. For all tests, a significance level

of 0.05 was employed.

To gauge the stability of features, the above statistical tests were performed for each

grip force feature while considering all signatures written by a participant as well as

subsets of the first 5, 10, and 15 signatures from each session. When all signatures

were considered, each test was repeated 10 times with a random subset of signatures,

the cardinality of which equaled that of the first 5 signatures data set. The participant

was considered to have a significant difference in the feature values between the two

phases when at least four of the 10 repetitions resulted with a p-value less than 0.05.

The percentage of participants that had a significant difference in grip kinetic features

between the two phases based on each statistical test was tallied.

Between-participant kinetic variation

To study the variation of forces among participants over time, inter-participant discrimi-

nation analysis was performed on the basis of the three aforementioned grip force features.

For each participant, authentic signatures were assigned a ‘true’ label while signatures

from other participants were labeled as ‘false’. A linear discriminant classifier was trained

for each participant using samples from phase 1. Misclassification rates (MCRs) were

estimated via ten iterations of 10 fold cross validation. In each fold, 90% of phase 1 data

were used for training while a subset of the remaining 10% of phase 1 data and 10% of

phase 2 data (randomly selected) were used for testing. Note that the number of samples

Chapter 3. 62

for phase 1 test were chosen to be equal to the number of samples from phase 2 (10%

of phase 2 data) in each fold. MCRs were tabulated for phase 1 and phase 2 test data

separately and subsequently compared using a Wilcoxon rank-sum test.

The above analysis was repeated, only considering the first five signatures of each

session in both phases 1 and 2, to gauge whether or not a minimal data set would suffice

to represent the kinetic variation over time. It was felt that five signatures constituted a

tolerable upper limit of repetition for a biometric or clinical application (Houmani et al.,

2012). The inter-participant discrimination analysis was also repeated with successively

smaller phase 1 training sets, in 10% decrements, and with the three training scenar-

ios depicted in Table 3.1, to ascertain, respectively, the effect of training set size and

composition on inter-participant separability.

3.4 Results

3.4.1 Intra-participant statistical analysis

The range of values and the extent of intra- and inter-participant variability of the grip

force features based on phase 1 and phase 2 data are illustrated in Figure 3.2. Each

subplot corresponds to one of the three grip force features and includes 2 boxes for each

participant, one for the grip force features based on phase 1 data (black) and the other

for the grip force features based on phase 2 data (magenta). The average number of

signatures per participant was 552 for phase 1 and 248 for phase 2.

Figure 3.3 presents the results of the three statistical tests on the phase 1 and 2

distributions of features. The heat map entries are the percentage of participants that

exhibited a significant difference between phases 1 and 2. Only results pertaining to all

signatures in each session (left heat map) and the first five signatures of each session

(right heat map) are shown. The comparisons based on the first 10 or 15 signatures of

each session were similar to those for the first five signatures and are thus not shown.

Chapter 3. 63

0

0.2

0.4

0.6

0.8

1

1 2 3 4 6 7 8 9 10 11 13 14 15 16 17 18 19 20Participant

NC

C

5

10

15

20

25

30

35

1 2 3 4 6 7 8 9 10 11 13 14 15 16 17 18 19 20Participant

TA

F (

N)

0

5

10

15

1 2 3 4 6 7 8 9 10 11 13 14 15 16 17 18 19 20Participant

TF

IQR

(N

)

A

B

C

Figure 3.2: Box plots of the three grip force features based on phase 1 and phase2 data. For each participant, the first box represents the phase 1 feature distributionwhile the second box is the phase 2 distribution of the same feature. NCC= normalizedcorrelation coefficient; TAF= total average force; TFIQR= total force interquartile range.

A number of observations are in order. Generally, a slightly smaller percentage of

participants exhibited a statistical difference when only the first five signatures from

Chapter 3. 64

83 67 67

94 78 67

72 61 56

All signatures

Statisticaltest

NCC TAF TFIQR

RS

KS

AB

83 44 72

89 61 72

56 56 44

First 5 signatures

Grip force featureNCC TAF TFIQR

RS

KS

AB

10

20

30

40

50

60

70

80

90

100

Grip force feature

Figure 3.3: Heat maps showing percentage of participants exhibiting significantkinetic differences between phases 1 and 2. The left subplot presents the resultsfor the “all signatures” case while the right subplot presents the results based on the first5 signatures. Each heat map shows the percentage of participants exhibiting a significantdifference for each grip force feature (horizontal axis NCC= normalized correlation co-efficient; TAF= total average force; TFIQR= total force interquartile range) using eachstatistical test (vertical axis RS= Wilcoxon rank-sum test; KS= Kolmogorov-Simrnovtest; AB= Ansari-Bradley test).

each session were analyzed. Where differences between phases arose, there were no clear

patterns. With some participants, feature values increased between phases while with

others, feature values dropped.

3.4.2 Inter-participant discrimination analysis

Figure 3.4 exemplifies the feature distributions for participant 13. The open circles

denote authentic signatures (true samples) of the participant while the ’x’ symbol signifies

signatures of other participants (false samples). The separating plane between classes is

shown in black. Clearly, in phase 1, there seems to be reasonable separation between

true and false samples as the composition of symbols on each side of the boundary is

nearly homogeneous. This separability seems to be well-maintained into phase 2 for

this participant. Likewise, we note that the within-participant variation among the

Chapter 3. 65

three features appears to be compact relative to the variation among other participants.

This intra-participant consistency resulted in sustained, low misclassification rates for

participant 13 for both phases 1 and 2 as shown in Figure 3.5.

−0.50

0.51

0

10

20

300

5

10

15

20

NCCTAF

TF

IQR

Phase 1 participant 13Phase 1 other participants

−0.50

0.51

0

10

20

300

5

10

15

20

NCCTAF

TF

IQR

Phase 2 participant 13Phase 2 other participants

Figure 3.4: Feature distributions for phase 1 (left) and phase 2 (right) signa-tures. Data from participant 13 are shown. Circles denote feature vectors from authenticsignatures from participant 13. X’s denote feature vectors from other participants. Thedark diagonal line is the separating plane determined by linear discriminant analysis.(TFIQR= total force interquartile range; TAF= total average force; NCC= normalizedcorrelation coefficient)

Figure 3.5 shows the phase 1 (clear bar) and phase 2 (shaded bar) MCRs based on all

signature samples. MCRs varied from participant to participant but overall, the average

MCR across all 18 participants was slightly higher in phase 2 (13.9%) than in phase

1 (10.6%). In fact, 11 participants had a significant change in MCR between phases 1

and 2; eight had a significant increase and another three had a significant decrease. The

corresponding plot with the first five signatures from each session is not shown as the

results were similar to the all-signature case (average MCR of 10.5% for phase 1 and

14.3% for phase 2).

Chapter 3. 66

2 4 6 8 10 12 14 16 18 200

10

20

30

40

Participant

% M

CR

10.613.9

*

* *

*

**

*

*

**

*

Phase 1 TestPhase 2 Test

Phase 2 testPhase 1 test

Figure 3.5: Misclassification rates for phases 1 and 2. Asterisks indicate that theparticipant has a significant difference between phase 1 and phase 2 MCRs. The dashedlines show the average MCRs across all 18 participants.

As training set size increased, the MCR did decrease in both phases 1 and 2 (p < 0.05,

R2 ≥ 0.63, regression test). However, the changes were small: a decrease of 0.3% in phase

1 and 0.5% in phase 2.

The effect of the training set composition is summarized at the bottom of Table 3.1.

In general, the average MCR for phase 2 signatures was slightly higher than that of

phase 1. However, within a given phase, the average MCR changed only slightly across

different training scenarios (maximum 0.8%), suggesting that the MCR is independent

of the training set compositions considered here.

Chapter 3. 67

Table 3.1: The effect of training set composition

Scenario1 2 3

Training set First 50% ofphase 1 data

Randomly selected50% of phase 1 data

Randomly selected50% of phase 1 data+ Randomly selected50% of phase 2 data

Testing set Phase 1 Second 50% ofphase 1 data

The remaining 50% ofphase 1 data

The remaining 50% ofphase 1 data

Phase 2 All phase 2 data All phase 2 data The remaining 50% ofphase 2 data

MCR Phase 1 10.1% 10.2% 10.8%Phase 2 14.0% 13.9% 13.2%

3.5 Discussion

3.5.1 Intra-participant variation of grip kinetics

Low NCC values (e.g., participants 3, 6, and 15 in phase 1 as well as participants 1, 6,

8, 11, and 18 in phase 2), were most likely due to pen rotation and grasp adjustments

during writing. These behaviors were observed during data collection and evident in

the grasp pictures even though participants were instructed otherwise. Grip adjustment

and pen rotation may be characteristics of personalized writing styles and has been

noted elsewhere in adult writing (Wada & Hangai, 2009). Initial unfamiliarity with

the instrumented pen, nervousness, or fatigue may have also been contributing factors

(Summers & Catarro, 2003).

The total average force values ranged between 5 and 20 Newtons, which resonate

with values reported in Baur, Furholzer, Marquardt, and Hermsdorfer (2009) and reflect

the number and strength of hand muscles that are activated during handwriting. Higher

values of force variability (TFIQR) were associated with higher values of total average

forces (e.g., participants 4 and 18), a finding that echoes the observations of Herrick and

Chapter 3. 68

Otto (1961) and Chau et al. (2006), which indicates that higher dynamics in the grip

kinetics are expected with stronger grips.

The slightly greater stability of kinetic features over time when considering only

the first five signatures may be due to a natural mitigation of the sources of variation

when writing for very short periods of time. These sources can include pen rotation,

grasp adjustment or other biomechanical changes within a session. Indeed, increases in

grip forces and decreases in force dynamics have been associated with extended writing

(Kushki et al., 2011). Our finding suggests that obtaining fewer signatures per session

provides an equal or, in some cases, a more stable representation of individual handwriting

grip kinetics over time. This finding can be used as a guide in the collection of grip kinetics

to model and characterize these grip kinetics in an individual for clinical or biometric

applications.

The direction of change of the magnitude of the grip kinetic features over the long

term varied across participants with increases and decreases being equally probable. For

many participants, the variability of the grip force features was higher in phase 1 (short

term) than in phase 2 (long term).

From signature verification literature, it is known that signature writing is associated

with some intra-subject variability of many static and dynamic features of handwriting

(Dimauro et al., 2002; Huang & Yan, 2003; Ahmad et al., 2008). Many factors can

contribute towards the intra-participant variation such as the state of mind, emotion,

health and writing posture (Ahmad et al., 2008). It has been reported in Dimauro et

al. (2002) that psychological and writing conditions (e.g., required speed, displacement

distance and accuracy) can produce short term variability while modifications in the

musculoskeletal system and motor program can lead to long term variability. Movement

variability can also be introduced by the neuromuscular and central nervous systems,

which integrate to produce writing movements since these systems have many degrees of

freedom; a change in the initial conditions of these systems (e.g., cognitive, biomechanical

Chapter 3. 69

and environmental context) can produce variability in the output (Djioua & Plamondon,

2009; Longstaff & Heath, 1999).

3.5.2 Inter-participant grip kinetic variation

The observed high inter-subject variability can be explained by the complexity and

individuality of handwriting as a fine motor skill. Herrick and Otto (1961) reported

inter-participant variability in finger pressure patterns and wild variations in inter-finger

absolute pressures across individuals. Bashir and Kempf (2009, 2012) have also found

person-specific features in grip force signals but did not examine the intra-subject vari-

ability over time. High inter-subject variability in spatiotemporal, kinematic, and pen-

on-paper pressure features has provided a basis for discriminating between authentic and

forged signatures (Lei & Govindaraju, 2005; Bashir & Kempf, 2009; Rashidi et al., 2012).

It appears that the long term data variability did not significantly affect the MCR

for most of the participants. MCR did however increase significantly in the face of

pen rotation. By examining the pictures taken in each session, the participant with

the greatest difference in MCR between the two phases (participant 1) clearly held the

instrumented pen with a different orientation in each phase. This resulted in very low

NCC values and consequently a very high MCR for the phase 2 test. When excluding

the MCR of participant 1, the average MCR of phase 2 test drops to 11.9%, which is

slightly higher than the phase 1 MCR of 10.4%. This pen rotation issue can be addressed

analytically by registering the grip pressure distribution images.

Our findings suggest that in practice, modest training sets (as few as 100 training

samples) could be used for writer verification with only a mild compromise in MCR

(less than 0.5%). Also, different training set compositions are admissible. Even when

samples of the first few sessions were used for training, the classification of the long

term data produced, on average, similar MCRs as when samples of the long term data

were available. These findings are in line with the requirements for a feasible signature

Chapter 3. 70

verification system (Impedovo & Pirlo, 2008).

In summary, this study showed that despite the presence of intra-subject variability

of grip kinetic features experienced by many participants, the inter-subject variability

was generally higher in the long term, yielding stability of MCR. This finding suggests

that each participant has unique grip kinetics, distinct from those of other participants.

Additionally, higher stability in grip force features is achieved when considering fewer

signatures per session.

3.6 Acknowledgments

The authors would like to acknowledge NSERC and the Canada Research Chairs pro-

gram for their in part financial support of this project. The authors would also like

to acknowledge Nayanashri Thalanki Anantha, Jennifer Chan, Laura Bell, and Sarah

Stoops for their help during the data collection, Ka Lun Tam, and Pierre Duez for their

support as well as the participants for their time.

Chapter 4

A Comparison of Handwriting Grip

Kinetics Associated with Authentic

and Well-Practiced Bogus

Signatures

This chapter is a reproduction from the following journal article: Ghali, B., Mamun, K.,

& Chau, T. A comparison of handwriting grip kinetics associated with authentic and

well-practiced bogus signatures. (Under review).

The background section of this chapter and some parts of the methods section (par-

ticularly 4.3.1, 4.3.2, 4.3.3 and 4.3.4) contain common information with Chapters 1 and

2. Therefore, the reader is advised to skip these parts of this chapter.

4.1 Abstract

Handwriting biomechanics may bear biometric value. In particular, kinematic and ki-

netic handwriting characteristics of authentic and forged handwriting samples have been

71

Chapter 4. 72

contrasted in previous research. However, past research has only considered pen-on-

paper forces while grip kinetics, i.e., the forces applied by the writer’s fingers on the pen

barrel, have not been examined in this context. This study extends the instrumental

and analytical techniques from clinical handwriting research to compare multiple grip

kinetic features between repeated samples of authentic signatures and skilled forgeries in

a sample of 20 functional adult writers. Grip kinetic features differed between authentic

and well-practiced bogus signatures in less than half of the participants. In instances

where forces differed between authentic and bogus, there was no clear trend in terms of

the direction of change in force magnitude or dispersion. Forgeries are not necessarily

associated with different or more variable grip kinetics. As long as the written text is

well-practiced and written naturally, the handwriting kinetics tend to be similar to those

of authentic signature writing.

Keywords: handwriting biomechanics, grip kinetics, signatures, intra- and inter-

session variability

4.2 Background

Handwriting grip kinetics are the forces applied by the hand on the pen barrel while

writing. Using instrumented pens, many studies have considered grip forces for clinical

and rehabilitation applications (Hooke et al., 2008; Chau et al., 2006; Falk et al., 2010;

Kushki et al., 2011; Hermsdorfer et al., 2011). Grip kinetics are also being investigated

in the fields of biometrics and forensics. For example, grip force patterns have demon-

strated biometric value in gun control applications (Shang & Veldhuis, 2008a, 2008b,

2008c). Similarly, grip force patterns may also possess discriminatory features for writer

identification and forgery detection (Koppenhaver, 2007; Ghali, Anantha, et al., 2013).

Some studies have compared handwriting characteristics between authentic and forged

signatures. When kinematic features were compared between authentic samples of a

Chapter 4. 73

model writer and simulations of 10 other participants, it was found that forgeries were

associated with longer reaction time, slower movement velocities, more dysfluencies (re-

versals of velocity) and higher limb stiffness (G. Van Galen & Van Gemmert, 1996). A

more recent study investigated the kinematic and kinetic differences between authentic

signatures and forgeries (Franke, 2009), finding that some forgers exhibited slower move-

ments, multiple pen stops and higher axial forces, while other forgers simulated their

normal writing velocity with no hesitations and comparable or even lower pen tip forces.

The difference between writing a true versus a deceptive message has also been examined

biomechanically, with the latter being associated with a significantly higher mean axial

pressure, stroke length and height (Luria & Rosenblum, 2010). These differences were

attributed to the higher cognitive load required to forge another person’s handwriting or

to write a deceptive message.

None of the above studies have considered the grip kinetics of authentic and forged

handwriting. Therefore, in this study, we compared the magnitude and dispersion of grip

kinetics associated with repeated writing of the participant’s authentic signature and a

well-practiced bogus signature. The findings of this study can help to inform the use of

grip kinetics for writer discrimination and signature verification.

4.3 Methods

The participants and data collection protocol are the same as in Ghali, Anantha, et al.

(2013) but are reiterated briefly below. The well-practiced bogus signature data analyzed

herein have not been previously reported.

4.3.1 Participants

Twenty adult participants (8 males; 17 right handed; 27 ± 6 years of age) were recruited

from students and staff of an academic health sciences center. Individuals with known his-

Chapter 4. 74

tory of musculoskeletal injuries or neurological impairments that can affect handwriting

function were excluded from the study. The research ethics board of the health sciences

center approved the study and each participant provided informed, written consent.


An instrumented writing utensil was used to obtain the grip force signals (the forces

applied on the pen barrel by the fingers) through an array of Tekscan 9811 force sensors

that covered the pen barrel. The original sensor array consists of 96 sensors; however,

only the section of the array covering the pen barrel (32 sensors) was considered. The

force sensors were systematically calibrated every two or three days during the data

collection to derive calibration curves. The array was replaced regularly due to wear and

tear. The grip force signals were acquired by computer at 250 Hz via a custom-made

interface box. A Wacom Cintiq 12WX digitizing LCD display served as the writing

surface and captured the axial force, pen tip position, pen tilt and rotation angles at a

frequency of 105 Hz. The various signals were synchronized by data acquisition software.

A grounding strap was worn by the participant to reduce noise in the grip force signals.

The instrumentation setup is illustrated in Figure 4.1. For further details regarding

utensil construction and the calibration procedure, the reader is referred to Chau et al.

(2006) and Ghali, Anantha, et al. (2013).

4.3.3 Experimental protocol

Before the actual data collection sessions, each participant practiced a bogus signature on

paper, 25 times each day, for two weeks, in order to become familiar with the signature

and to develop idiosyncratic signing patterns. All participants practiced the same bogus

signature shown in Figure 4.2.

For each participant, data collection included 30 sessions spread over 10 days. Three

sessions were performed each day (morning, afternoon, and evening). In each session, the

Chapter 4. 75

Grounding

Strap

Writing surface

Instrumented

pen

Interface box

Figure 4.1: Data collection instrumentation set-up.

Figure 4.2: A sample of the bogus signature.

participant wrote with the instrumented pen, on the digital writing surface, 20 samples

of the well-practiced bogus signature followed by 20 samples of his or her own authentic

signature. In each session, the following steps also occurred: customized software was

launched to guide the participant through data collection; the force sensors were checked;

and pictures of the grip were taken at the midpoint and conclusion of each session. In

addition, a 10 second baseline was collected at the beginning of each session to determine

the pre-grip value of each sensor, which was used in subsequent off-line data preprocessing.

All data collection took place in a laboratory within Holland Bloorview Kids Rehabili-

tation Hospital and was completed in 20.4±3.6 days on average depending on participant

availability. In total, 600 well-practiced bogus signatures and 600 authentic signatures

were obtained from each participant over a total of 30 sessions. All of these signature

samples were considered in this study. The authentic signatures were reported in Ghali,

Anantha, et al. (2013) in the context of a different analysis.

Chapter 4. 76

4.3.4 Data pre-processing

Some signature samples were discarded due to writing mistakes, a long pause or a sensor

malfunction during writing. Signature samples that were contaminated with extra writing

before or after the signature were trimmed accordingly. A Butterworth low-pass filter

with a cut off frequency of 10 Hz suppressed high frequency noise from the grip force

signals. Some signature samples were discarded because of low frequency noise within

the range of handwriting frequencies. In total, 1,522 (12.7%) bogus signatures and 960

(8%) authentic signatures were excluded from further analysis.

The grip force signals of the remaining signature samples were pared down to a

zero pre-grip value by subtracting from each sensor reading its corresponding 10 second

baseline average from the associated session. The grip force recording from each sensor

was then converted to units of physical force via the corresponding calibration curve.

These preprocessing steps are further detailed in Ghali, Anantha, et al. (2013).


Features were extracted from the topographical and functional representations of the grip

force signals to facilitate comparison between authentic and bogus signature writing. The

topographical representation of the kth signature consisted of a grip force matrix, GFk,

which is an 8 by 4 matrix of non-negative real numbers, where each element denotes the

force on a sensor, averaged over the duration of the signature. We will use GFk to denote

the grip force matrix whose values have been normalized to [0,1] (e.g., Figure 4.3B). The

mean grip force matrix, GF p, of participant p is the element-by-element average of all

normalized grip force matrices for that participant, i.e., GF p = 1Np

∑Np

k=1 GFk, where Np

is the number of signatures by participant p. Topographical features are detailed below.

• The 2-dimensional normalized correlation coefficient (NCC2) between the normal-

ized grip force matrix (GFk) of the kth signature and the mean grip force matrix

Chapter 4. 77

of the corresponding participant (GF p) is calculated as follows:

NCC2 (GFk, GF p) =1

32

∑8i=1

∑4j=1(GFk(i, j)−GFk)(GF p(i, j)−GF p)

σGFkσGF p

(4.1)

where the spatial mean and standard deviation of the grip force matrix are re-

spectively, GFk = 132

∑i

∑j

GFk(i, j) and σGFk=

√132

∑i

∑j(

GFk(i, j)−GFk)2.

Likewise, the spatial mean, GF p and standard deviation σGF p of the mean grip

force matrix for participant p are defined similarly. The NCC2 feature determined

the consistency of the grip shape within each participant.

• The total unnormalized force (TUF ) of the kth signature is the sum over all sensors

of the unnormalized grip force readings

TUF =8∑

i=1

4∑j=1

GFk(i, j) (4.2)

• Grip height of the kth signature is the force-weighted average position of finger to

barrel contact (Chau et al., 2006), namely,

Grip height =

∑8i=1(i

∑4j=1 GFk(i, j))∑8

i=1

∑4j=1 GFs(i, j)

(4.3)

The units of grip height are the number of sensors above the proximal edge of the

barrel (the end closest to the pen tip) and ranged from 1 to 8.

The functional representation of a signature consisted of the total grip force profile

over time, TGF (t), namely,

TGF (t) =8∑

i=1

4∑j=1

Fij(t) (4.4)

Chapter 4. 78

where Fij(t) is the force reading at time t from the sensor on the ith row of sensors above

the pen apex and jth sensor strip running longitudinally down the pen barrel (See for

example Figure 4.3A). A sample total grip force profile is shown in Figure 4.3C. The mean

total grip force profile, TGF p(t), for participant p is the curve obtained by averaging at

each sampling instance, all individual signature grip force profiles for that participant,

i.e.,

TGF p(t) =1

Np

Np∑k=1

TGFk(t) (4.5)

where Np is the total number of signatures available for the pth participant. Sepa-

rate mean total grip force profiles were estimated for authentic and bogus signatures.

As above, we will denote the amplitude normalized versions of the force profiles asTGF (t) and TGF p(t). Note that in the functional representation, normalization refers

to standardization to 0 mean and unit variance. The total force signals were also time-

normalized in a participant-specific manner by re-sampling the signatures to a common

length, taken as the average length of the signatures of that participant. Note that bogus

and authentic signatures were time-normalized separately.

The functional features used in this study are introduced below.

• The maximum total force of the kth signature is the maximum over time of the

total grip force of that signature,

TGFmax = maxt

TGF (t) (4.6)

• The total force interquartile range (TGFIQR) is the interquartile range of the total

grip force profile of each signature.

TGFIQR = γ0.75 − γ0.25 (4.7)

where γq is the qth quartile of the amplitude distribution of force values in a given

Chapter 4. 79

force profile TGF (t). In other words, if D(x) is the amplitude distribution of

TGF (t), then γq is defined implicitly as q =∫ γq−∞ D(x)dx.

• The 1-dimensional NCC between the total force profile of the kth signature, TGFk(t)

and the mean total force profile for participant p, TGF p(t), is given by

NCC1 (TGFk, TGF p) =1

T

∑Tt=1(TGFk(t)− TGFk)(TGF p(t)− TGF p)

σTGFkσTGF p

(4.8)

where T is the normalized signature duration, TGFk =1T

∑t TGFk(t) is the mean

total grip force over the duration of the kth signature and σTGFk=

√1T

∑t(TGFk(t)− TGFk)2

is the corresponding standard deviation. The quantities TGF p and σTGFp for the

pth participant’s average temporal force profiles are obtained in like fashion. This

feature determined the consistency of the force profile across signatures (either

bogus or authentic) of each participant.

• The root mean square error (RMSE) between the normalized total force profile

of the kth signature ( TGFk(t)) and the normalized mean total force profile of the

corresponding participant ( TGF p(t)) is defined as

RMSE ( TGFk, TGF p) =

√∑Tt=1(

TGFk(t)− TGFp(t))2

T(4.9)

4.3.6 Data analysis

Bogus and authentic signatures were compared on the basis of the aforementioned to-

pographical and functional features. Sessional means and spread of these features were

compared given their greater stability over corresponding estimates derived from indi-

vidual signatures (Ghali, Anantha, et al., 2013).

Given the non-normality of the features, the non-parametric two-sample Kolmogorov-

Chapter 4. 80

0 1000 2000 30000

2

4

6

8

10The grip force signals

Time (msec)

Sen

sor

grip

forc

e (N

)

The grip force matrix

Sensor columnS

enso

r ro

w

2 4

1

2

3

4

5

6

7

8

0 1000 2000 30000

5

10

15

20

25

30The total grip force profile

Time (msec)

Tot

al g

rip fo

rce

(N)

0

0.5

1

B CA

Figure 4.3: Different representations of the grip force signals associated witha bogus signature shown in Figure 4.2. ‘A’: a functional representation of the gripforce signals on each sensor; ‘B’: a topographical representation of the grip force signals,each square represents a sensor and its value is the normalized average force appliedon that sensor; ‘C’: the functional representation of the total grip force profile over thecourse of a signature, which is the sum of the signals shown in ‘A’.

Smirnov (KS) test was invoked to test the equality of location and shape of the empirical

cumulative distribution functions (CDF) of authentic and bogus features (Hill & Lewicki,

2006). The Ansari-Bradley (AB) test was deployed to test the equality of dispersion

between median-removed versions of the authentic and bogus features (Reimann, Filz-

moser, Garrett, & Dutter, 2008). For all tests, a significance level of 0.05 was employed

and comparisons were performed feature by feature on a per participant basis.

4.4 Results and discussion

Figure 4.4 graphically represents the percentage of participants who exhibited statistically

significant differences in grip kinetic features between authentic and well-practiced bogus

signatures. The lighter the shading, the greater the percentage of participants showing

differences. The left graph depicts differences in the median while the right graph sum-

marizes differences in the interquartile range. For example, in the top-left hand corner

Chapter 4. 81

10 10 25 20

25 25 5 0

10 10 5 0

15 40 5 0

20 35 0 15

20 45 25 15

45 20 10 10

Feature location (median)

NCC

2

TUF

Grip height

TGFmax

TGFIQR

NCC1

RMSE

KS Test AB TestB<A B> A B<A B>A

15 5 30 10

20 15 15 10

0 5 10 0

20 10 15 10

20 15 10 10

45 20 30 5

20 20 20 5

Feature spread (IQR)

NCC

2

TUF

Grip height

TGFmax

TGFIQR

NCC1

RMSE

KS Test AB TestB<A B> A B<A B>A

20

40

60

80

100

Figure 4.4: Heat maps depicting the percentage of participants for whom signif-icant kinetic differences arose between signatures. Authentic and well-practicedbogus signatures comparison of feature medians is shown on the left graph and featurespread is shown on the right graph. Dark coloring denotes low percentages. Features arespecified on the vertical axis while the nature of the difference between authentic (A)and well-practiced bogus (B) signatures appears on the horizontal axis. Each numericaloverlay corresponds to the percentage of participants showing the specified difference.

of the median graph, 10% of participants exhibited lower NCC2 values while writing

the bogus signatures, according to the KS test. Given the overall dark shading of the

graphs, we observe that generally, a minority of participants exhibited significant kinetic

differences between authentic and bogus signature writing. In the following, we discuss

some specific observations arising.

1. Bogus signatures were not necessarily associated with a different or more variable

grip shape when compared to that of authentic signatures. Likewise, total aver-

age force and grip height were generally comparable between bogus and authentic

signatures.

2. 40% of the participants applied a significantly higher maximum total grip force

while writing the bogus signature. This finding is consistent with G. Van Galen and

Van Gemmert (1996) and Van Den Heuvel et al. (1998), who reported higher pen

tip pressure secondary to increased limb stiffness for handwriting that demanded

greater cognitive processing such as forging a signature. Nonetheless, Franke (2009)

Chapter 4. 82

contends that higher forces can also be associated with authentic signatures as was

the case in 15% of our participants. While these papers only considered the axial

pen tip force, we know that axial and grip forces are strongly correlated (Herrick

& Otto, 1961; Chau et al., 2006).

3. Just over a third of the participants had higher TGFIQR values while writing the

bogus rather than authentic signature. Since participants wrote the bogus speci-

mens before the authentic signatures, the recent finding of diminishing grip force

variability over a 10 minute writing session might in part explain this observation

(Kushki et al., 2011). Nonetheless, G. Van Galen and Van Gemmert (1996) re-

ported that forgeries are associated with less variation in pen tip pressure, which

would appear to be the case in 20% of our participants. Some of the observed

difference may have been due in part to the dissimilar demands of authentic and

bogus signatures, as the extent of pen force variation has been attributed to the

level of task complexity (Kao, Shek, & Lee, 1983).

4. Just under half of the participants had higher NCC1 values with bogus signature

writing. This is corroborated by the lower RMSE values for the same participants

for bogus signature writing. Both findings indicate a higher consistency of the force

profile while writing the bogus signatures. A similar observation was reported in

G. Van Galen and Van Gemmert (1996) where variances of spatial and kinematic

variables in repeated forgeries were smaller than the variances of these variables for

repeated samples of authentic writing.

Overall fewer than 50% of the participants had any significant differences in grip

kinetic features between the bogus and authentic signature writing. This finding sug-

gests that the two-week practice period was sufficient for participants to become familiar

with the bogus signature, to the point that grip kinetics were akin to those of skilled

handwriting (Luria & Rosenblum, 2010).

Chapter 4. 83

4.5 Conclusions

In this study, we compared the handwriting grip kinetics associated with repeated sam-

ples of a well-practiced bogus signature and authentic signatures for 20 adult participants.

The magnitude and the extent of variability of multiple grip kinetic features were com-

pared. In general, only a few participants exhibited any significant difference in grip ki-

netic features between writing authentic and bogus signatures. These differences were not

consistent across participants. The kinetic variability associated with the well-practiced

bogus signatures did not exceed that of the authentic signatures. These findings suggest

that it is feasible to use bogus signatures to investigate the intra- and inter-subject vari-

ability of the handwriting grip kinetic profile and to identify discriminatory features for

writer discrimination and signature verification purposes.

4.6 Conflict of interest

No author has any financial or personal relationship that could inappropriately influence

the work submitted for publication.


The authors would like to acknowledge the Canada Research Chairs program, and the

Natural Sciences and Engineering Research Council of Canada for supporting this re-

search financially. The authors would also like to acknowledge Ms. Nayanashri Thalanki

Anantha, Ms. Jennifer Chan, Ms. Laura Bell, and Ms. Sarah Stoops for their assistance

with the data collection for this study.

Chapter 5

Grip Kinetic Profile Variability in

Adult Signature Writing

Grip kinetic profile variability in adult signature writing This chapter is a reproduction

from the following journal article: Ghali, B., Mamun, K., & Chau, T. (2013) Grip kinetic

profile variability in adult signature writing. Journal of Biometrics and Biostatistics.

(Accepted).

The introduction section of this chapter and some parts of the methods section (par-

ticularly 5.3.1, 5.3.2, 5.3.3 and 5.3.4) contain common information with Chapter 1 and

Chapter 2. Therefore, the reader is advised to skip these parts of this chapter.

5.1 Abstract

Previous studies of handwriting grip kinetics have demonstrated the ability to classify

writers based on the topography of grip forces associated with signature writing. How-

ever, the topographic representation requires a large array of individual sensors in prac-

tice. The possibility of differentiating participants on the basis of a summative, temporal

force profile is yet unknown. In this study, we investigated the variability of features de-

rived from a time-evolving total grip force profile. Using an instrumented writing utensil,

84

Chapter 5. 85

twenty adult participants provided 600 samples of a well-practised bogus signature over

a period of 10 days. Deploying a combination of temporal, spectral and information-

theoretic features, a linear discriminant analysis classifier outperformed nonparametric

and nonlinear classifier alternatives and discriminated among participants with an aver-

age misclassification rate of 5.8% as estimated by cross-validation. These results suggest

the existence of a unique kinetic profile for each writer even when generating the same

written product. Our findings highlight the potential of using grip kinetics as a biometric

measure.

Keywords: Handwriting kinetics, Grip force profile, Signature verification, Classifica-

tion, Inter-writer variability, Feature selection

5.2 Introduction

Signature writing is a well-learned (Ghali, Anantha, et al., 2013) but highly complex per-

ceptual motor task (Ramsay, 2000; Van Drempt et al., 2011), invoking the coordinated

activation of both proximal (e.g., thenar) and distal (e.g., trapezius) muscles (Naider-

Steinhart & Katz-Leurer, 2007), relying upon the central role of proprioception and

the secondary role of vision (Hepp-Reymond, Chakarov, Schulte-Monting, Huethe, &

Kristeva, 2009), integrating kinesthetic input (Sudsawad, Trombly, Henderson, & Tickle-

Degnen, 2002) and harnessing short-term memory (G. P. Van Galen, Smyth, Meulen-

broek, & Hylkema, 1989). The complexity of these biomechanical and cognitive systems

introduces variations between and within individuals (Ramsay, 2000).

The advent of kinetic utensils that measure the forces applied by the fingers on the

pen (Chau et al., 2006; Hooke et al., 2008; Baur, Furholzer, Marquardt, & Hermsdorfer,

2009) has spawned numerous investigations of handwriting grip kinetics. Most of these

studies have been clinical in nature, with the goal of using handwriting grip forces to

inform diagnosis and treatment of handwriting disorders (Hooke et al., 2008; Chau et al.,

Chapter 5. 86

2006; Falk et al., 2010; Hermsdorfer et al., 2011). However, studies of handwriting grip

kinetic variability in the adult population are very limited (Van Drempt et al., 2011).

Recently, we studied the variability of grip kinetics associated with signature writing in

adults (Ghali, Anantha, et al., 2013; Ghali, Mamun, & Chau, n.d.-b) and found that the

variability of kinetic topographies (i.e., grip shape) between individuals was much higher

than the variability within an individual, even when considering signatures collected

over several months. These findings encouraged the study of variations in a summative

handwriting grip kinetic profile, which is the time series of total force variation over the

course of a signature.

In sports such as tennis, baseball and golf, the within- and between-subject variations

of kinetic profiles have been studied with the aim of optimizing player performance (Komi

et al., 2008). The grip force profile of a golf swing was found to be repeatable within

a player and distinctive between players (Komi et al., 2008; E. Schmidt et al., 2006;

Komi et al., 2007). Gait studies have found that the kinetics associated with walking in

adult participants are repeatable for the same person on multiple days (Kadaba et al.,

1989; Winter, 1984). Grip force patterns have also proven to be valuable for biometric

verification in gun control applications, which suggests grip consistency within individu-

als (Shang & Veldhuis, 2008a, 2008c). A recent review of keyboarding-based biometrics

showed that, in addition to considering the time to type, the latency between keystrokes,

and many other features, few studies have considered the keystroke pressure applied by

the fingers on the keys, a potential discriminative feature (Karnan et al., 2011). Salami

et al. (2011) and Sulong et al. (2009) proposed a keyboard embedded with sensors capa-

ble of measuring the force applied on each key and the latency between keystrokes as a

mean to authenticate a user while typing. Using multiple classifiers, it was found that

the combination of pressure and latency yielded better user authentication than that

achievable with either feature alone. In similar spirit, finger pressure has been deemed

to be more discriminative than hold-time and inter-key duration for the authentication

Chapter 5. 87

of touch pad users (Saevanee & Bhattarakosol, 2009).

In the field of handwriting authentication and signature verification, intra- and inter-

participant variations of axial pen pressure, spatiotemporal features and kinematic char-

acteristics have been explored (Ramsay, 2000; Guest, 2004; Lei & Govindaraju, 2005;

Shakil et al., 2008; Ahmad et al., 2008; Impedovo, Pirlo, Sarcinella, et al., 2012). Ramsay

(2000) modeled the dynamics of spatiotemporal information of a handwriting sample us-

ing a differential equation that considered the variation in scripts across replications and

was used to classify handwriting samples of different individuals. Lei and Govindaraju

(2005) examined the consistency and discriminative power of multiple features commonly

used in on-line signature verification systems, concluding that the pen-tip coordinates,

speed, and angle between the speed vector and the horizontal axis of the writing surface

were among the most consistent features. Another study found that the dynamic features

(speed, angle, axial pressure, and acceleration) surpassed static features in discriminative

capability between genuine writing and skilled forgeries (Shakil et al., 2008). Bashir and

Kempf (2009, 2012) recently identified person-specific features in grip force signals and

reported improved writer recognition when a grip force signal was added to the classi-

fier. However, these studies were based on samples collected in one session and did not

examine the effect of intra-subject variability over time. The discriminative potential

of handwriting grip kinetics has yet to be fully ascertained. This study thus set out to

investigate one aspect of this potential, namely, to quantify the variability of grip kinetic

profiles between adults while writing the same well-practiced signature over multiple days

and multiple times within the same day.

Chapter 5. 88

5.3 Methods

5.3.1 Participants

To generate the required database, we recruited a convenient sample of 20 participants

with an age range of 18 to 45 years and a mean of 27 ± 6 years. The sample included

8 males/12 females and 17 right-handed/3 left-handed participants. Individuals with a

known history of musculoskeletal injuries or neurological impairments were excluded from

the study. The study protocol was approved by the research ethics boards of Holland

Bloorview Kids Rehabilitation Hospital and the University of Toronto. An informed

written consent was signed by each participant. Demographic information such as age,

gender and handedness were also collected from each participant.


To collect the required data, the instrumentation setup shown in Figure 5.1 was used.

Grip force signals, which are the forces applied by the fingers on the pen barrel, were

acquired at 250 Hz via an instrumented writing utensil adorned with an array of Tekscan

9811 force sensors (Chau et al., 2006; Ghali, Anantha, et al., 2013). A custom-made data

acquisition box transferred these signals to the data collection computer where they were

saved for processing. A systematic calibration procedure, detailed in Ghali, Anantha,

et al. (2013), was performed on the force sensors every 2 to 3 days to derive calibration

curves needed during pre-processing of the grip force data. During calibration and data

analysis, only the subset of sensors that covered the pen barrel (32 sensors of the 96

sensors array) was considered. The sensor array was replaced when a sensor malfunction

due to wear and tear was observed. The axial forces applied by the pen on the writing

surface along with the pen tip position and pen angles (twist, altitude and azimuth)

were acquired by a Wacom Cintiq 12WX digitizing LCD display at a frequency of 105

Hz. These latter signals were synchronized with the grip force signals using the developed

Chapter 5. 89

data acquisition software. A grounding strap was placed on the non-dominant hand of

each participant to reduce noise in the grip force signals.

Computer Custom

interface box

Writing surface

Grounding

strap

Instrumented

Pen

Figure 5.1: Data collection instrumentation setup.


The bogus signature shown in Figure 5.2 was given to all participants. Each participant

practiced the bogus signature by writing it repeatedly on paper 25 times a day for two

weeks. After the practice period, each participant completed 30 sessions of data collec-

tion over 10 days that spanned an average period of 20.4 ± 3.6 days depending on the

participant’s availability. On each day, three sessions were performed at different times of

the day. In each session, the participant sat comfortably on a chair, donned the ground-

ing strap on the non-dominant hand, held the instrumented pen with the dominant hand

and wrote multiple signature samples within the specified area on the digitizing tablet. A

researcher was always present to check the force sensors at the beginning of each session

and to note any writing mistakes or events that could affect the data. In each session,

a 10 second baseline of the force sensors was collected prior to writing to determine

the pre-grip value of each sensor. Twenty samples of the bogus signature and twenty

Chapter 5. 90

samples of the participant’s authentic signature were collected during each session. A

total of 600 well-practiced bogus signatures and 600 authentic signatures were obtained

from each participant over the 30 sessions. In this study, only the bogus signatures are

considered. For more details regarding the data collection steps, refer to Ghali, Anantha,

et al. (2013).

Figure 5.2: The bogus signature. Each participant practiced this signature for twoweeks prior to the data collection to develop familiarity with the signature.

5.3.4 Data pre-processing

Through visual inspection of the bogus signatures and their associated grip force signals,

and a review of the researcher notes taken during each session, some signature samples

were identified as possessing a long pause, a mistake or a sensor malfunction while writ-

ing. These samples (417 bogus signatures across all participants) were excluded from

subsequent analyses. Other signature samples that exhibited extra strokes because of

accidental contact with the writing surface before or after writing were salvaged by ad-

justing the start or end time of the signature, respectively .

The high frequency noise in the grip force signals was removed using a Butterworth

low pass filter with a cut off frequency of 10 Hz, below which resided more than 95% of

the signal power. Some samples (1105 bogus signatures) had a low frequency oscillating

noise that could not be removed and were thus excluded from further analyses. The

remaining 10478 signature samples (87.3% of the 12000 samples; average 524 samples per

participant) were translated into signals with physical force units (Newtons) as detailed

Chapter 5. 91

in Ghali, Anantha, et al. (2013).


The total grip force signal of each signature sample was obtained by adding the pre-

processed grip force signals of the 32 individual sensors. Figure 5.3 exemplifies a bogus

signature sample, the associated 32 pre-processed grip force signals and the summative

total grip force signal.

100 150 200 250 300 350 4000

20

40

1 s

2 s

3 s

4 s

x (pixels)

y (p

ixel

s)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

2

4

Time (Sec)

Sen

sor

grip

forc

e (N

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

Time (Sec)

Tot

al g

rip fo

rce

(N)

Figure 5.3: A signature sample, its grip force signals and total grip force profile.Top: a signature sample and the associated timing of selected points; Middle: the pre-processed grip force signals of the 32 force sensors; Bottom: the total grip force signalover the course of a signature, which is the sum of the signals shown in the middle figure.

Two genre of features were extracted from the total grip force signals: (1) signature-

exclusive features which are extracted only from the total grip force signal during signa-

Chapter 5. 92

ture writing and (2) referenced features which represent the closeness of a given writing

sample to the reference signal of a participant. These signature-exclusive features include:

• Mean of the total force signal as a measure of location of the signal values

• Maximum of the total force signal as a measure of the grip strength

• Interquartile range of the total force signal as a robust measure of kinetic dispersion

• Coefficient of variation (CV) of the total force signal as a normalized measure of

kinetic dispersion. CV is the ratio of the standard deviation to the mean of the

signal.

• Skewness of the total force signal, which is a measure of asymmetry of the signal

distribution

• Kurtosis of the total force signal, which is a measure of the peakedness of the signal

distribution

• Number of zero crossings of the detrended total force signal as a crude measure of

the frequency content of the signal

• Number of peaks in the total force signal

• Centroid frequency of the power spectral density of the total force signal

• Bandwidth of the power spectral density of the total force signal

• Maximum power of the power spectral density of the total force signal

• Sub-band power of the total force signal. Since most of the energy content was

below 5 Hz, the sub-band power was calculated in 5 frequency bands each with a

1 Hz window size.

Chapter 5. 93

• Entropy rate of the total force signal, which is a measure of the regularity of the

signal

A more detailed explanation of many of these features can be found in J. Lee (2009).

For the second group of features, a reference total force signal of each participant was

first estimated according to the following steps:

1. Time normalization: The total force signals of all participants were resampled as

necessary such that all total grip force signals shared a common length, which was

chosen to be the average length across all participants and all signature samples.

2. Registration: To correct any temporal misalignment among the time-normalized

total force signals of each participant, the signals were subjected to curve regis-

tration as described in Chau, Young, and Redekop (2005). Figure 5.4 portrays an

example of the total force signals before and after registration and the associated

mean signals for one of the participants.

3. The reference signal calculation: The mean total force signal for each participant

was estimated as the average of the registered total force signals across signatures

of the given participant. Figure 5.5 depicts the overall mean total force signal based

on all 20 participants along with the mean total force signals of 2 participants as

examples.

The second group of features measures the similarity between the reference curve of

each participant and all other total force signals belonging to that participant (within-

participant similarity measure) and belonging to other participants (between-participant

similarity measure). These features were:

• Pearson correlation coefficient (NCC) between two signals, which is a measure of

the strength of linear dependence (correlation) between two signals.

Chapter 5. 94

1 2 3 4

3

4

5

6

7

8

9

10

11

12

Time (Sec)

Tota

l grip f

orc

e (

N)

Unregistered signals

1 2 3 4

3

4

5

6

7

8

9

10

11

12

Time (Sec)

Tota

l grip f

orc

e (

N)

Registered signals

1 2 3 44

5

6

7

8

9

10

Time (Sec)

Tota

l grip f

orc

e (

N)

Mean signals

Unregistred

Registered

Figure 5.4: Example of total force signals for one participant before (left graph)and after (center graph) registration. To facilitate visualization, only a subset oftotal force signals is shown. Pre- and post-registration mean total force profiles for thegiven participant appear in the rightmost graph.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

5

10

15

20

25

Time (Sec)

Tot

al g

rip fo

rce

(N)

Overall meanParticipant #4 Participant #19

Figure 5.5: Examples of mean total force signals. The solid line shows the overallmean total grip force signal based on all participants while each dotted line exemplifiesthe mean total grip force signal of a participant.

• Root mean square error (RMSE) between two magnitude-normalized signals (i.e.

zero mean and unit standard deviation signals), which reflects the distance between

two signals.

• Cost of registering two signals, which is the sum-of-squares criterion function de-

tailed in Chau et al. (2005).

Chapter 5. 95

5.3.6 Pattern classification

To ascertain the within-participant consistency of the total force signals and the extent of

the between-participant variability, a binary classifier was created for each participant.

For the ith classifier, i = 1, ..., 20, the true signatures class included the bogus signa-

tures that belonged to the ith participant, while the false signatures class entailed an

equal number of bogus signatures randomly selected from the other 19 participants. For

each classifier, the inputs were the features extracted from the total force signal of each

signature and the output was a binary output indicating whether the signature sample

belonged to the ith participant (true sample) or not (false sample). For each participant,

the mean misclassification rate (MCR) was estimated based on ten iterations of 10 fold

cross validation. In each iteration of the cross validation, a different random set of false

signature samples were selected.

Several different classifiers were considered including a simple linear classifier, the

linear discriminant analysis (LDA) classifier (Duda et al., 2001), a probabilistic classifier

(Naive Bayes), a nonparametric nonlinear classifier (K-nearest neighbor (KNN)) and a

parametric nonlinear classifier (support vector machine (SVM) with radial bases function

(RBF)). For each classifier, the mean MCR as well as the percentage of false positives

(FP) and false negatives (FN) were tabulated based on 100 folds (10 iterations × 10

folds).

Classification was first performed using all 20 extracted features. To remove potential

feature redundancy and to reduce dimensionality, a subset of 9 features was systematically

selected according to the procedure below.

1. The sample covariance matrix of the features vectors was calculated. Six features

were excluded due to high inter-feature correlations.

2. With the 14 remaining features, weighted sequential feature selection (WSFS) (Mamun

et al., 2012) was invoked to find the most discriminatory set of features in each iter-

Chapter 5. 96

ation for each participant. Features were ranked based on their individual discrim-

inability. The optimal subset of features for each iteration of 10 folds was identified

as features that surfaced the most frequently while yielding the lowest MCR.

3. To minimize feature space dimensionality and to hone in on a uniform set of features

across participants, only features that were frequently selected across participants

were admitted to the final feature set. Specifically, 9 features emerged: mean, CV,

skewness, centroid frequency, bandwidth, entropy rate, sub-band power (2 Hz ≤ f

< 3Hz), NCC and RMSE.

The above analysis was performed with an unordered (i.e., randomly selected) set of

true samples from each participant. Random selection ensured that the training set in-

cluded samples across sessions. Therefore, both training and testing sets likely contained

signature samples from the same session. To determine the effect of training and testing

with samples from different sessions on MCR values, the same analysis was repeated with

sequentially ordered true samples. In this latter case, the testing set included samples

from sessions that were not part of the training set. A Wilcoxon rank sum test was

performed for each participant to compare the two groups of MCRs.

The effect of reducing the number of samples on classification performance was also

examined. Subsets of decreasing size, from 100% to 10% of the samples available for each

participant were considered. For each subset, the mean MCR was calculated based on

10 iterations of 10 fold cross validation.

5.4 Results

Figure 5.6 presents the average MCRs of the four classifiers using all 20 features (un-

shaded bars) and using 9 selected features (shaded bars). On average, 943 (90%) training

samples and 105 (10%) testing samples were used in each fold of cross validation. Only

the SVM classifier performance improved with the feature selection. By statistically com-

Chapter 5. 97

paring the average MCR, FP and FN obtained with the 20-feature LDA classifier and the

same quantities for classifiers of decreasing feature dimension, it was found classification

performance is preserved down to 9 features (p = 0.126, 0.07, and 0.36 respectively).

With only 8 features, FP increased significantly (p = 0.044). Likewise, with only 7 fea-

tures, MCR was significantly higher (p = 0.046). Since the simple LDA classifier with all

20 features yielded the best performance overall, it will be the focus of the subsequent

analyses.

LDA Bayes KNN SVM0

5

10

15

20

Classifier

Mea

n M

CR

%

20 features9 features

7.8

9.4 9.9

6.7

9.48.4

5.8

15.3

Figure 5.6: The means (bars) and standard deviations (error bars) of the MCRsof the different classifiers with full (unshaded bars) and reduced feature sets(shaded bars).

Figure 5.7 provides a more detailed breakdown of the LDA classifier performance

across participants, in terms of percentage false positives and false negatives. These

results arise from considering an unordered full set of true samples with all 20 features.

Unordered and ordered sets of true samples yielded similar MCR values for all par-

ticipants (p > 0.05; Wilcoxon rank sum) except for participant 11 (p=0.0014) where the

unordered set yielded a lower MCR value.

The effect of reducing the sample size on mean MRC is illustrated in Figure 5.8. This

analysis was performed separately for each participant and the average MCRs across

Chapter 5. 98

2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

7

Mea

n F

P a

nd F

N %

Participant

3.3

2.5

FPFN

FNFP

Figure 5.7: Performance of the LDA classifier for each participant. The percent-age of false positives (FP) and false negatives (FN) are shown for each participant. Theaverage values across participants are shown as the dotted lines with their values on theright side of the figure.

participants are reported in the figure with respect to the number of samples in each

fold. Reducing the sample size did not significantly increase the error rate (p = 0.125;

robust regression test).

0 200 400 600 800 1000 12002

4

6

8

10

12

Number of samples

Mea

n M

CR

%

Figure 5.8: The number of samples and the average MCR obtained when chang-ing the percentage of data considered.

Chapter 5. 99

5.5 Discussion

This study presents the first investigation into the variability of time-evolving grip kinetic

profiles of 20 adult participants writing the same, well-practiced signature over multiple

days and at various times each day. The signatures studied herein can be considered free-

hand or skilled forgeries given the extended practice period (Impedovo & Pirlo, 2008).

Overall, our findings corroborate previous reports that grip kinetics, albeit analyzed from

a topographic perspective, generally do not differ significantly between well-practiced and

authentic signatures (Ghali, Mamun, & Chau, n.d.-a).

A closer examination of Figure 5.5 reveals some common kinetic fluctuations across

participants. Generally, the grip force gradually increases while writing the first name

and sharply declines during the completion of the second ’l’. The notable kinetic dip

that follows is due the cessation in writing as the writer moves the pen horizontally to

commence the last name. Similar to the first name, the grip force gradually increases as

the word is written and tails off sharply with the writing of the last letter.

Despite these general similarities, the mean total force signals varied among writ-

ers in terms of their magnitude, their difference between words and their fluctuations

within each word. Similar inter-individual differences have been reported in the study of

grip kinetics associated with golf swings (Komi et al., 2008). The between-participant

variability in the grip kinetic profile is likely attributable to the personalized nature of

handwriting motor skills (Jasper et al., 2009). Indeed, early study of handwriting kinet-

ics (Herrick & Otto, 1961) qualitatively reported between-participant variability in finger

pressure patterns.

Within-participant variations in the total force profile did exist as well, as exemplified

in Figure 5.4. This variation included a change in the magnitude and shape of the profile

over time. Some of the variability might be due to grasp adjustments and pen rotations,

which were observed by the researcher during the data collection and retrospectively,

through a review of the pictures taken at each session. These changes were particularly

Chapter 5. 100

evident for participant 6 and explain the high MCR values for this participant in Figure

5.7. Grasp adjustments change the position and orientation of the sensor array with

respect to the hand. Since there is some inevitable ’dead space’ between neighboring

sensors on the array, grasp adjustments may alter the measurement of total force. Other

contributors to within-participant force profile variation may have included circadian

fluctuations in the grip strength and writer motivation (Jasper et al., 2009), calibration

errors, mental and physical fatigue, as well as changes in body and arm posture while

writing (Parvatikar & Mukkannavar, 2009).

Although all 32 sensors were considered in this study, future research may consider the

potential to classify writers on the basis of a smaller subset of sensors. In a previous study

(Ghali, Anantha, et al., 2013), it was noted that handwriting grip forces are captured by

only a small subset of sensors around the barrel. Future research may thus consider the

judicious elimination of uninformative sensors.

In this study, the bogus signature is considered a text-based signature since each letter

can be identified. A visual inspection of the authentic signatures of all 20 participants

revealed that all but one participant employed a text-based form of signature writing;

participant 7 was the only one who had a non-text signature where none of the letters

could be identified. However, the MCR of participant 7 was still within the range of

MCRs obtained across participants as evident in Figure 5.7. In a future study, it would

be interesting to examine if the present findings would generalize to non-text writing

more broadly.

The classification analysis suggested that even in the presence of within-participant

variability in the grip kinetic profiles, the between-participant variations tend to be

greater, allowing for inter-participant separation. The low MCR with the LDA clas-

sifier suggests that the features derived from the grip kinetic profiles are in fact linearly

separable. The lack of difference in MCRs for ordered and unordered samples implies that

this separability is consistent over time. Finally, the inter-participant separation seemed

Chapter 5. 101

to be intact even if the pool of signatures was reduced dramatically, an important con-

sideration for signature verification systems (Impedovo & Pirlo, 2008; Radhika, Sekhar,

& Venkatesha, 2009). Overall, the findings of this study support further investigation of

grip kinetic profiles associated with signature writing as a biometric measure.

5.6 Conclusion

In this study, we examined the total grip force profile generated while writing multiple it-

erations of a well-practiced signature by 20 participants. The algorithmic discrimination

between writers based on features extracted from the total grip force profile indicated

that despite intra-participant variability, each participant had a unique grip kinetic pro-

file. Further, classification performance was robust to reductions in sample size and the

temporal ordering of test signatures. Collectively, these findings indicate that the grip

kinetic profile may be a valuable measure for signature verification applications.


The authors would like to acknowledge the Canada Research Chairs program, Syngrafii

Inc., and the Natural Sciences and Engineering Research Council of Canada for support-

ing this research financially. The authors would also like to acknowledge Ms. Nayanashri

Thalanki Anantha, Ms. Jennifer Chan, Ms. Laura Bell, and Ms. Sarah Stoops for their

assistance with the data collection for this study.

Chapter 6

Conclusions

6.1 Summary of Contributions

This thesis makes a number of original contributions to the field of biomedical engineer-

ing, and more specifically to the areas of biometrics and handwriting biomechanics. In

summary, this thesis:

1. Demonstrated that writers had unique grip shape kinetics that were repeatable

over time but distinct from those of other participants. In fact, an examination

of the topographic distribution of the forces associated with each grip shape in-

dicated that the grip shape images were distinct between participants even if two

participants invoked the same grip shape. Also, despite some grip adjustments

within-individuals, intra-participant variation in grip kinetics was generally much

smaller than inter-participant force variations. These individual-specific kinetic

grip shapes were algorithmically discernible from one another with an error rate

as low as 1.2± 0.4% when the entire force distribution around the pen barrel was

considered (Ghali, Anantha, et al., 2013). This indicates that the grip force images

can be a valuable measure for discriminating among individuals.

2. Verified that the inter-subject variability in grip kinetics was still higher than the

102

Chapter 6. 103

intra-subject variability in the long term for most participants. Even though the

statistical analysis showed that significant within-individual changes in grip kinetic

features may arise over an extended time period, the performance of the discrimi-

nation analysis did not decrease dramatically (Ghali et al., n.d.-b). This study also

showed that inter-participant discrimination was stable even when smaller data

sets and different classifier training scenarios were considered. These promising

findings support further study of grip kinetics as a biometric measure for personal

verification applications.

3. Showed that the well-practiced bogus signatures were not necessarily associated

with different or more variable grip kinetics. Only a few participants exhibited a

significant difference in grip kinetic features between writing authentic and well-

practiced bogus signatures and these differences were not consistent across partic-

ipants (Ghali et al., n.d.-a). Also, the amount of variability associated with the

well-practiced bogus signatures did not exceed that of the authentic signatures. The

findings of this study indicated that as long as the written text is well-practiced

and written naturally, the handwriting kinetics are, in many cases, similar to the

kinetics associated with authentic signature writing. This conclusion justified the

use of the well-practiced bogus signatures to investigate intra- and inter-subject

variability of the grip kinetic profile in Chapter 5.

4. Demonstrated that there was a unique kinetic profile between repeated signatures

written by the same participant and that these kinetic profiles were sufficiently

different between participants even though all participants were writing the same

signature. A linear discriminant analysis classifier was able to verify the signatures

of each participant with an average MCR of about 5.8% (Ghali, Mamun, & Chau,

2013). Training the classifier with a smaller data set and with samples from different

sessions did not affect the performance of the verification algorithm. The findings

Chapter 6. 104

of this study highlight the potential of using grip kinetics as a biometric measure.

A signature is a special case of handwriting-based authentication. More gener-

ally, handwriting-based biometric authentication is content independent (Yampolskiy

& Govindaraju, 2008; Zhu, Tan, & Wang, 2000). Conceivably methods developed for the

specific problem of signature verification could eventually be generalized to the broader

problem of handwriting-based authentication. These findings can also be generalized to

other motor tasks such as typing and walking as well as playing sports and different mu-

sical instruments because of the focus that can be placed on the kinetics associated with

executing these tasks and its effect on their performance. Studies related to these tasks

have not considered the forces applied by an individual while performing the task and

in some cases, the consideration of the force applied was minimal and did not study the

variation of the forces across sessions and over time (Yampolskiy & Govindaraju, 2008;

Karnan et al., 2011; Salami et al., 2011; Komi et al., 2008; Dalla Bella & Palmer, 2011).

This thesis has implications in the clinical quantification of fine motor difficulties

as well. The analysis of handwriting grip kinetics in adults can help to better inform

clinical assessments and rehabilitation programs (Van Drempt et al., 2011). It can also

help in the development of personalized neuromotor interventions or customizable grips

in clinical applications. Grip forces may also inform the design of new pens that reduce

the muscle load and fatigue during extended periods of continuous writing (Udo et al.,

2000; Goonetilleke, Hoffmann, & Luximon, 2009) as well as provide easier interactions

in the case of digital pens (Song et al., 2011).

6.2 Future Work

The findings of this thesis highlight the potential of using grip kinetics as a biometric

measure and confirm the importance of considering handwriting biomechanics in such an

application. Therefore, future work in this area can include the following:

Chapter 6. 105

• Uncovering inter-participant differences by examining the profile of force signals

produced on each individual force sensor since the inter-finger absolute pressures

have been found to vary widely between individuals (Herrick & Otto, 1961).

• Improving the overall verification performance by combining grip kinetic features of

different representations (topographical and functional) with axial force, kinematic,

and spatiotemporal features that have been extensively used in the literature to

provide higher within-subject consistency while offering maximum discrimination

among individuals.

• Performing the verification with a method similar to the methods employed in the

literature (Houmani et al., 2012; Yeung et al., 2004).

• Examining the performance of grip kinetics for signature verification using a bigger

database consisting of 400 participants forging a signature multiple times in a signal

session and using this database to study the correlation, if any, between grip kinetic

features and some demographic information such as gender, age, handedness, and

occupation.

6.3 Resulting Publications

1. Ghali, B., Anantha, N. T., Chan, J., & Chau, T. (2013). Variability of grip kinetics

during adult signature writing. PLoS One, 8 (5), e63216.

2. Ghali, B., Mamun, K., & Chau, T. Long term stability of handwriting grip kinetics

in adults. (Under review).

3. Ghali, B., Mamun, K., & Chau, T. A comparison of handwriting grip kinetics

associated with authentic and well-practiced bogus signatures. (Under review).

Chapter 6. 106

4. Ghali, B., Mamun, K., & Chau, T. (2013). Grip kinetic profile variability in adult

signature writing. Journal of Biometrics and Biostatistics. (Accepted).

6.4 Limitations

Some of the limitations of the work performed in this thesis are:

• Number of participants: Only 20 participants were involved in phase 1 of the

data collection and 18 participants in phase 2 of the data collection because of

limited availability. More participants would be needed to confirm that conclusions

drawn in this thesis apply to the general population of adults with no handwriting

difficulties.

• Type of writing samples: Only signatures were used as the written product in this

thesis. It could be possible to generalize the results to other written messages.

• Instrumentation: The type of sensors and the calibration method employed could

have affected the results. Using a sensor sheet that does not have a spacing be-

tween the sensors might improve the results. Also, the calibration process could be

improved to increase its reliability and speed up the process.

• Time frame: The limited time frame of the data collection is another limitation.

Collecting data over a longer period of time might be needed to confirm that the

within subject variability of grip kinetics does not increase over time

• Average-based analysis: Basing the analysis on the temporal and spatial average of

the grip kinetics might have limited the results obtained in this thesis. Therefore,

using the original grip force signal could improve the results.

• Components of grip forces: Only the normal component of the grip force that is

applied on the pen barrel was considered in this thesis. We did not consider the

Chapter 6. 107

tangential component of grip forces which can provide additional discriminatory

information.

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Appendix A

A.1 Overview of handwriting grip shapes

Pen grip shape or pencil grasp pattern is the way each individual arrange the fingers to

hold the utensil during handwriting. Many studies have been preformed to study the

development of grip shapes in children from the radial cross palmar grasp to one of the

mature grip shapes utilized by adults (Dennis & Swinth, 2001; Burton & Dancisak, 2000;

Tseng, 1998). The most common mature grip shapes are the dynamic tripod grasp and

the lateral tripod grasp (Selin, 2003). Another efficient grip that can be used by adults

is the quadrupod grasp in which four fingers are utilized to stabilize the pen. The static

tripod grasp which was used by two participants has the same fingers position as the

dynamic tripod grasp, but it lacks the stability found in the dynamic tripod grasp that is

produced by controlling the intrinsic hand muscles. In this static grasp the hand moves

as a unit.

The most typical grip shape used by each participant was determined based on pic-

tures of the grip taken during each session. Figure A.1 shows examples of the taken

pictures for three participants utilizing three different grip shapes. By reviewing the

collected photos and based on the different grip patters defined in the literature, the grip

shape of each participant was determined. To confirm the accuracy of the classification

of the first rater and establish inter-rater reliability, a second rater examined the pictures

121

Appendix A. 122

to determine the grip shape of the participant and the agreement between the raters was

ensured.

Dynamic tripod

grasp

Lateral tripod

grasp

Quadrupod

grasp

Figure A.1: Photos taken during the data collection of the three most typicalgrip shapes.

A.2 Definition of kinematics and kinetics

Kinematics is the study of motion without considering the forces associated with it

whereas kinetics is the study of forces associated with a motion (Zatsiorsky, 1998, 2002).

Therefor, in handwriting, the kinematics include the pen tip position, speed and accel-

eration associated with the movement of the writing utensil. On the other hand, the

handwriting kinetics involves two forces (Van Drempt et al., 2011). The first one is the

pen tip force, also known as the axial or normal force, which is the force applied down-

ward by the pen tip onto the writing surface. The second force is the grip force which

is the force applied radially by the fingers onto the pen barrel. This thesis focused on

studying the second force associated with signature writing.

Appendix A. 123

A.3 Introduction to some analytical methods

A.3.1 Box plot

A box plot is a method to graphically examine one or more data sets and to compare

their distributions (McGill, Tukey, & Larsen, 1978; Der & Everitt, 2007). It summarizes

the distribution of a data set by five numbers as shown in Figure A.2:

1. The median

2. The upper quartile being the 75th percentile which is the upper end of the box

3. The lower quartile being the 25th percentile which is the lower end of the box

4. The maximum limit shown as the upper whisker which extends to 1.5 × the in-

terquartile range above the upper quartile

5. The minimum limit shown as the lower whisker which extends to 1.5 × the in-

terquartile range below the lower quartile

The whiskers extend to the most extreme data points not considered outliers. Any data

points beyond the maximum and minimum limits are considered outliers.

The notch is an interval that can be used to compare medians of two data sets. Two

medians are considered significantly different at the 5% significance level if their notched

intervals do not overlap. The notched interval endpoints correspond to the following:

median ±1.57(IQR)/√

(n) where IQR is the interquartile range which is the difference

between the 75th and 25th percentiles, respectively, and n is the number of observations.

A.3.2 Linear discriminant analysis

Linear discriminant analysis (LDA) also known as the fisher discriminant analysis is a

linear classification technique which aims to find a linear function that best separate the

different classes of data (Yang, 2010; Duda et al., 2001). The linear function f(x) is a

Appendix A. 124

Outlier

Median Notch

25th Percentile

75th Percentile

Upper whisker

Lower whisker

Figure A.2: An example of a box plot and its interpretation.

hyper plane that constitute the decision boundary. An example is shown in Figure 3.4.

The data belongs to one class when f(x) > 0, and it belongs to the other class when

f(x) < 0. The linear function is defined as follows

f(x) = bias+w · x (A.1)

where w is the weight vector that is found based on the fisher criteria to maximize the

separation between the two classes. The fisher criteria defines the separation between

classes to be the ratio of the dispersion between classes over the dispersion within classes:

s =σ2between

σ2within

=(w ·m1 −w ·m2)

2

wTcov1w +wTcov2w(A.2)

where s is the score of the fisher criteria; m1 and m2 are the mean vectors of the two

classes; cov1 and cov2 and the covariance matrices of the two classes. Therefore, the

Appendix A. 125

weight vector that maximizes s is:

w =m1 −m2

cov1 + cov2

(A.3)

Based on the training data the weight vector is determined and then it is used to

determine the class of data in the test set. This method can be extended to multiple

classes problems where multiple hyper planes are generated.

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