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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
3.3.4 Data collection protocol . . . . . . . . . . . . . . . . . . . . . . . 56
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
4.3.2 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.3 Experimental protocol . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.4 Data pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.5 Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.6 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
viii
4.6 Conflict of interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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
5.3.2 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3.3 Data collection protocol . . . . . . . . . . . . . . . . . . . . . . . 89
5.3.4 Data pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3.5 Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3.6 Pattern classification . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.7 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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
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Participant 20
2 4
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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
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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.
3.3.4 Data collection protocol
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.
4.3.2 Instrumentation
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).
4.3.5 Feature extraction
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.
4.7 Acknowledgements
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.
5.3.2 Instrumentation
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.
5.3.3 Data collection protocol
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).
5.3.5 Feature extraction
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.
5.7 Acknowledgements
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.