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FSI-6959; No. of Pages 5 Forensic Science International xxx (2012) xxx–xxx

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Forensic Science International journal homepage: www.elsevier.com/locate/forsciint

Nonadherence to the isochrony principle in forged signatures Michael P. Caligiuri a,*, Linton A. Mohammed b, Bryan Found c,d, Doug Rogers c a

University of California, San Diego, La Jolla, CA, United States Forensic Science Consultants, Inc., San Bruno, CA, United States c Handwriting Analysis and Research Laboratory, School of Human Biosciences, La Trobe University, Bundoora, Victoria, Australia d Document Examination Unit, Digital and Documents Evidence Branch, Victoria Police Forensic Services Department, Macleod, Victoria, Australia b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 25 March 2012 Received in revised form 28 August 2012 Accepted 25 September 2012 Available online xxx

Highly programmed skilled movements are executed in such a way that their kinematic features adhere to certain rules referred to as minimization principles. One such principle is the isochrony principle, which states that the duration of voluntary movement remains approximately constant across a range of movement distances; that is, movement duration is independent of movement extent. The concept of isochrony suggests that some information stored in the motor program is constant, thus reducing the storage demands of the program. The aim of the present study was to examine whether forged signatures can be distinguished from genuine signatures on the basis of isochrony kinematics. Sixty writers were asked to write their own signatures and to forge model signatures representing three different writing styles: text-based, stylized, and mixed. All signatures were digitized to enable high precision dynamic analyses of stroke kinematics. Vertical stroke duration and absolute amplitude were measured for each pen stroke of the signatures using MovAlyzeR1 software. Slope coefficients derived from simple regression models of the relationship between stroke duration and amplitude served as our measure of isochrony. The slope coefficient reflects the degree to which stroke duration increases in relation to stroke amplitude. Higher coefficients indicate greater increases in stroke duration for a given stroke amplitude and thus violate the isochrony principle. We hypothesized that the duration–amplitude coefficients for forged signatures would be significantly greater than for genuine signatures suggesting non-adherence to the isochrony principle. Results indicated that regardless of the style of the writer, genuine signatures were associated with low slope coefficients Pen strokes forming forged signatures had significantly greater duration–amplitude slope coefficients than genuine signatures. These findings suggest that when forging signatures, writers execute pen movements having steeper duration– amplitude relationships than for genuine signatures. ß 2012 Elsevier Ireland Ltd. All rights reserved.

Keywords: Signature authentication Cost-minimization principle Kinematics

1. Introduction One approach to understanding the nature of various strategies employed by writers attempting to forge another signature is to consider the strategy as a modification in the execution of the writer’s inherent handwriting motor program. Assuming that forged signatures represent the altered output of an individual’s handwriting motor program, it then becomes possible to examine specific elements of the handwriting motor program for differences between genuine and altered signature formation. There is compelling empirical support for the existence of a handwriting motor program [1–5]. Keele and Summers [6] maintain that a fundamental component of skilled motor behavior

* Corresponding author at: Department of Psychiatry (0603), University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, United States. Tel.: +1 858 657 5100. E-mail address: [email protected] (M.P. Caligiuri).

begins with the sequencing of discrete movements. The central representation of this sequence then becomes a motor program. Thus, a motor program is a theoretical memory structure capable of transforming an abstract code into an action sequence [7]. With regard to handwriting, Thomassen and Van Galen [1] noted the high degree of consistency in the form of an individual’s script when written using different limbs offers compelling evidence in support of an abstract motor program. In theory, when a writer attempts to forge a signature, the coded sequence of handwriting movements that represent the writer’s natural signature are replaced by a novel relatively unprogrammed set of movements. These novel movement sequences (i.e. forged signatures) are not likely to exhibit the characteristics of a highly programmed movement sequence (i.e. genuine signature). For example, studies of programmed movements have shown that the kinematic features of individual movements adhere to certain rules referred to as minimization principles. Minimization principles have been applied to a range of scientific disciplines such as physics, evolutionary biology, engineering, as

0379-0738/$ – see front matter ß 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.forsciint.2012.09.008

Please cite this article in press as: M.P. Caligiuri, et al., Nonadherence to the isochrony principle in forged signatures, Forensic Sci. Int. (2012), http://dx.doi.org/10.1016/j.forsciint.2012.09.008

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well as human motor control [8,9]. In biology, minimization principles describe a means by which animals attempt to achieve maximum effectiveness with minimum effort when executing a goal-directed movement. In motor control, minimization principles enable computational modeling of error reduction and include the minimum jerk model [10], isochrony [11], and the 2/3 power law [12]. The present study focuses on adherence to the isochrony principle. The isochrony principle states that the velocity of voluntary movement increases with the extent of the movement, thus keeping movement time approximately constant [8,11]. In a previous study of the kinematics of forged signatures we demonstrated that when forging signatures, writers failed to scale stroke velocity in relation to stroke distance [5]. As an indirect measure of isochrony, failure to scale movement velocity in relation to distance supports the notion that forged signatures are produced with less efficiency than natural genuine signatures using relatively unprogrammed motor sequences. The aim of the present study was to extend the results of our previous finding by examining whether forged signatures can be distinguished from genuine signatures on the basis of a more direct measure of isochrony kinematics. Because of their highly programmed nature genuine natural handwriting movements are thought to adhere to principles of minimization of effort such as isochrony. Conversely, we would hypothesize that non-programmed movements, such as forgeries would violate these principles. That is, a forged signature is not likely to be programmed nor produced with kinematic efficiency. If this hypothesis were supported, this method could provide the FDE with a quantifiable means of judging whether a signature was genuine, or forged; thus improving reliability.

were extracted from each vertical stroke. We chose to study vertical strokes because in Western script, most strokes go up or down with only a few horizontal. More importantly, the vertical component is better suited than the horizontal component for segmenting patterns into strokes (H.-L. Teulings, personal communication). The number of strokes varied across signatures depending on the number of characters contained in the signature and whether the signature is written in text-based, stylized, or mixed style. The mean (standard deviation) number of strokes across all writers and trials was 231 (75) for genuine signature, 448 (11) for text-based forgeries, 213 (37) for stylized forgeries, and 441 (11) for mixed forgeries. For each writer and each condition, signature pen strokes were subjected to linear regression analyses to derive a slope coefficient for the linear relationship between stroke duration and stroke amplitude. Assuming that pen movements for overly-learned highly programmed movements (e.g. a person natural signature) adhere to the isochrony principle (within a narrow range of stroke amplitudes), then the stroke duration–amplitude regression coefficient for a genuine signature represents a quantitative index of the writer’s adherence to the isochrony principle. Moreover, pen movements characterized by significant departures from a writer’s normal stroke duration–amplitude relationship would reflect non-adherence to isochrony. A two-way repeated measures analyses of variance (ANOVA) was used to test main effects of writer style (3 levels: text-based, stylizes, and mixed) and condition (2 levels: genuine and forged) with condition entered as a repeated measure. For significant main effects, post hoc analyses were performed using least square difference tests. Alpha levels less than or equal to 0.05 were considered statistically significant.

3. Results Fig. 1 shows exemplars from a single writer depicting the relationships between stroke duration and stroke amplitude. The 3000 Genuine

2. Methods 2.1. Writers Sixty writers, 24 males and 36 females, participated in the forgery experiment. Subjects comprised 20 writers in each of three signature style groups: text-based, mixed, and stylized. We did not collect the writer’s exact age; rather we noted the age bracket of the writer. Eighty-seven percent of the writers were under the age of 50 years and all writers were right-handed. All subjects read and signed an Institutional Review Board-approved consent form informing them of the purpose of the research.

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2.3. Data reduction and statistical analyses Dynamic data from each signature were collected and processed using MovAlyzeR1 software. For the purpose of this study, duration and absolute amplitude

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Acquisition of signature kinematics was the same for each experiment. Writers were asked to provide genuine and forged signatures using an inking pen on a Wacom digitizing tablet. For the genuine signatures, the subjects were asked to write their normal signature as they would on a bank check. Subjects were asked to forge each of the three model signatures 18 times. The first three trials were considered practice and excluded from further analyses. The forgers were randomly divided into three groups. In each group, the forger first provided 10 genuine signatures. The first group forged the models in the sequence of text-based, mixed, then stylized; the second group stylized, mixed, then text-based; and the third group mixed, text-based, then stylized. This was done to correct for any possible systematic influence of changing between signature styles. It is noted that individuals may normally perform more than one form of genuine signature. For example, a formal signature may be executed on documents such as wills and deeds and a less formal signature may be used for everyday routine transactions. To control for this variable, copies of the same facsimile check were provided to subjects as the sample collection document. For each signing event, the check was positioned over a Wacom digitizing tablet sampling at 200 samples/s and providing 5 m resolution. The tablet was placed on a horizontal table and writers assumed a comfortable writing position while seated. The writers were allowed to shift the tablet to assume the angle of writing most comfortable for them. The check was placed in the same position on the tablet for each trial to correct for possible variations in the sensitivity of the tablet surface [13]. Kinematic signature data from the same 60 writers were previously reported in a study of velocity scaling [5]. The present study, however, is a re-analysis of the genuine and forged signatures yielding new findings on stroke duration.

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Vertical Stroke Size, in cm Fig. 1. Scatterplots showing the relationship between stroke duration and stroke amplitude for genuine (top) and forged (bottom) signatures. Data are from a single writer using natural stylized signature for both signatures. Lines of best fit derived from linear regression analyses are shown. The slope coefficient for the genuine signature is 0.019 s/cm, suggesting relatively constant stroke duration across the range of amplitudes. The slope coefficient for the forged signature is 0.417 s/cm, suggesting an incremental increase in stroke duration across the range of amplitudes.

Please cite this article in press as: M.P. Caligiuri, et al., Nonadherence to the isochrony principle in forged signatures, Forensic Sci. Int. (2012), http://dx.doi.org/10.1016/j.forsciint.2012.09.008

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FSI-6959; No. of Pages 5 M.P. Caligiuri et al. / Forensic Science International xxx (2012) xxx–xxx Table 1 Mean (and standard deviation) slope coefficients for the linear relationship between stroke duration and stroke amplitude for three groups of writers producing genuine signatures and forgeries of three styles (text-based, stylized, and mixed). Values are scaled in s/cm. Forged: text

Forged: stylized

Forged: mixed

0.058 (0.032) 0.029 (0.024) 0.048 (0.029)

0.113 (0.061) 0.080 (0.052) 0.100 (0.068)

0.170 (0.180) 0.103 (0.106) 0.108 (0.060)

0.157 (0.103) 0.091 (0.075) 0.113 (0.106)

0.22 0.20 0.18 0.16

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contrast in the slope of the regression line between genuine and forged signatures is clearly evident in this example. To execute the forgery, this writer not only increased both stroke duration and amplitude, but the slope of the duration–amplitude relationship also increased from 0.019 to 0.417 s/cm. Table 1 shows the mean slope coefficients for the linear relationship between stroke duration and stroke amplitude for genuine and three sets of forged signatures. ANOVA revealed a significant main effect for writer style (F2,7 = 4.11; p < 0.05). Post hoc analyses revealed that stylized writers exhibited significantly lower slope coefficients than text-based writers (p < 0.01). There was a significant main effect for condition (F3,171 = 14.12; p < 0.00001). Post hoc tests revealed that slope coefficients for genuine signatures were significantly lower than coefficients for text-based (p < 0.0001), stylized (p < 0.0001) and mixed (p < 0.0001) forgeries. Additionally stylized forgeries were produced with lower slope coefficients than text-based forgeries (p < 0.05). The signature condition by writer style interaction was not statically significant suggesting that the genuine–forgery differences were not dependent on writer style. These results are shown in Fig. 2. It is important to note that not every writer failed to adhere to the isochrony principle when forging a signature. To examine homogeneity in adherence across writers, we determined the proportion of writers exhibiting slope coefficients for forged signatures that exceeded the 95% confidence interval (cut-point) for the genuine signatures (within style). Among text-based writers, 70% exhibited slope coefficients that exceeded the cutpoint for text-based forgeries; 75% exceeded the cut-point for stylized forgeries, and 95% exceeded the cut-point for mixed-style

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Fig. 2. Mean (with standard error bars) slope coefficients s/cm for three groups of writers for genuine signatures and three styles of forgery: mixed, stylized, and textbased. Lower slope coefficients.

forgeries. Among stylized writers, 65% exhibited slope coefficients that exceeded the cut-point for text-based forgeries; 75% exceeded the cut-point for stylized forgeries, and 75% exceeded the cut-point for mixed-style forgeries. Among text-based writers, 80% exhibited slope coefficients that exceeded the cut-point for text-based forgeries; 65% exceeded the cut-point for stylized forgeries, and 75% exceeded the cut-point for mixed-style forgeries. Overall more that 75% of writers failed to adhere to the isochrony principle when producing a forged signature. Individual slope coefficients for genuine and forged signatures grouped by writing style are shown in Fig. 3. 4. Discussion Several new findings emerged from this study. First, based on regression slope coefficients showing minimal increase in stroke duration as a function of stroke amplitude, when producing genuine signatures stroke duration was relatively independent of stroke amplitude. Thus, for natural signatures, writers generally adhered to the isochrony principle. Moreover, this adherence was

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Writer Style Fig. 3. Scatterplots showing the range of individual writer slope coefficients (in s/cm) for genuine signatures (left) and forgeries (right) for three groups of writers: mixed style (MX), stylized writers (ST) and text-based writers (TB). Only forgery slope coefficients were from samples written in the writers natural style are shown in this figure.

Please cite this article in press as: M.P. Caligiuri, et al., Nonadherence to the isochrony principle in forged signatures, Forensic Sci. Int. (2012), http://dx.doi.org/10.1016/j.forsciint.2012.09.008

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evident across the three styles of writing with marked homogeneity. Second, we found that when producing forged signatures, stroke duration showed an incremental relationship with stroke amplitude for writers as a group. Unlike production of genuine signatures, writers generally failed to adhere to the isochrony principle for forgeries. We found that over 75% (range: 65–95%) of the writers produced forged signatures with duration–amplitude slope coefficients that exceeded the 95th percentile for genuine signatures. Third, the degree of non-adherence to the isochrony principle for forged signatures varied across writer and forgery style. Specifically, text-based writers exhibited greater slope coefficients for non-text forgeries than either stylized or mixed style writers. Text-based and mixed style writers exhibited similar levels of adherence across the three forgery styles. Overall, writers exhibited lower slope coefficients for stylized forgers than textbased or mixed-style forgeries. We reasoned that if genuine natural handwriting movements adhere to principles of minimization of effort and are programmed to ensure efficiency, then one would expect non-programmed movements, such as forged signatures to violate these principles. That is, a forged signature is not likely to be programmed nor produced with kinematic efficiency. We hypothesized that handwriting kinematics for normal genuine signatures will adhere to the isochrony principle, whereas kinematics for forged signatures would not. Our results support this hypothesis. Since genuine signatures are often the product of open loop control and forged signatures generally being the product of closed loop control (i.e. greater reliance upon visual feedback), our results are consistent with findings from studies of isochrony in children’s handwriting [14]. Vinter and Mounoud [14] found that the handwriting of 5–6 year old children conformed to the isochrony principle. However, the investigators noted that for a brief time between the ages of 6 and 8 years the young writer utilizes more feedback to their handwriting with regard to the length of strokes and there is less evidence of isochrony in the handwriting kinematics. With age, as the child becomes a more experienced writer and relies less on visual feedback, evidence of isochrony returns. Just as immature writers who lack a fully developed handwriting motor program produce handwriting movements that violate the isochrony principle, writers attempting to disguise or forge a signature conceal the effects of an immature handwriting motor program incapable of adhering to the isochrony principle. It is conceivable that execution of a novel unlearned movement sequences, such as a forged signature would be characterized by inefficiency and prone to error. In the production of a forged signature, it may be hypothesized that the forger is trying to replicate the habits perceived in the model signature and simultaneously discard his own writing habits. In terms of motor control, the forger’s program for executing signatures will be altered as demonstrated by the altered relationship between stroke duration and stroke amplitude. In their original work on isochrony and handwriting Viviani and Terzoulo [11] and observed that within each unit of action (i.e. stroke), the angle of the trajectory (and thus its length) was produced in roughly equal durations. When handwriting consists largely of curved strokes, individual letters are likely the manifestation of concatenated segments each of which can be characterized by its own kinematic properties such as angle, angular velocity, time, and length from which isochrony may be observed. However, not all signatures can be resolved into individual letters, which raises doubt about the universality of the isochrony principle as a governing rule during signature production. In the present study, one-third of the subjects wrote their natural signatures using stylized script comprised of unrecognizable characters and curvilinear strokes. It is therefore conceivable that stylized writers would rely on an alternate

minimization principle than for example text-based writers to achieve efficient movement sequences. One such alternative could be the 2/3 power law. When a movement trajectory is predominantly curvilinear (as is the case with most stylized signatures) the 2/3 power law governs the relationship between stroke velocity and movement extent. The 2/3 power law describes the lawful relationship between angular velocity and curvature of movement [12]. Derived from research on drawing movements, the 2/3 power law indicates that as the arc of the curvature of movement becomes more acute, the angular velocity increases. Addressing the question of whether the handwriting motor program for different writing styles favors one particular minimization principle (e.g. 2/3 power law) over another (e.g. isochrony) is beyond the scope of this paper. However, results from the present study from a variety of writing styles indicate that stylized writers actually had lower slope coefficients than the other groups when producing natural genuine signatures (see Fig. 2) suggesting that isochrony may play an important role in the handwriting motor program for these writers. Text-based writers exhibited greater departure from isochrony when producing forged signatures compared to stylized or mixedstyle writers. The one exception was for text-based forgeries, suggesting some elements of the handwriting program for natural signatures may transfer to forgeries of the same style. Alternatively, is may be especially difficult for text-based writers are to forge stylized or mixed-style signatures with kinematic efficiency. Based on stroke duration–amplitude slope coefficients as one measure of kinematic efficiency, stylized writers demonstrated greater efficiency than other writers. This observation was evident for both genuine and forged signatures suggesting that the handwriting motor program for stylized writers involves greater reliance on isochrony as cost minimization strategy than other writers. The present study has some limitations. The subjects were allowed three practice forgeries of each model. Given more efforts to practice, they may have been able to produce better results. Further experimentation with expert penmen such as trained calligraphers [15] may provide additional useful data, as the quality of forgeries they produce should be uniformly better. Second, we do not know if isochrony analyses can be used to classify signatures as genuine or forged (or disguised). Ideally, such analyses would yield a cut-off score above which there would be a high degree of certainty that the signature is not genuine. Discriminant function analyses, including receiver operating characteristics or ROC curves of the isochrony phenomenon in questioned signatures may yield interesting findings. Such information would be particularly useful for distinguishing forged from disguised signatures. It may be argued that our present findings, based on digitized signature samples, are of limited direct value to FDEs tasked with examining historical and contemporary static signatures. FDEs customarily do not have access to dynamic signature samples from which stroke velocity may be extracted from which to estimate isochrony kinematics. Nevertheless, the primary aim of the present study was to examine whether forged signatures are produced with less kinematic efficiency than genuine signatures. Our findings demonstrating that forged signatures are produced with less kinematic efficiency than genuine signatures provide potential scientific validation of what FDEs have observed as degraded quality of forged signatures [16]. To the extent that the motor program for natural signatures is built in part upon costminimization principles, suspicious signatures showing dynamic or static signs of inefficiency are not likely the product of an established automatic motor program. In conclusion, examining adherence to the isochrony principle during signature production can provide insight into whether the signatures are consistent with the writer’s natural efficient

Please cite this article in press as: M.P. Caligiuri, et al., Nonadherence to the isochrony principle in forged signatures, Forensic Sci. Int. (2012), http://dx.doi.org/10.1016/j.forsciint.2012.09.008

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handwriting motor program or not. When producing a forged signature, the forger adopts the handwriting patterns perceived in the model signature while simultaneously attempting to inhibit his or her own handwriting patterns. That is, the forger works to overwrite his or her own motor program for handwriting while rapidly learning a new one. This process inevitably leads to the inefficient production of movement sequences and stroke parameters that violate the isochrony principle. References [1] A.J.W.M. Thomassen, G.P. Van Galen, Handwriting as a motor task: experimentation, modeling and simulation, in: J.J. Summers (Ed.), Approaches to the Study of Motor control and Learning, North Holland, Amsterdam, 1992, pp. 113–144. [2] H.L.H.L. Teulings, Handwriting movement control, in: S.W. Keele, H. Heuer (Eds.), Handbook of Perception and Action, vol. 2: Motor Skills, Academic Press, London, 1996, pp. 561–613. [3] R.R. Plamondon, M.M. Djioua, A multi-level representation paradigm for handwriting stroke generation, Hum. Movement Sci. 25 (2006) 586–607. [4] D.A. Rosenbaum, Human Motor Control, second edition, Academic Press, University Park, PA, 2010. [5] M.P. Caligiuri, L.A. Mohammed, The Neuroscience of Handwriting: Applications for Forensic Document Examination, CRC Press, Boca Raton, 2012.

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[6] S.W. Keele, J.J. Summers, The structure of motor programs, in: G.E. Stelmach (Ed.), Motor Control: Issues and Trends, Academic Press, New York, 1976, pp. 109–142. [7] R.A. Schmidt, et al., Motor output variability: a theory for the accuracy of rapid motor acts, Psychol. Rev. 86 (1979) 415–451. [8] P. Viviani, T Flash, minimum-jerk, two-thirds power law, and isochrony: converging approaches to movement planning, J. Exp. Psychol. Hum. Percept. Perform. 21 (1995) 32–53. [9] S. Engelbrecht, Minimum principles in motor control, J. Math. Psychol. 45 (2001) 497–542. [10] T. Flash, N.N. Hogan, The coordination of arm movements: an experimentally confirmed mathematical model, J. Neurosci. 5 (1985) 1688–1703. [11] P. Viviani, C. Terzoulo, Space–time invariance in learned motor patterns, in: G.A. Stelmach, J. Requin (Eds.), Tutorials in Motor Behavior, North-Holland, Amsterdam, 1980, pp. 525–533. [12] F. Lacquaniti, C.A. Terzuolo, P. Viviani, The law relating kinematic and figural aspects of drawing movements, Acta Psychol. (Amst.) 54 (1983) 115–130. [13] M. Meeks, T. Kulinski, Measurement of dynamic digitizer performance, in: R. Plamondon, C.G. Leedham (Eds.), Computer Processing of Handwriting, World Scientific Publishing, Singapore, 1990, pp. 89–110. [14] A. Vinter, P. Mounoud, Isochrony and accuracy of drawing movements in children; effects of age and context, in: J. Wann, A.M. Wing, N. So˜vik (Eds.), Development of Graphic Skills, Academic Press, London, 1991, pp. 113–114. [15] T. Dewhurst, B. Found, D.D. Rogers, Are expert penmen better than lay people at producing simulations of a model signature? Forensic Sci. Int. 180 (2008) 50–53. [16] L. Michel, Disguised signatures, J. Forensic Sci. Soc. 18 (1978) 25–29.

Please cite this article in press as: M.P. Caligiuri, et al., Nonadherence to the isochrony principle in forged signatures, Forensic Sci. Int. (2012), http://dx.doi.org/10.1016/j.forsciint.2012.09.008