Pattern Recognition 35 (2002) 1039–1047
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A 3D motion-tracking method in graphonomic research: possible applications in future handwriting recognition studies Chris F. Bouwhuisen ∗ , Ruud G.J. Meulenbroek , Arnold J.W.M. Thomassen Nijmegen Institute for Cognition and Information, PO Box 9104, 6500 HE Nijmegen, The Netherlands Received 17 July 2000; accepted 19 April 2001
Abstract A three-dimensional (3D) motion tracking method as applied in graphonomic research is described. In addition to movements of the writing stylus, rotations of joints in the arm, hand, and index 7nger are recorded in a straightforward manner by making use of rigid bodies that de7ne the position and orientation of the segments of a writer’s arm and his or her pen. The method is developed in a visually-oriented, component-based programming environment which simpli7es further software development and facilitates the use of the method alongside existing research paradigms. A modest example of the method and possible applications in future handwriting recognition studies are discussed. ? 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved. Keywords: 3D motion tracking; Joint movements; Writer identi7cation; Handwriting
1. Introduction A simple way to record handwriting movements such that these movements can be easily processed by means of a computer is by making use of a digitizer (cf. [1]). The information that can be obtained from digitizers is generally restricted to the displacements of the pen tip in the two-dimensional graphic workplane. Some digitizers also provide data on the tilt of the writing stylus. More information about the way in which handwriting movements are being produced can be obtained by using a three-dimensional (3D) motion tracking system (see e.g. [2,3]). Such a system cannot only provide data of the movements of the pen but also of the movements of individual joints in the arm, hand, and 7nger of the writer. Time series representing joint rotations realized during ∗ Corresponding author. Tel.: +31-24-3612629; fax: +3124-3616066. E-mail addresses:
[email protected] (C.F. Bouwhuisen),
[email protected] (R.G.J. Meulenbroek),
[email protected] (A.J.W.M. Thomassen).
handwriting can provide the basis for the study of various issues. For example, idiosyncratic ways in which people may hold the pen and move their arm, hand, and 7ngers while performing handwriting tasks can be assessed. Furthermore, principles that govern interjoint coordination in handwriting can be investigated. Additionally, causal relations that may exist between the joint-coordination patterns which a writer adopts and the spatio-temporal features of the writing trajectories he=she produces could be explored. Finally, analyses of the rotations of joints in the arm, hand, and 7ngers of writers may also be useful to validate and=or enhance existing formal models of handwriting production (e.g. [4]) and recognition. Before a modest example of the latter application of 3D motion tracking in graphonomic research is discussed, we will 7rst describe the technical aspects of such a method as recently applied in our laboratory. In general, the use of 3D motion tracking systems in behavioral research is not without problems. It requires, for example, specialized knowledge of 3D geometric transformations. Furthermore, optical 3D motion tracking systems make use of markers which either reDect or
0031-3203/02/$22.00 ? 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 1 - 3 2 0 3 ( 0 1 ) 0 0 0 9 2 - 9
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emit (infrared) light and these markers have to be 7rmly attached to speci7c areas on the participant’s skin. Usually palpable bone structures near the joints of interest to the experimenter are chosen as suitable places on the subject’s body for attaching the markers, in part with the aim to reduce possible artifacts due to movements of the skin relative to the joints. Following the recording of the marker displacements in 3D workspace, complex data transformations are required such as the transformation of data from individual markers to data representing the rotations of the joints. To accommodate these implications of the use of optical 3D motion tracking systems, we recently simpli7ed the use of this powerful recording technique in two ways: (i) by using a rigid-body technique to record the relative motion of neighboring limb segments of the writer’s arm including the pen tip, and (ii) by using a visually-oriented, component-based programming environment which facilitates both the development of additional software needed to conduct experiments and the use of the method in combination with other data-acquisition methods. 2. Apparatus The Optotrak 3020 system is used in a variety of motor control studies in our laboratory. The system makes use of active markers, i.e. infrared light emitting diodes (IREDs) that need to be attached to the participant’s body. The positions of the markers are recorded by three cameras. Since markers are 7red consecutively, the maximal number of markers that can be used simultaneously depends on the desired sampling rate and the length of the marker period. The marker period is the time interval during which a marker is activated. In our laboratory a marker period of at least 0:4 ms is generally used in order to provide an adequate signal level. In this case up to 25 markers can be used in combination with a sampling rate of 100 Hz, a sampling rate commonly used in real-time handwriting studies. Using 25 markers has proven to be suHcient to capture the major part of the movements of the writer’s arm, hand, index 7nger, in conjunction with those of the writing stylus. When more markers are required, either a shorter marker period or a lower sampling rate, or both, must be used. The spatial accuracy of the system as used in our lab is in between 0:1 and 0:2 mm in the X; Y , and Z dimensions. The Optotrak system provides digitized marker positions (in mm) de7ned in a default coordinate system which is oriented to the camera unit. The experimenter has the option, however, to de7ne his or her own coordinate system in such a way that the obtained data become easier to interpret in the context of the movements under study. In graphonomic research it is likely that the experimenter will use the writing table surface for this purpose. He or she may thus de7ne a reference coordinate
system of which the X axis corresponds with the front edge of the writing table (closest to the subject), the Y axis corresponds to the left-hand side of the table, and the Z axis is perpendicular to the writing surface. If this reference coordinate system is used, horizontal pen-tip displacements occur along the X axis, vertical pen-tip displacements along the Y axis, and pen-up=pen-down movements along the Z axis. Alternatively, the reference coordinate system might also be de7ned relative to the orientation of the lineation on the writing sheet which a subject prefers to use. 3. Method 3.1. Rigid-body technique When employing a 3D motion tracking system involving active markers (such as the Optotrak system), several conditions have to be met with respect to how the experimenter attaches the markers on the participant’s body. The most important ones are (i) the markers have to remain in view of the infrared cameras throughout the recording interval and (ii) the subject’s ‘natural’ way of moving must not be limited in any way by the markers on his or her body. In addition, attaching the markers to the participant’s body must not be time-consuming and the markers should be attached in such a way that the movement-related information of interest to the experimenter is easy to extract. A convenient way to meet the above-mentioned requirements is making use of the rigid-body technique. A rigid body consists of three or more markers which are 7xed on a solid object in such a way that these markers cannot move relative to each other. After having made a rigid-body de4nition 4le according to the procedure described in the next section, the Optotrak system can be used to track the position of the rigid body (in X; Y , and Z coordinates) as well as its orientation (in pitch, yaw, and roll angles relative to the three orthogonal axes) in a prede7ned 3D workspace. Moreover, the position (in mm) and orientation (in radians or deg) of a rigid body can be recorded relative to the (instantaneous) position and orientation of another rigid body. When the latter facility is combined with the appropriate 7xation of rigid bodies on pairs of adjacent limb segments of a subject, one can record joint rotations in a straightforward manner. For example, by recording the position and orientation of a rigid body attached to the upper arm of a subject relative to a rigid body attached to the trunk, shoulder angles (Dexion–extension, abduction–adduction, endorotation– exorotation) can be obtained separately and independently from the, possibly continuously changing, position and orientation of the trunk. Theoretically, data from three markers are suHcient for the calculation of the position and orientation of the
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Fig. 1. Rigid bodies used to record 3D movements of trunk, upper arm, forearm, hand, proximal phalanx of index 7nger (phalanx1), and middle phalanx of index 7nger (phalanx2), and pen. Each rigid body consists of an aluminum plate on which three infrared light emitting diodes (IREDs) are attached.
rigid body. However, more than three markers can be used for the following purposes: (i) to improve signal quality by enabling the Optotrak system to use averaging of the data of redundant markers, and (ii) to enable the Optotrak system to calculate the position of the rigid body even when one or more markers are out of view of the cameras, as long as at least three markers remain visible. The rigid-body technique can also be used to record both pen-tip displacements and pen-tilt changes. For this purpose a rigid body is attached to the top of the barrel of the pen, and the rigid-body de7nition is transformed in such a way that the origin of the rigid body’s coordinate system corresponds to the tip of the pen. Compared with a modern tilt-sensitive digitizer, the recording of the pen-tip position and displacements by means of the Optotrak system has about the same accuracy. The recording of the pen tilt, however, is much more accurate. 3.2. Constructing and de4ning rigid bodies Special-purpose rigid bodies to record rotations of the shoulder, elbow, wrist, metacarpo-phalangeal joint, and interphalangeal joints of the index 7nger and, 7nally, of pen-tip displacements, are displayed in Fig. 1. For each rigid body, the IREDs are 7xed onto an aluminum plate which, in turn, is connected to a semi-Dexible cuJ (for
the upper arm and forearm), to a semi-Dexible ring (for the phalanges of the index 7nger), or to material that can be directly taped onto the subject’s skin (for the subject’s trunk and for the top side of the hand). The choice of the speci7c size of the aluminum plates onto which the IREDs are attached is a matter of compromise. In order to achieve optimal angular measurement accuracy, large-sized aluminum plates are preferable. Clearly, the size of the limb segments imposes limitations in this respect. In the present situation this is particularly the case for the rigid bodies that are designed to be used on the two phalanges of the index 7nger. The eJect of the size of the rigid body on signal quality will be discussed further in Section 3.4. In order to make use of a rigid body, a rigid-body definition 4le must be constructed that de7nes the positions of the markers on a rigid body relative to each other. For this purpose, a separate Optotrak recording of the rigid body is made. Subsequently, the required rigid-body definition 7le is calculated from the data of this recording by making use of available software (i.e. the Rigmaker program). Further details about the procedure involved in constructing rigid-body de7nition 7les can be found in the Optotrak’s documentation (Rigmaker guide). 1 1 Documentation about the Optotrak system can be obtained from the manufacturer: Northern Digital Inc., 403 Albert Street, Waterloo, Ont., Canada N2L 3V2.
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3.3. Rigid-body alignment procedure To allow the straightforward interpretation of the data obtained with the Optotrak system and the rigid-body technique described above, the rigid bodies have to be positioned on the subject’s body in such a way that the orientation of the local coordinate system of each rigid body corresponds to the mechanical degrees of freedom of the joints of interest to the experimenter. To avoid the need for 7xing the rigid bodies at precisely prede7ned positions and to maintain the freedom of placing the rigid bodies in such a manner that they remain visible for the cameras during the subject’s task performance without interfering with his or her movements, we applied the following procedure. First, the rigid bodies are attached to the most suitable places on the limb segments of interest. At this stage, the experimenter does not need to align the rigid bodies in any particular way within the coordinate system. Subsequently, a rigid-body alignment recording is made during which the subject is asked to adopt a posture such that the relevant limb segments are aligned as well as possible to the axes of the prede7ned coordinate system. For example, a subject may be asked to stand straight up in front of the writing table such that the line running through his or her shoulders runs in parallel with the front edge of the writing table. If this condition is met, upper arm elevation will correspond to a movement in a sagittal plane of the prede7ned reference coordinate system which in the example given above is de7ned relative to the writing table. A similar approach is used with respect to the other anatomical degrees of freedom of interest to the experimenter. Thus, prior to the rigid-body alignment recording, the experimenter needs to instruct the subject to adopt a series of postures such that movements of the limb segments of interest correspond to rotations around the axes of the reference coordinate system. During the rigid-body alignment recording (a few seconds is suHcient) the subject should move as little as possible. On the basis of this recording the rigid bodies’ coordinate frames are subsequently rotated computationally in such a way that they all become aligned to the reference coordinate system. Because of the speci7c posture which the subject is instructed to adopt, the rigid bodies also become aligned to the degrees of freedom of the joints of interest to the researcher. Due to the properties of the rigid-body concept, the software rotation has the same eJect as a physical rotation. With respect to the pen, a diJerent rigid-body alignment procedure must be used since in this case the experimenter is mainly interested in the translation of the pen tip. To record horizontal and vertical pen-tip displacements on the writing surface (and above this surface when the pen is lifted), the de7nition of the rigid body that is attached to the pen must be transformed in such a way that the origin of the rigid body’s coordinate
system corresponds to the tip of the pen. This transformation can easily be done by using available system software (the Optotrak’s Rigmaker program) and a so-called Pivot Data File. A Pivot Data File is an Optotrak recording made while rotating (pivoting) a rigid body around the desired origin (the pen tip in this case). If the local rigid body’s coordinate frame is transformed in this way, the movements of the pen tip correspond with the translation of the rigid body along the X; Y , and Z axes of the reference coordinate system (in the present example, the writing table). As stated above, pen-tilt information can be obtained from the instantaneous orientation of the rigid body on the pen. For more detailed information about the use of rigid bodies we refer to Optotrak’s Rigmaker guide. 3.4. Rigid body dimensions and signal quality In order to minimize interference with the subject’s movements it is advisable to keep the dimensions of the rigid bodies as small as possible. This is particularly the case for rigid bodies that are to be 7xed to small limb segments such as, for instance, the phalanges of the 7ngers. The signal quality of the angular movement recordings, however, decreases with the size of the rigid bodies, so one needs to 7nd a compromise between dimensions and signal quality. To evaluate the signal quality of rigid bodies of diJerent size we conducted the following test. A rigid body was 7xed to a pendulum and the movement of the rigid body was recorded by the Optotrak system. Since a pendulum’s movements are approximately sinusoidal, most errors in the recording will be shown as deviations from the sine wave. Small pendulum movements were used of which the amplitude was comparable to the amplitude of rotations of joints in the hand and index 7nger during handwriting. Two rigid bodies were used, each containing three markers, one small rigid body, suitable for small limb segments like the phalanges of the 7ngers, and one larger rigid body that could be used on the arm. The results for the larger rigid body are shown in Fig. 2A. The top left function in Fig. 2A shows six seconds of the recorded signal, the top right function represents the deviation of this signal from a pure sine wave of the same amplitude, frequency and phase. In addition to the angular position-time signal of the rigid body’s sinusoidal movements, the derived angular speed and angular acceleration signals are shown. The high-frequency noise in these signals was reduced by applying low-pass 7ltering (a dual-pass 2nd-order Butterworth 7lter with a cut-oJ frequency of 12 Hz) subsequent to the calculation of each derivative, a procedure that is commonly used in processing handwriting signals. The corresponding deviations from pure sines are shown in the righthand column. From the 7gure it can be concluded that these signals are of acceptable quality for many analysis purposes. However, the use of even larger rigid bodies
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Fig. 2. Examples of the signal quality of two diJerent sized rigid bodies, one with a mean marker distance of 52 mm (A) and one with a mean marker distance of 20 mm (B). The top left signal in each panel is the recorded signal. Below the angular position-time signal (pos) the derived angular speed (vel) and angular acceleration (acc) signals are shown. The right-hand column shows the deviations of these time functions from pure sine waves of the same amplitude, frequency and phase.
is advisable in cases where their size does not interfere with the subject’s movements. Fig. 2B shows the results for the smaller rigid body. Although, as expected, the noise level is considerably higher than for the larger rigid body, these signals can still be used for analysis. Nevertheless it is again apparent that larger rigid bodies must be used whenever possible.
Signal quality can be improved not only by increasing the size of the rigid bodies, but also by using more than three markers. However, since already eight rigid bodies are needed to record the movements of all but one of the adjacent limb segments in the kinematic chain in the arm of a writer, and because the number of markers that can be used is restricted (see above), this method is often not feasible in this context.
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3.5. Component-based visually oriented programming environment The Optotrak system provides basic software that can be used for motion-tracking purposes. In behavioural research involving drawing or handwriting tasks, however, one often needs additional software facilities to control stimulus presentation, reaction-time measurement, real-time feedback of task performance, and on-line processing (for example segmentation and identi7cation) algorithms. In these cases the standard recording software provided with the Optotrak system is insuHcient and more elaborate facilities have to be developed. Software that is dedicated to a speci7c experiment can also be easier to use since, if well designed, it does not require the experimenter to be concerned with details that are not relevant to his application. Developing special-purpose software can be simpli7ed by making use of component based, visually-oriented software developing environments such as Delphi or Visual C++. In these environments, components function as building blocks of a computer program. Components need to be developed in such a way that without showing any complex program code they form a logical unit from the viewpoint of the user. In fact, in this approach the complex code is encapsulated. By combining components according to a few pre-described rules, simple programs can be made. The visually oriented part of such environments refers to the fact that various components can be combined in a graphic manner by means of simple mouse actions. Because applications built in this way can be extended with additional code written in programming languages such as C++ or Pascal, visually oriented software-development environments do not pose any restrictions on the programmer as compared to the classical or non-visual oriented programming methods. Since components are objects in the sense of object-oriented programming they oJer all the advantages of this powerful programming method. In order to develop a software environment for the use of the Optotrak system according to the component-based visually oriented programming approach, one needs a set of components in which the various Optotrak functions are encapsulated. Because, to date, such components are not generally available, they were developed in our laboratory. The components were developed on the basis of the Application Programmer’s Interface which forms an integral part of the Optotrak software package. Delphi was used as the programming development environment. The most important components that have been developed are the following: (i) The Optotrak component. This component represents the Optotrak camera unit and related equipment; it is the central component with which an application can be built; (ii) The Collection component. This component describes various features of a recording or a trial such as the duration of the
recording interval, the number of markers used, and the sampling rate; (iii) The OptotrakData components. This is a set of components which contain the data collected during a recording. The group is divided into data 7les and real-time data. The former are stored on disk in 7les which are accessible when a recording is completed, the latter are accessible during a recording for data checks or real-time feedback to the participant. Rigid-body components also belong to this category; (iv) The FrameOfReference component. This component de7nes the coordinate system in which the data are collected. By making use of this component, the experimenter can de7ne in which dimensions of the workspace the data will be expressed. As described above, for a typical handwriting experiment, the X axis is usually de7ned in parallel with the front edge of the writing table, the Y axis in parallel with the left-hand side of the writing table, and the Z axis perpendicular to the writing surface. This component, however, allows the experimenter to calibrate the Optotrak system to any suitable coordinate system. The above-mentioned components contain all the functions necessary to develop a simple Optotrak application. Only a minimum of additional programming code is needed. Conventions adopted in earlier research with respect to, for example, the particular coordinate system in which pen-tip displacement time series are expressed, can be chosen Dexibly in this environment. 4. Results In our laboratory four experiments have been conducted using software that was developed according to the visually-oriented component based method as described above. In three of these experiments, the rigid-body technique was successfully used to record data streams that directly represented the participant’s joint rotations (see [5 –7]). The time needed to develop the applications ranged between 1 and 4 weeks. In earlier projects in which the classical programming techniques were used, the development of such programs usually took several months. Due to the object-oriented character of the programming environment, new applications can be developed very quickly by building upon earlier applications. The reason for this is that new programs can inherit functionality of programs developed earlier. The use of rigid bodies attached to the participants’ limb segments in order to record joint rotations has proven to be straightforward and to yield satisfactory results. To illustrate the possible use of 3D motion tracking in the domain of writer identi7cation we conducted a simple test using data collected in one of the experiments mentioned above [6]. In the experiment, 12 subjects were asked to write the sentence ‘The quick brown fox jumps over the lazy dog’. From the pen-tip displacement and joint-rotation data — where the joints of interest were
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Fig. 3. Instances of the character ‘o’ written by two diJerent subjects. A and D show the characters in the XY plane, B and E show the isolated 7rst down strokes (also in the XY plane), and C and F show the relation between corresponding 7nger and wrist movement. A, B and C relate to subject 1 while D, E and F relate to subject 2.
the shoulder, elbow, wrist, metacarpophalangeal joint of the index 7nger, and middle joint of the index 7nger— of two subjects, we isolated two occurrences of the letter ‘o’. The 7rst ‘o’ was isolated from the word ‘brown’, the second from the word ‘dog’. Fig. 3A shows these two letters of one subject, Fig. 3D those of the other subject. Of each of the isolated characters, the 7rst down stroke of the corpus of the letter ‘o’ was isolated. These down strokes are shown in Figs. 3B and E for the two subjects separately. The start of the strokes is indicated by the 7lled circles. A global comparison of the latter strokes shows that apart from their size there are no striking differences, neither between the two instances produced by the same subject, nor between the two subjects. However, when plotting the 7nger excursions that were realized when the isolated down strokes of the letter ‘o’ were produced against the wrist excursions (Figs. 3C and F), we can clearly distinguish between the two writers. Whereas one subject shows downward paths in the 7nger-wrist plane during both down strokes of the two instances of the letter ‘o’, the other subject shows a downward path
in the 7nger-wrist plane for the ‘o’ stemming from the word ‘brown’, and an upward path in this plane for the ‘o’ stemming from the word ‘dog’. Consequently, whereas both within- and between-subject spatial correspondence is demonstrated in the two-dimensional graphic workplane in which the pen tip moved (Figs. 3B and E), substantial within- and between-subject variabilities become apparent when analyzing the corresponding rotations of the wrist and index 7nger of the subjects. This added power of the 3D motion-tracking method deserves to be explored further in future writer-identi7cation and handwriting recognition studies. 5. Discussion This paper focused on the technical aspects of a 3D motion-tracking method as applied to graphonomic research. A possible application of the method in the 7eld of writer identi7cation was illustrated. Studying the kinematics of excursions of joints in the arm, hand, and
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index 7nger in conjunction with the kinematics of pen-tip displacements may have other applications in the 7eld of handwriting recognition. For example, the information provided by this methodology may be used to study any systematic relationships between joint-coordination patterns that people adopt while writing and speci7c spatiotemporal features of their writing trajectories. Such relationships may exist despite the fact that people are known to be highly Dexible in recruiting their eJector system while maintaining invariance in their motor output [8–12], even under continuously changing conditions such as the position on the baseline of writing at which letters are written [13]. Further research is needed to elaborate on this issue. Less exploratory applications of the research method described here concern the validation of existing handwriting recognition and=or writer-identi7cation methods. An illustrative example of the latter is provided by the recent research of Zhang and MacLeod [14,15]. These researchers describe a pen-hand model representing the geometrical properties of the hand of an individual writer as he=she handles a writing stylus. The model was developed in order to predict on the basis of recorded pen-tip displacement data, the pen-tilt changes which a writer realizes during task performance. Zhang and MacLeod compared predicted and observed pen-tilt variations by using a tilt- sensitive digitizer. According to the researchers, their model and experimental 7ndings can be used to improve methods aimed at establishing a writers’ identity. One restriction of the pen-hand model constructed by Zhang and MacLeod stems from the fact that their model is based on information about pen movements only. Moreover, their model relies on an assumption regarding a 7xed position on the writing surface around which the hand-pen system is assumed to pivot as a limited number of letters are produced. Obviously this assumption could be validated in research employing the 3D motion-tracking method as described here. Moreover, we believe that a more accurate model than the one proposed by Zhang and MacLeod could be built if information about the actual orientations of the individual joints in hand and 7nger of a writer were to be taken into consideration. To this end, the method presently described may prove to be invaluable. In general terms, 3D motion tracking in graphonomic research will be useful in any validation studies in which assumptions regarding the relationship between anatomical main axes in handwriting and features of handwriting traces are to be veri7ed ([16 –18]).
6. Conclusions With respect to the use of 3D recording methods in combination with rigid body techniques for tracking
individual joint rotations we can conclude that our system is easy to use and produces satisfactory accuracy. When compared with the information that can be obtained from a digitizer, the information about individual joints oJers new possibilities in the 7eld of writer identi7cation and handwriting recognition. With respect to the use of component based software development we can conclude that the time needed for developing new applications has been substantially reduced as compared to the time needed with classical programming techniques. Dedicated application programs can be quickly developed for speci7c projects such that applications result that are easy to use, especially for less experienced computer users. References [1] H.L. Teulings, F.J. Maarse, Digital recording and processing of handwriting movements, Hum. Movement Sci. 3 (1984) 193–217. [2] C.L. MacKenzie, R.G. Marteniuk, C. Dugas, D. Liske, Three-dimensional movement trajectories in Fitts’ task: implications for control, Q. J. Exp. Psychol.: Hum. Exp. Psychol. 39 (4A) (1987) 629–647. [3] B. McKeon, Increased accuracy from a three-dimensional movement-tracking system, Behav. Res. Methods Instrum. Comput. 18 (3) (1986) 304–306. [4] J.J. Schillings, A.J.W.M. Thomassen, R.G.J. Meulenbroek, Comfort constrains graphic workspace: test results of a 3D forearm model, Psychol. Res. 63 (1) (2000) 70–82. [5] R.G.J. Meulenbroek, A.J.W.M. Thomassen, H.P.M. Van Lieshout, S.P. Swinnen, The stability of pen-joint and interjoint coordination in loop writing, Acta Psychol. 100 (1998) 55–70. [6] R.G.J. Meulenbroek, C.F. Bouwhuisen, A.J.W.M. Thomassen, D.A. Rosenbaum, Variability of pen-tip displacements and joint excursions in spatially and temporally constrained drawing, in: G. Leedham, M. Leung, V. Sagar, X. Xuhong (Eds.), Proceedings of the ninth biennial conference of the international graphonomics society, Nijmegen: IGS, 1999, pp. 19 –24. [7] A.J.W.M. Thomassen, R.G.J. Meulenbroek, C.F. Bouwhuisen, Facilitation of writing by the non-diminant hand under bimanual conditions, in: G. Leedham, M. Leung, V. Sagar, X. Xuhong (Eds.), Proceedings of the ninth biennial conference of the international graphonomics society, Nijmegen: IGS, 1999, pp. 1–8. [8] P.A. Merton, How we control the contraction of our muscles, Sci. Am. 226 (1972) 30–37. [9] M.H. Raibert, Motor control and learning by the statespace model, Technical Report AI-M-351, MIT, 1977. [10] C.E. Wright, Generalized motor programs: reexamining claims of eJector independence in writing, in: M.J. Jeannerod (Eds.), Attention and performance XIII, Hillsdale, NJ: Lawrence Erlbaum, 1990, pp. 294 –320. [11] R.G.J. Meulenbroek, D.A. Rosenbaum, A.J.W.M. Thomassen, L.D. Loukopoulos, J. Vaughan, Adaptation of a reaching model to handwriting: how diJerent eJectors
C.F. Bouwhuisen et al. / Pattern Recognition 35 (2002) 1039–1047 can produce the same written output, and other results, Psychol. Res. 59 (1996) 64–74. [12] D. Rogers, B. Found, The objective measurement of spatial invariance in handwriting, in: M.L. Simner, C.G. Leedham, A.J.W.M. Thomassen (Eds.), Handwriting and drawing research: basic and applied issues, IOS Press, Amsterdam, 1996, pp. 15–27. [13] A.J.W.M. Thomassen, R.G.J. Meulenbroek, J.J. Schillings, Adaptive shifts in hand-7nger coordination during handwriting across the page, in: M.L. Simner, C.G. Leedham, A.J.W.M. Thomassen (Eds.), Handwriting and drawing research: basic and applied issues, IOS Press, Amsterdam, 1996, pp. 15–27. [14] X. Zhang, User speci7c aspects op pen-based input for identity veri7cation, PhD thesis, Australian National University, 1999, unpublished.
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[15] X. Zhang, I. Macleod, Writer-speci7c aspects of “oJ-axis” components of wrist and 7nger movements, in: M.L. Simner, C.G. Leedham, A.J.W.M. Thomassen (Eds.), Handwriting and drawing research: basic and applied issues, IOS Press, Amsterdam, 1996, pp. 443–457. [16] J.M. Hollerbach, An oscillation theory of handwriting, Biol. Cybernet. 39 (1981) 139–156. [17] D. Bullock, D. Grossberg, C. Mannes, A neural network model for cursive script production, Biol. Cybernet. 70 (1993) 15–28. [18] A.B.M. Lelivelt, R.G.J. Meulenbroek, A.J.W.M. Thomassen, Mapping abstract main axes in handwriting to hand and 7nger joints, in: M.L. Simner, C.G. Leedham, A.J.W.M. Thomassen (Eds.), Handwriting and drawing research: basic and applied issues, IOS Press, Amsterdam, 1996, pp. 29–40.
About the Author—CHRIS F. BOUWHUISEN was born on June 11th 1944. He studied Electronics and Computer Science at the University of Technology in Delft, The Netherlands. Since 1976 he has been working in the University of Nijmegen as Scienti7c Programmer and Adviser in the 7eld of Computer Applications in Experimental Psychology. His interests include Computer Applications in Experimental Psychology, human movement recording, and signal processing. About the Author—RUUD G.J. MEULENBROEK was born on July 27th, 1958. He completed his PhD at the University of Nijmegen in 1989. He was a Research Associate of Nijmegen Institute for Cognition and Information, University of Nijmegen from 1989 to 1993. He received the Research Associate of Nijmegen Institute for Cognition and Information, University of Nijmegen=Fellowship awarded by The Royal Netherlands Academy of Arts and Sciences, from 1993 to 1998. He has been Assistant-Associate Professor, University of Nijmegen since 1998. His interests include neural and cognitive substrates of perceptual-motor behavior. About the Author—ARNOLD J.W.M. THOMASSEN (1935) is Professor and Head of Department of Experimental Psychology at the University of Nijmegen, The Netherlands. His research interests over the past 25 years have primarily been in the motor control of handwriting. Apart from many articles, he edited several books and journal volumes on this issue. He founded the International Graphonomics Society and acted as its President between 1985 and 1995.
