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Modelling velocity profiles of rapid movements: a comparative study

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Abstract

In this paper we compare 23 different models that can be used to describe the asymmetric bell-shaped velocity profiles of rapid-aimed movements. The comparison is performed with the help of an analysis-bysynthesis experiment over a database of 1052 straight lines produced by nine human subjects. For each line and for each model, a set of parameters is extracted that minimizes the error between the original and the reconstructed data. Performance analysis on the basis of the mean-square-error clearly reflects the superiority of the support-bounded lognormal model to globally describe the velocity profile characterizing rapid movements.

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References

  • Abend W, Bizzi E, Morasso P (1982) Human arm trajectory formation. Brain 105:331–348

    Google Scholar 

  • Arbenz K, Wohlhauser A (1980) Analyse numérique, tome 1. Presses Polytechniques, Lausanne Romande

    Google Scholar 

  • Aitchinson J, Brown JAC (1966) The lognormal distribution. Cambridge University Press, London

    Google Scholar 

  • Atkenson CG, Hollerbach JM (1985) Kinematic features of unrestrained vertical arm movements. J Neurosci 5:2318–2330

    Google Scholar 

  • Badaud J, Witkin AP, Baudin M, Duda RP (1986) Uniqueness of the gaussian kernel for scale-space filtering, IEEE Trans Pattern Anal Machine Intell 8:26–33

    Google Scholar 

  • Beggs WDA, Howarth CI (1972) The movement of the hand towards a target. Q J Exp Psychol 24:448–453

    Google Scholar 

  • Bernstein N (1967) The coordination and regulation of movements. Pergamon Press, London

    Google Scholar 

  • Bullock D, Grossberg S (1988) Neural dynamics of planned arm movements: emergent variants and speed-accuracy properties during trajectory formation. In: Grossberg S (eds) Neural networks and pattern recognition. MIT Press, Cambridge, MA, pp 553–622

    Google Scholar 

  • Burr DJ (1982) A normalizing transform for cursive script recognition. Proceedings of the 6th International Conference on Pattern Recognition, Munich, pp 1027–1030

  • Campbell AB (1973) A new sampling theorem for causal (non-band limited) functions. PhD dissertation, University of New Mexico, Albuquerque

    Google Scholar 

  • Denier van der Gon JJ, Thuring JP, Strackee J (1962) A handwriting simulator. Physics Med Biol 6:407–414

    Google Scholar 

  • Dooijes EH (1983) Analysis of handwriting movements. Acta Psychol 54:99–114

    Google Scholar 

  • Edelman S, Flash T (1987) A model of handwriting. Biol Cybern 57:25–36

    Google Scholar 

  • Eden M (1962) Handwriting and pattern recognition. IRE Trans Inform Theory 8:160–166

    Google Scholar 

  • Flash T (1983) Organizing principles underlying the formation of arm trajectories. PhD dissertation, Massachusetts Institute of Technology, Cambridge, MA

    Google Scholar 

  • Flash T, Hogan N (1985) The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 5:1688–1703

    Google Scholar 

  • Georgopoulos AP, Kalaska JF, Massey JT (1981) Spatial trajectories and reaction time of aimed movements: effects of practice, uncertainty, and change in target location. J Neurophysiol 64:725–743

    Google Scholar 

  • Gibson AR, Houk JC, Kohlerman NJ (1985) Relation between red nucleus discharge and movement parameters in trained macaque monkeys. J Physiol (Lond) 358:551–570

    Google Scholar 

  • Gutman SR, Gottlieb GL (1991) Exponential model with nonlinear time of reaching movement: trajectory time profile, strategies, variability. Third IBRO World Congress of Neuroscience, Montréal, Canada, August, paper P39.23, p 262

  • Hogan N (1984) An organizing principle for a class of voluntary movements. J Neurosci 4:2745–2754

    Google Scholar 

  • Hollerbach JM (1981) An oscillation theory of handwriting. Biol Cybern 39:139–156

    Google Scholar 

  • Houk JC, Gibson AR (1987) Sensimotor processing through the cerebellum. In: King JJ (ed) New concepts in cerebellar neurobiology. Liss, New York, pp 387–416

    Google Scholar 

  • Houk JC (1989) Burst of discharge recorded from the red nucleus may provide measures of Gottlieb's excitation pulses. Behav Brain Sci 12:224–225

    Google Scholar 

  • Katz D (1951) Gestalt psychology. Methuen, London

    Google Scholar 

  • Lashley KS (1951) The problem of serial order in behaviour. In: Jeffress LA (ed) Cerebral mechanisms in behaviour. Wiley, New York, pp 112–146

    Google Scholar 

  • Leclerc F (1989) Validation d'un modèle générateur de vitesse à profil gaussien sur des signatures manuscrites. MScA dissertation, école polytechnique, Montréal

    Google Scholar 

  • Leclerc F, Plamondon R (1990) Validation d'un modèle de la fonction de transfert du bras sur des signatures manuscrites. Proceedings Vision Interface '90, pp 105–111

  • Maarse F (1987) The study of handwriting movement. PhD dissertation, University of Nijmegen, The Netherlands

    Google Scholar 

  • MacDonald JS (1964) Experimental studies of handwriting signals. PhD dissertation, Massachusetts Institute of Technology, Cambridge, MA

    Google Scholar 

  • Mermelstein P, Eden M (1964) Experiments on computer recognition of connected handwritten words. Inform Contr 7:225–270

    Google Scholar 

  • Morasso P (1981) Spatial control of arm movements. Exp Brain Res 42:223–227

    Google Scholar 

  • Morasso P, Mussa-Ivaldi FA (1982) Trajectory formation and handwriting: a computational model. Biol Cybern 45:131–142

    Google Scholar 

  • Nagasaki H (1989) Asymmetric velocity and acceleration profiles of human arm movements. Exp Brain Res 74:319–326

    Google Scholar 

  • Nelson WL (1983) Physical principles for economies of skilled movements. Biol Cybern 46:135–147

    Google Scholar 

  • Plamondon R (1987) What does differential geometry tell us about handwriting generation? Proceedings of the 3rd international symposium on handwriting and computer applications, Montréal, pp 11–13

  • Plamondon R (1989a) A handwriting model based on differential geometry. In: Plamondon R, Suen CY, Simner ML (eds) Computer recognition and human production of handwriting. World Scientific, Singapore, pp 179–192

    Google Scholar 

  • Plamondon R (1989b) Handwriting control: a functional model. In: Cotterill MJR (eds) Models of brain function. Cambridge University Press, Cambridge, UK, pp 563–574

    Google Scholar 

  • Plamondon R (1991) On the origin of asymmetric bell-shaped velocity profiles in rapid-aimed movements. In: Stelmach GE, Requin J (eds) Tutorials in motor neuroscience. Kluwer, Dordrecht, pp 283–295

    Google Scholar 

  • Plamondon R (1992a) A model-based segmentation framework for computer processing of handwriting. Proceedings of the 11th Conference on Pattern Recognition, The Hague, pp 303–312

  • Plamondon R (1992b) A theory of rapid movements. In: Stelmach GE, Requin J (eds) Tutorials in motor behavior II. Elsevier, Amsterdam, pp 55–69

    Google Scholar 

  • Plamondon R (1993) Looking through handwriting generation from a velocity control perspective. Acta Psychol 82:89–101

    Google Scholar 

  • Plamondon R, Clément B (1991) Dependence of peripheral and central parameters describing handwriting generation on movement direction. Hum Mov Sci 10:193–221

    Google Scholar 

  • Plamondon R, Lamarche F (1986) Modelization of handwriting: a system approach. In: Kao HSR, van Galen GP, Hoosain R (eds) Graphonomics: contemporary research in handwriting. Elsevier, Amsterdam, pp 169–183

    Google Scholar 

  • Plamondon R, Maarse FJ (1989) An evaluation of motor models of handwriting. IEEE Trans Systems Man Cybern 19:1060–1072

    Google Scholar 

  • Plamondon R, Parizeau M (1988) tSignature verification from position velocity and acceleration signals: a comparative study. Proceedings of the 8th international conference on pattern recognition, Rome, pp 260–265

  • Plamondon R, Yergeau P (1990) A system for the analysis and synthesis of handwriting. Proceedings international workshop on frontier in handwriting recognition, Montréal, pp 105–111

  • Plamondon R, Stelmach GE, Teasdale N (1990) Motor program coding representation from a handwriting generator: the production of line responses. Biol Cybern 63:443–451

    Google Scholar 

  • Plamondon R, Li-de Yu, Stelmach GE, Clément B (1991) On the automatic extraction of biomechanical information from handwriting signals. IEEE Trans Systems Man Cybern 21:90–101

    Google Scholar 

  • Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1989) Numerical recipes in C. Cambridge University Press, Cambridge, UK

    Google Scholar 

  • Schomaker RB, Teulings HL (1990) A handwriting recognition system based on the properties and architectures of the human motor system. Proceedings international workshop on frontier in handwriting recognition, Montréal, pp 195–209

  • Soechting JF, Lacquaniti F (1981) Invariant characteristics of a pointing movement in man. J Neurosci 1:710–720

    Google Scholar 

  • Van Galen GP (1980) Handwriting and drawing: a two stage model of motor behaviour. In: Stelmach GE, Requin J (eds) Tutorials in motor behaviour. North-holland, Amsterdam, pp 567–578

    Google Scholar 

  • Vredenbregt J, Koster WG (1971) Analysis and synthesis of handwriting. Philips Tech Rev 32:73–78

    Google Scholar 

  • Wells W (1986) Efficient synthesis of gaussian filters by cascaded uniform filters. IEEE Trans Pattern Anal Machine Intell 8:234–239

    Google Scholar 

  • Yasuhara M (1975) Experimental studies on handwriting process. Rep Univ Electro Comm 25:233–254

    Google Scholar 

  • Zelaznik HN, Schmidt RA, Gielen SCAM (1986) Kinematic properties of rapid-aimed head movements. J Motor Behav 18:353–372

    Google Scholar 

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Plamondon, R., Alimi, A.M., Yergeau, P. et al. Modelling velocity profiles of rapid movements: a comparative study. Biol. Cybern. 69, 119–128 (1993). https://doi.org/10.1007/BF00226195

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  • DOI: https://doi.org/10.1007/BF00226195

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