Advertisement

Biological Cybernetics

, Volume 57, Issue 1–2, pp 25–36 | Cite as

A model of handwriting

  • Shimon Edelman
  • Tamar Flash
Article

Abstract

The research reported here is concerned with hand trajectory planning for the class of movements involved in handwriting. Previous studies show that the kinematics of human two-joint arm movements in the horizontal plane can be described by a model which is based on dynamic minimization of the square of the third derivative of hand position (jerk), integrated over the entire movement. We extend this approach to both the analysis and the synthesis of the trajectories occurring in the generation of handwritten characters. Several basic strokes are identified and possible stroke concatenation rules are suggested. Given a concise symbolic representation of a stroke shape, a simple algorithm computes the complete kinematic specification of the corresponding trajectory. A handwriting generation model based on a kinematics from shape principle and on dynamic optimization is formulated and tested. Good qualitative and quantitative agreement was found between subject recordings and trajectories generated by the model. The simple symbolic representation of hand motion suggested here may permit the central nervous system to learn, store and modify motor action plans for writing in an efficient manner.

Keywords

Hand Position Symbolic Representation Trajectory Planning Handwritten Character Hand Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abend W, Bizzi E, Morasso P (1982) Human arm trajectory formation. Brain 105:331–348PubMedGoogle Scholar
  2. Atkinson LV, Harley PJ (1983) An introduction to numerical methods with Pascal. Addison-Wesley, LondonGoogle Scholar
  3. Bendat JS, Piersol AG (1966) Measurement and analysis of random data. Wiley, New YorkGoogle Scholar
  4. Bernstein NA (1984) Coordination and localization problems. In: Whiting HTA (ed) Human motor actions (Bernstein revisited). Advances in psychology, vol 17. North-Holland, AmsterdamGoogle Scholar
  5. Boor C de, Lynch RE (1966) On splines and their minimum properties. J Math Mech 15:953–969Google Scholar
  6. Bryson AE, Ho YC (1975) Applied optimal control. HempshireGoogle Scholar
  7. Chen CT (1979) One-dimensional digital signal processing. Dekker, New YorkGoogle Scholar
  8. Flash T (1983) Organizing principles underlying the formation of arm trajectories. Harvard-MIT Div of Health Sciences and Technology, MIT PhD thesisGoogle Scholar
  9. Flash T, Hogan N (1985) The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 5(7):1688–1703PubMedGoogle Scholar
  10. Hogan N (1982) Control and coordination of voluntary arm movements. In: Rabins MJ, Bar-Shalom Y (eds) Proceedings of the 1982 American Control Conference, pp 522–528Google Scholar
  11. Hogan N (1984) An organizing principle for a class of voluntary movements. J Neurosci 4(11):2745–2754PubMedGoogle Scholar
  12. Hollerbach JM (1981) An oscillation theory of handwriting. Biol Cybern 39:139–156CrossRefGoogle Scholar
  13. Mermelstein P, Eden M (1964) Experiments on computer recognition of connected handwritten words. Information Control 7:255–270CrossRefGoogle Scholar
  14. Morasso P, Mussa Ivaldi FA (1982) Trajectory formation and handwriting: a computational model. Biol Cybern 45:131–142CrossRefPubMedGoogle Scholar
  15. Nelson WL (1983) Physical principles for economics of skilled movements. Biol Cybern 46:135–147CrossRefPubMedGoogle Scholar
  16. Torre V, Poggio T (1986) On edge detection. IEEE Trans Pattern Analysis Machine Intell PAMI-8(2):147–163Google Scholar
  17. Viviani P, Terzuolo C (1980) Space-time invariance in learned motor skills. In: Stelmach GE, Requin J (eds) Tutorials in motor behavior. North-Holland, Amsterdam, pp 525–533Google Scholar
  18. Viviani P, Terzuolo C (1982) Trajectory determines movement dynamics. Neuroscience 7(2):431–437CrossRefPubMedGoogle Scholar
  19. Wing AM (1980) Response timing in handwriting. In: Stelmach GE (ed) Information processing in motor control and learning. Academic Press, New York, pp 153–172Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Shimon Edelman
    • 1
  • Tamar Flash
    • 1
  1. 1.Department of Applied MathematicsThe Weizmann Institute of ScienceRehovotIsrael

Personalised recommendations