Signal, Image and Video Processing

, Volume 6, Issue 3, pp 437–443 | Cite as

A fractional calculus approach for the evaluation of the golf lip-out

  • Micael S. CouceiroEmail author
  • Gonçalo Dias
  • Fernando M. L. Martins
  • J. Miguel A. Luz
Original Paper


Golf is a sport in which competing players need to introduce the ball into the hole using the fewest number of strikes. However, this goal can sometimes be compromised when the ball suffers from lip-out phenomenon, that is, when the ball surrounds the hole’s edge without dropping in. Although some techniques may be presented in the literature to assess golfers’ performance (e.g., evaluation of the ball’s final position to the hole), none takes in consideration the putting lip-out. With this in mind, this article proposes a correction metric based on fractional calculus that considers past events in ball’s trajectory, thus slightly increasing player’s performance when putting lip-out occurs. On the opposite of integer derivatives which are considered as “local” operators, fractional derivatives implicitly have “memory” of all past events being well suited to describe the dynamic phenomena of ball’s trajectory. Therefore, this novel correction metric will provide a new virtual position of the ball based on its trajectory induced by the putting lip-out. This metric was evaluated analyzing the performance of 10 expert subjects who performed a total of 30 trials, with the lip-out occurring in 29 out of the 300 considered. Experimental results show an average improvement of 19.6 % in trials where the lip-out occurred and an average overall improvement of 1.82 % in player‘s performances, when applying the correction metric.


Golf putting Lip-out Correction metric Fractional calculus 


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  1. 1.
    Mackenzie S.J., Evans D.B.: Validity and reliability of a new method for measuring putting stroke kinematics using the TOMI1 system. J. Sports Sci. 8, 1–9 (2010)Google Scholar
  2. 2.
    Lee T.D., Ishikura T., Kegel S., Gonzalez D., Passmore S.: Head–Putter coordination patterns in expert and less skilled Golfers. J. Mot. Behav. 40(4), 267–272 (2008)CrossRefGoogle Scholar
  3. 3.
    Cañal-Bruland R., Pijpers J.R., Oudejans R.R.D.: The influence of anxiety on action-specific perception. Anxiety Stress Coping 23(3), 353–366 (2010)CrossRefGoogle Scholar
  4. 4.
    Mendes R., Dias G., Chiviacowsky S.: Golfe e Aprendizagem Motora: O Efeito da Interferência Contextual na Aprendizagem do Putt. Braz. J. Mot. Behav. 5(Supplement), 21–22 (2010)Google Scholar
  5. 5.
    Vicente, M.A.F., Martins, F., Mendes, R., Dias, G., Fonseca, J.: A method for segmented-trend estimate and geometric error analysis in motor learning. In: Proceedings of the International Conference on Mathematical Methods in Engineering (MME’10), pp. 433–442, ISEC/IPC, Coimbra, Portugal (2010)Google Scholar
  6. 6.
    Cohn, P.: CBS SportsLine—Putting Augusta’s greens takes extra focus. CBS Sports.,1329,881554_64,00.html (Last visited in Feb 2012), 1999
  7. 7.
    Holmes B.W.: Putting: how a golf ball and hole interact. Am. J. Phys. 59(2), 129–136 (1991)CrossRefGoogle Scholar
  8. 8.
    Hardy G.H., Littlewood J.E.: Lipping out and laying up: G.H. Hardy and J. E. Littlewood’s curious encounters with the mathematics of Golf. Math Horizons 17, 4 (2010)Google Scholar
  9. 9.
    Pelz D.: Putting Bible: The Complete Guide to Mastering the Green. Publication Doubleday, New York (2000)Google Scholar
  10. 10.
    Ortigueira M.D., Tenreiro Machado J.A.: Special issue on fractional signal processing. Signal Process 83, 2285–2480 (2003)CrossRefGoogle Scholar
  11. 11.
    Sabatier J., Agrawal O.P., Tenreiro Machado J.A.: Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007)zbMATHGoogle Scholar
  12. 12.
    Tenreiro Machado, J.A., Silva, M.F., Barbosa, R.S., Jesus, I.S., Reis, C.M., Marcos, M.G., Galhano, A.F.: Some Applications of Fractional Calculus in Engineering. Hindawi Publishing Corporation Mathematical Problems in Engineering, pp. 1–34 (2010)Google Scholar
  13. 13.
    Podlubny I.: Fractional Differential Equations. Mathematics in Science and Engineering, vol. 198. Academic Press, San Diego (1999)Google Scholar
  14. 14.
    Debnath L.: Recent applications of fractional calculus to science and engineering. Int. J. Math. Math. Sci. 54, 3413–3442 (2003)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Elshehawey E.F., Elbarbary E.M.E., Afifi N.A.S., El-Shahed M.: On the solution of the endolymph equation using fractional calculus. Appl. Math. Comput. 124, 337–341 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Camargo R.F., Chiacchio A.O., de Oliveira E.C.: Differentiation to fractional orders and the fractional telegraph equation. J. Math. Phys. 49(3), 033505–033505-12 (2008)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • Micael S. Couceiro
    • 1
    • 2
    Email author
  • Gonçalo Dias
    • 3
  • Fernando M. L. Martins
    • 4
    • 5
  • J. Miguel A. Luz
    • 4
  1. 1.RoboCorp, Department of Electrotechnical Engineering (DEE)Engineering Institute of Coimbra (ISEC)CoimbraPortugal
  2. 2.Institute of Systems and Robotics, Mobile Robotics LaboratoryUniversity of CoimbraCoimbraPortugal
  3. 3.RoboCorp, Faculty of Sport Sciences and Physical Education (FCDEF)University of Coimbra (UC)CoimbraPortugal
  4. 4.RoboCorp, Coimbra College of Education (ESEC)Politechnic Institute of CoimbraCoimbraPortugal
  5. 5.Instituto de Telecomunicações (Covilhã), DEECPolo II, Pinhal de Marrocos, Universidade de Coimbra (UC)CoimbraPortugal

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