Advertisement

Piecewise Linear Approximation of n-Dimensional Parametric Curves Using Particle Swarms

  • Christopher Wesley Cleghorn
  • Andries P. Engelbrecht
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7461)

Abstract

This paper derives a new algorithm for piecewise linear approximation of n-dimensional parametric curves, specifically to be used with particle swarm optimization. The aim of the algorithm is to find the optimal piecewise linear approximation for a predefined number of segments. The performance of this algorithm is evaluated on a set of functions of varying dimensionality.

Keywords

Particle Swarm Optimization Explicit Function Piecewise Linear Approximation Polygonal Approximation Little Square Error 
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. 1.
    Burden, R.L. and Faires, J.D.: Numerical Analysis. Brooks Cole (2007)Google Scholar
  2. 2.
    Kennedy, J., Eberhart, R.C.: Particle Swarm Optimization. In: Proceedings of the IEEE International Joint Conference on Neural Networks, pp. 1942–1948 (1995)Google Scholar
  3. 3.
    Kennedy, J., Mendes, R.: Population Structure and Particle Performance. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1671–1676 (2002)Google Scholar
  4. 4.
    Peer, E.S., van den Bergh, F., Engelbrecht, A.P.: Using Neighborhoods with the Guaranteed Convergence PSO. In: Proceedings of the IEEE Swarm Intelligence Symposium, pp. 235–242 (2003)Google Scholar
  5. 5.
    Sklansky, J., Gonzalez, V.: Fast polygonal approximation of digitized curves. Pattern Recognition 12(5), 327–331 (1980)CrossRefGoogle Scholar
  6. 6.
    Salotti, M.: An efficient algorithm for the optimal polygonal approximation of digitized curves. Pattern Recognition Letters 22(2), 215–221 (2001)zbMATHCrossRefGoogle Scholar
  7. 7.
    do Carmo, M.: Differential Geometry of Curves and Surfaces. Prentice-Hall (1976)Google Scholar
  8. 8.
    Velho, L., de Figueiredo, L.H., Gomes, J.: Journal of the Brazilian Computer Society 3(3), 1–14 (1997)CrossRefGoogle Scholar
  9. 9.
    Imamoto, A., Tang, B.: A Recursive Descent Algorithm for Finding the Optimal Minimax Piecewise Linear Approximation of Convex Functions. In: Advances in Electrical and Electronics Engineering, pp. 287–289 (2008)Google Scholar
  10. 10.
    Manis, G., Papakonstantinou, G., Tsanakas, P.: Optimal Piecewise Linear Approximation of Digitized Curves. In: Proceedings of International Conference on Digital Signal Processing, pp. 1079–1081 (1997)Google Scholar
  11. 11.
    Horst, J.A., Beichl, I.: A Simple Algorithm for Eficient Piecewise Linear Approximation of Space Curves. In: Proceedings of International Conference on Image Processing, pp. 744–747 (1997)Google Scholar
  12. 12.
    Pavlidis, T.: Polygonal Approximations by Newton’s Method. IEEE Transactions on Computers 25(8), 800–807 (1977)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Dunham, J.G.: Optimum uniform piecewise linear approximation of planar curves. IEEE Transactionson Pattern Analysis and Machine Intelligence PAMI-8(1), 67–75 (1986)CrossRefGoogle Scholar
  14. 14.
    Stone, H.: Approximation of Curves by Line Segments. Mathematics of Computation 15(73), 40–47 (1961)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Engelbrecht, A.P.: Particle Swarm Optimization: Velocity Initialization. Accepted for IEEE Congress on Eevolutionary Computation (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christopher Wesley Cleghorn
    • 1
  • Andries P. Engelbrecht
    • 1
  1. 1.Department of Computer ScienceUniversity of PretoriaSouth Africa

Personalised recommendations