Curve Fitting Using Coevolutionary Genetic Algorithms

  • Nejat A. Afshar
  • Mohsen Soryani
  • Adel T. Rahmani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7077)


Curve fitting has many applications in lots of domains. The literature is full of fitting methods which are suitable for specific kinds of problems. In this paper we introduce a more general method to cover more range of problems. Our goal is to fit some cubic Bezier curves to data points of any distribution and order. The curves should be good representatives of the points and be connected and smooth. Theses constraints and the big search space make the fitting process difficult. We use the good capabilities of the coevolutionary algorithms in large problem spaces to fit the curves to the clusters of the data. The data are clustered using hierarchical techniques before the fitting process.


Curve fitting Bezier curves coevolutionary genetic algorithms hierarchical clustering 


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  1. 1.
    Renner, G., Ekart, A.: Genetic algorithms in computer aided design. Computer-Aided Design 35, 709–726 (2003)CrossRefGoogle Scholar
  2. 2.
    Yoshimoto, F., Harada, T., Yoshimoto, Y.: Data fitting with a spline using a real-coded genetic algorithm. Computer-Aided Design 35, 751–760 (2003)CrossRefGoogle Scholar
  3. 3.
    Manela, M., Thornhill, N., Campbell, J.: Fitting spline functions to noisy data using a genetic algorithm. In: Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 549–556. Morgan Kaufmann Publishers Inc. (1993)Google Scholar
  4. 4.
    Markus, A., Renner, G., Vancza, J.: Spline interpolation with genetic algorithms. In: Proceedings of the International Conference on Shape Modeling and Applications, pp. 47–54. IEEE (2002)Google Scholar
  5. 5.
    Yin, P.: Polygonal approximation using genetic algorithms. Pattern Recognition, 838–838 (1999)Google Scholar
  6. 6.
    Gulsen, M., Smith, A., Tate, D.: A genetic algorithm approach to curve fitting. International Journal of Production Research 33, 1911–1924 (1995)CrossRefzbMATHGoogle Scholar
  7. 7.
    Yang, H., Wang, W., Sun, J.: Control point adjustment for B-spline curve approximation. Computer-Aided Design 36, 639–652 (2004)CrossRefGoogle Scholar
  8. 8.
    Wang, H., Kearney, J., Atkinson, K.: Robust and efficient computation of the closest point on a spline curve, pp. 397–406 (2002)Google Scholar
  9. 9.
    Eiben, A., Smith, J.: Introduction to evolutionary computing. Springer, Heidelberg (2003)CrossRefzbMATHGoogle Scholar
  10. 10.
    Pei, S.C., Horng, J.H.: Fitting digital curve using circular arcs. Pattern Recognition 28, 107–116 (1995)CrossRefGoogle Scholar
  11. 11.
    Pei, S.C., Horng, J.H.: Optimum approximation of digital planar curves using circular arcs. Pattern Recognition 29, 383–388 (1996)CrossRefGoogle Scholar
  12. 12.
    Horng, J.H., Li, J.T.: A dynamic programming approach for fitting digital planar curves with line segments and circular arcs. Pattern Recognition Letters 22, 183–197 (2001)CrossRefzbMATHGoogle Scholar
  13. 13.
    Sarkar, B., Singh, L.K., Sarkar, D.: Approximation of digital curves with line segments and circular arcs using genetic algorithms. Pattern Recognition Letters 24, 2585–2595 (2003)CrossRefGoogle Scholar
  14. 14.
    Pal, S., Ganguly, P., Biswas, P.: Cubic Bézier approximation of a digitized curve. Pattern Recognition 40, 2730–2741 (2007)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Nejat A. Afshar
    • 1
  • Mohsen Soryani
    • 1
  • Adel T. Rahmani
    • 1
  1. 1.Department of Computer EngineeringIran University of Science & TechnologyTehranIran

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