Polygonal Approximation of Digital Curves Using a Multi-objective Genetic Algorithm

  • Herve Locteau
  • Romain Raveaux
  • Sebastien Adam
  • Yves Lecourtier
  • Pierre Heroux
  • Eric Trupin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3926)

Abstract

In this paper, a polygonal approximation approach based on a multi-objective genetic algorithm is proposed. In this method, the optimization/exploration algorithm locates breakpoints on the digital curve by minimizing simultaneously the number of breakpoints and the approximation error. Using such an approach, the algorithm proposes a set of solutions at its end. This set which is called the Pareto Front in the multi objective optimization field contains solutions that represent trade-offs between the two classical quality criteria of polygonal approximation : the Integral Square Error (ISE) and the number of vertices. The user may choose his own solution according to its objective. The proposed approach is evaluated on curves issued from the literature and compared with many classical approaches.

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References

  1. 1.
    Salotti, M.: An efficient algorithm for the optimal polygonal approximation of digitized curves. PRL 22, 215–221 (2001)CrossRefMATHGoogle Scholar
  2. 2.
    Ramer, U.: An iterative procedure for the polygonal approximation of plane curves. CGIP 1, 291–297 (1972)Google Scholar
  3. 3.
    Pavlidis, T., Horowitz, S.L.: Segmentation of plane curves. IEEE Transaction on Computers 23, 860–870 (1974)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Wall, K., Danielsson, P.E.: A fast sequential method for polygonal approximation of digitized curves. CVGIP 28, 220–227 (1984)Google Scholar
  5. 5.
    Gupta, A., Chaudhury, S., Parthasarathy, G.: A new approach for aggregating edge points into line segments. PR 26, 1069–1086 (1993)Google Scholar
  6. 6.
    Hu, J., Yan, H.: Polygonal approximation of digital curves based on the principles of perceptual organization. PR 30, 701–718 (2002)Google Scholar
  7. 7.
    Teh, C., Chin, R.T.: On the detection of dominant points on digital curves. IEEE transaction on PAMI 23, 859–872 (1989)CrossRefGoogle Scholar
  8. 8.
    Ansari, N., Delp, E.J.: On detecting dominant points. PR 24, 441–451 (1991)Google Scholar
  9. 9.
    Ray, B.K., Ray, K.S.: An algorithm for detecting dominant points and polygonal approximation of digitized curves. PRL 13, 849–856 (1992)CrossRefGoogle Scholar
  10. 10.
    Ray, B.K., Ray, K.S.: Detection of significant points and polygonal approximation of digitized curves. PRL 12, 443–452 (1992)CrossRefGoogle Scholar
  11. 11.
    Cornic, P.: Another look at the dominant point detection of digitized curves. PRL 18, 13–25 (1997)CrossRefMATHGoogle Scholar
  12. 12.
    Marji, M., Siy, P.: A new algorithm for dominant points detection and polygonization of digital curves. PR 36, 2239–2251 (2003)MATHGoogle Scholar
  13. 13.
    Chung, P.C., Tsai, C.T., Chen, E.L., Sun, Y.N.: Polygonal approximation using a competitive Hopfield neural network. PR 27, 1505–1512 (1994)Google Scholar
  14. 14.
    Perez, J.C., Vidal, E.: Optimum polygonal approximation of digitized curves. PRL 15, 743–750 (1994)CrossRefMATHGoogle Scholar
  15. 15.
    Horng, J.H., Li, J.T.: An automatic and efficient dynamic programming algorithm for polygonal approximation of digital curves. PRL 23, 171–182 (2002)CrossRefMATHGoogle Scholar
  16. 16.
    Yin, P.Y.: A new method for polygonal approximation of digital curves. PRL 19, 1017–1026 (1998)CrossRefMATHGoogle Scholar
  17. 17.
    Huang, S.C., Sun, Y.N.: Polygonal approximation using genetic algorithm. PR 32, 1409–1420 (1999)Google Scholar
  18. 18.
    Sarkar, B., Singh, L.K., Sarkar, D.: Approximation of digital curves with line segments and circular arcs using genetic algorithms. PRL 24, 2585–2595 (2003)CrossRefGoogle Scholar
  19. 19.
    Yin, P.Y.: A new circle/ellipse detector using genetic algorithm. PRL 20, 731–740 (1999)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Deb, K.: Multi-Objective optimization using Evolutionary algorithms. Wiley, London (2001)MATHGoogle Scholar
  21. 21.
    Schaffer, J.D., Grefenstette, J.J.: Multiobjective learning via genetic algorithms. In: Proceedings of the 9th IJCAI, pp. 593–595 (1985)Google Scholar
  22. 22.
    Fonseca, C.M., Fleming, P.J.: Genetic algorithm for multi-objective optimization: formulation, discussion and generalization. In: The proceedings of the fifth ICGA, pp. 416–423 (1993)Google Scholar
  23. 23.
    Srinivas, N., Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithm. EC 2, 221–248 (1994)Google Scholar
  24. 24.
    Deb, K., Agrawal, S., Pratab, A., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on EC 6, 182–197 (2000)Google Scholar
  25. 25.
    Knowles, J.D., Corne, D.W.: Approximating the nondominated front using the Pareto archived evolution strategy. EC 8, 149–172 (2000)Google Scholar
  26. 26.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative study and the strength pareto approach. IEEE Transactions on EC 3, 257–271 (1999)Google Scholar
  27. 27.
    Coello Coello, C.A.: A short tutorial on Evolutionary Multiobjective Optimisation. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 21–40. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  28. 28.
    Chafekar, D., Xuan, J., Rasheed, K.: Constrained Multi-objective Optimization Using Steady State Genetic Algorithms. In: Proceedings of GECC, pp. 813–824 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Herve Locteau
    • 1
  • Romain Raveaux
    • 1
  • Sebastien Adam
    • 1
  • Yves Lecourtier
    • 1
  • Pierre Heroux
    • 1
  • Eric Trupin
    • 1
  1. 1.LITISUniversité de RouenSaint-Etienne du RouvrayFrance

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