An Evolutionary Approach to Fitting Constrained Degenerate Second Order Surfaces

  • C. Robertson
  • R. B. Fisher
  • N. Werghi
  • A. P. Ashbrook
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1596)

Abstract

In this work we examine the applicability of an evolutionary strategy to the problem of fitting constrained second-order surfaces to both synthetic and acquired 3D data. In particular we concentrate on the Genocop III algorithm proposed by Michalewicz [8] for the optimization of constrained functions. This is a novel application of this algorithm which has demonstrably good results when applied using parametric models. Example times for convergence are given which compare the approach to standard techniques.

Keywords

Evolutionary algorithms surface fitting Genocop III 

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References

  1. 1.
    Eggert, D., Fitzgibbon, A.W., Fisher, R.B.: Simultaneous registration of multiple range views for use in reverse engineering. In: Proc. Int. Conf. on Pat. Recog., Vienna, August 1996, pp. 243–247 (1996)Google Scholar
  2. 2.
    Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface Reconstruction from Unorganized Points. Computer Graphics 26(2), 71–78 (1992)CrossRefGoogle Scholar
  3. 3.
    Taubin, G.: Estimating the tensor of curvature of a surface from a polyhedral approximation. In: Proc. 5th Int. Conf. on Computer Vision, pp. 902–907 (1995)Google Scholar
  4. 4.
    Taubin, G.: Estimation of planar curves, surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation. In: Proc. IEEE PAMI, vol. 13(11), pp. 1115–1138 (1991)Google Scholar
  5. 5.
    Werghi, N., Fisher, R.B., Ashbrook, A., Robertson, C.: Improving model shape acquisition by incorporating geometric constraints. In: Proc. British Machine Vision Conference BMVC 1997, Essex, September 1997, pp. 520–529 (1997)Google Scholar
  6. 6.
    Michalewicz, Z., Dasgupta, D., Le Riche, R.G., Schoenauer, M.: Evolutionary algorithms for constrained engineering problems, special issue on Genetic Algorithms and Industrial Engineering. Gen, M., Wasserman, G.S., Smith, A.E. (eds.) International Journal of Computers and Industrial Engineering (1996)Google Scholar
  7. 7.
    Robertson, C., Corne, D., Fisher, R.B., Werghi, N., Ashbrook., A.: Investigating Evolutionary Optimisation of Constrained Functions to Capture Shape Descriptions from Range Data. In: Proc. 3rd On-line World Conference on Soft Computing (WSC3) see also In: Roy, R., Furuhashi, T., Chawdhry, P.K. (eds.) Advances in Soft Computing Engineering Design and Manufacturing. Springer, Heidelberg (1998), http://www.cranfield.ac.uk/wsc3/
  8. 8.
    Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, 3rd edn. Springer, Heidelberg (1996)MATHGoogle Scholar
  9. 9.
    Hoover, A., Jean-Baptiste, G., Jiang, X., Flynn, P.J., Bunke, H., Goldgof, D., Bowyer, K., Eggert, D., Fitzgibbon, A., Fisher, R.: An Experimental Comparison of Range Segmentation Algorithms. IEEE Trans. Pat. Anal. and Mach. Intel. 18(7), 673–689 (1996)CrossRefGoogle Scholar
  10. 10.
    Gen, M., Cheng, R.: A Survey of Penalty techniques in Genetic Algorithms. In: Proceedings of the IEEE International Conference on Evolutionary Computation 1996 (1996)Google Scholar
  11. 11.
    Michalewicz, Z., Attia, N.: Evolutionary Optimization of Constrained Problems. In: Proceedings of the 3rd Annual Conference on Evolutionary Programming, San Diego, CA, pp. 98–108. World Scientific, Singapore (1994)Google Scholar
  12. 12.
    Attia, N.F.: New Methods of Constrained Optimization Using Penalty Functions, Ph.D Thesis, Essex University, United Kingdom (1985)Google Scholar
  13. 13.
    Fisher, R.B., Fitzgibbon, A.W., Eggert, D.: Extracting Surface Patches from Complete Range Descriptions. In: Proc. Int. Conf. on Recent Advances in 3-D Digital Imaging and Modeling, Ottawa, Canada, May 1997, pp. 148–155 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • C. Robertson
    • 1
  • R. B. Fisher
    • 1
  • N. Werghi
    • 1
  • A. P. Ashbrook
    • 1
  1. 1.Division of InformaticsUniversity of EdinburghEdinburghUK

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