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Numerical control of kohonen neural network for scattered data approximation

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Abstract

Surface reconstruction from scattered data using Kohonen neural network is presented in this paper. The network produces a topologically predefined grid from the unordered data which can be applied as a rough approximation of the input set or as a base surface for further process. The quality and computing time of the approximation can be controlled by numerical parameters. As a further application, ruled surface is produced from a set of unordered lines by the network.

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References

  1. J. Barhak and A. Fischer, Parameterization and reconstruction from 3D scattered points based on neural network and PDE techniques, IEEE Trans. Visual. Comput. Graphics 7 (2001) 1–16.

    Google Scholar 

  2. J. Barhak and A. Fischer, Adaptive reconstruction of freeform objects with 3D SOM neural network grids, Computers Graphics 26 (2002) 745–751.

    Google Scholar 

  3. G. Echevarría, A. Iglesias and A. Gálvez, Extending neural networks for B-spline surface reconstruction, in: Lecture Notes in Computer Science, Vol. 2330 (Springer, New York, 2002) pp. 305–331.

    Google Scholar 

  4. J. Freeman and D. Skapura, Neural Networks: Algorithms, Applications and Programming Techniques (Addison-Wesley, Reading, MA, 1991).

    Google Scholar 

  5. B. Fritzke, Growing cell structures – a self-organizing network for unsupervised and supervised learning, Neural Networks 7 (1994) 1441–1460.

    Google Scholar 

  6. V. Hlavaty, Differential Line Geometry (Nordhoff, Leiden, 1953).

    Google Scholar 

  7. M. Hoffmann, Modified Kohonen neural network for surface reconstruction, Publ. Math. 54 (1999) 857–864.

    Google Scholar 

  8. M. Hoffmann and L. Várady, Free-form surfaces for scattered data by neural networks, J. Geometry Graphics 2 (1998) 1–6.

    Google Scholar 

  9. I.P. Ivrissimtzis, W.-K. Jeong and H.-P. Seidel, Using growing cell structures for surface reconstruction, in: Proc. of the Shape Modeling International ‘03 (2003) pp. 78–86.

  10. I.P. Ivrissimtzis, W.-K. Jeong and H.-P. Seidel, Neural meshes: Statistical learning methods in surface reconstrution, Technical Report of Max-Planck Institut für Math., MPI-I-2003-4-007 (2003).

  11. W.-K. Jeong, I.P. Ivrissimtzis and H.-P. Seidel, Neural meshes: Statistical learning based on normals, in: Proc. of Pacific Graphics ‘03 (IEEE Computer Soc. Press, Los Alamitos, CA, 2003) to appear.

    Google Scholar 

  12. G.K. Knopf and A. Sangole, Interpolating scattered data using 2D self-organizing feature maps, Graphical Models 66 (2004) 50–69.

    Google Scholar 

  13. T. Kohonen, Self-organization and Associative Memory, 3rd ed. (Springer, Berlin, 1996).

    Google Scholar 

  14. F.L. Krause, A. Fischer, N. Gross and J. Barhak, Reconstruction of freeform objects with arbitrary topology using neural networks and subdivision techniques, CIRP Annals – Manufacturing Technology 52 (2003) 125–128.

    Google Scholar 

  15. W. Ma and P. He, B-spline surface local updating with unorganized points, Computer-Aided Design 30 (1998) 853–862.

    Google Scholar 

  16. L. Piegl and W. Tiller, Parametrization for surface fitting in reverse engineering, Computer-Aided Design 33 (2001) 593–603.

    Google Scholar 

  17. R. Rojas, Neural Networks. A Systematic Introduction (Springer, Berlin, 1996).

    Google Scholar 

  18. L. Várady, M. Hoffmann and E. Kovács, Improved free-form modelling of scattered data by dynamic neural networks, J. Geometry Graphics 3 (1999) 177–183.

    Google Scholar 

  19. T. Várady, R.R. Martin and J. Cox, Reverse engineering of geometric models – an introduction, Computer-Aided Design 29 (1997) 255–268.

    Google Scholar 

  20. V. Weiss, L. Andor, G. Renner and T. Várady, Advanced surface fitting techniques, Computer Aided Geom. Design 19 (2002) 19–42.

    Google Scholar 

  21. Y. Yu, Surface reconstruction from unorganized points using self-organizing neural networks, in: Proc. of IEEE Visualization 99 (1999) pp. 61–64.

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Correspondence to Miklós Hoffmann.

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68U07, 65D17, 68T20

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Hoffmann, M. Numerical control of kohonen neural network for scattered data approximation. Numer Algor 39, 175–186 (2005). https://doi.org/10.1007/s11075-004-3628-7

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  • DOI: https://doi.org/10.1007/s11075-004-3628-7

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