Skip to main content
Log in

Surface reconstruction based on extreme learning machine

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this paper, extreme learning machine (ELM) is used to reconstruct a surface with a high speed. It is shown that an improved ELM, called polyharmonic extreme learning machine (P-ELM), is proposed to reconstruct a smoother surface with a high accuracy and robust stability. The proposed P-ELM improves ELM in the sense of adding a polynomial in the single-hidden-layer feedforward networks to approximate the unknown function of the surface. The proposed P-ELM can not only retain the advantages of ELM with an extremely high learning speed and a good generalization performance but also reflect the intrinsic properties of the reconstructed surface. The detailed comparisons of the P-ELM, RBF algorithm, and ELM are carried out in the simulation to show the good performances and the effectiveness of the proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Boissonnat JD (1984) Geometric structures for three-dimensional shape representation. ACM Trans Graph 3(4):266–286

    Article  Google Scholar 

  2. Kolluri R, Shewchuk JR, O’Brien JF (2004) Spectral surface reconstruction from noisy point clouds. In: Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on geometry processing, pp 11–21

  3. Edelsbrunner H, Mücke EP (1994) Three-dimensional alpha shapes. In: Proceedings of the 1992 workshop on volume visualization, pp 43–72

  4. Bajaj CL, Bernardini F, Xu GL (1995) Automatic reconstruction of surfaces and scalar fields from 3D scans. In: Proceedings of the 22nd annual conference on computer graphics and interactive techniques, pp 10-18

  5. Bernardini F, Mittleman J, Rushmeier H, Silva C, Taubin G (1999) The ball-pivoting algorithm for surface reconstruction. IEEE Trans Visual Comput Graph 5(4):349–359

    Article  Google Scholar 

  6. Amenta N, Bern M, Kamvysselis M (1998) A new Voronoi-based surface reconstruction algorithm. In: Proceedings of the 25th annual conference on computer graphics and interactive techniques, pp 415–421

  7. Walder C, Schölkopf B, Chapelle O (2006) Implicit surface modelling with a globally regularised basis of compact support. Comput Graph Forum 25(3):635–644

    Article  Google Scholar 

  8. Yoon M, Lee YJ, Lee S, Ivrissimtzis I, Seidel HP (2007) Surface and normal ensembles for surface reconstruction. CAD 39(5):408–420

    Google Scholar 

  9. Pan RJ, Meng XX, Whangbo TK (2009) Hermite variational implicit surface reconstruction. Sci China Ser F 52(2):308–315

    Article  MATH  Google Scholar 

  10. Cybenko G (1989) Approximation by superposition of sigmoidal functions. Math Control Signal Syst 2(4):303–314

    Article  MathSciNet  MATH  Google Scholar 

  11. Funahashi KI (1989) On the approximate realization of continuous mappings by neural networks. Neural Netw 2:183–192

    Article  Google Scholar 

  12. Hornik K (1993) Some new results on neural network approximation. Neural Netw 6:1069–1072

    Article  Google Scholar 

  13. Chen TP, Chen H, Liu RW (1995) Approximation capability in by multiplayer feedforward networks and related problems. IEEE Trans Neural Netw 6:25–30

    Article  MATH  Google Scholar 

  14. Chen TP, Chen H (1995) Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems. IEEE Trans Neural Netw 6:911–917

    Article  Google Scholar 

  15. Cao FL, Xie TF, Xu ZB (2008) The estimate of approximation error for neural networks: a constructive approach. Neurocomputing 71:626–630

    Article  Google Scholar 

  16. Cao FL, Zhang YQ, He ZR (2009) Interpolation and rate of convergence for a class of neural networks. Appl Math Model 33(3):1441–1456

    Article  MathSciNet  MATH  Google Scholar 

  17. Muraki S (1991) Volumetric shape description of range data using “blobby model”. Comput Graph 25:227–235

    Article  Google Scholar 

  18. Floater MS, Iske A (1996) Multistep scattered data interpolation using compactly supported radial basis functions. J Comput Appl Math 73(1):65–78

    Article  MathSciNet  MATH  Google Scholar 

  19. Carr J, Beatson R, Cherrie H, Mitchel T, Fright W, Mccallum B, Evans T (2001) Reconstruction and representation of 3D objects with radial basis functions. SIGGRAPH, pp 67–76

  20. Turk G, O’Brien J (2002) Modelling with implicit surfaces that interpolate. ACM Trans Graphics 21(4):855–873

    Article  Google Scholar 

  21. Medeiros AD, Doria AD, Dantas JDM, Goncalves LMG (2008) An adaptive learning approach for 3-D surface reconstruction from point clouds. IEEE Trans Neural Netw 19(6):1130–1140

    Article  Google Scholar 

  22. Yoon M, Ivrissimtzis I, Lee S (2008) Self-organising maps for implicit surface reconstruction. EG UK Theory and Practice of Computer Graphics

  23. Rego RLME, Araujo, Neto FBDL (2010) Growing self-reconstruction maps. IEEE Trans Neural Netw 21(2):211–223

    Article  Google Scholar 

  24. Huang GB, Zhu QY, Siew CK (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. In: Proceedings of international joint conference on neural networks (IJCNN2004), Budapest, Hungary, vol 2(25–29):985–990

  25. Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. Wiley, New York

    Google Scholar 

  26. Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489–501

    Article  Google Scholar 

  27. Huang GB, Zhu QY, Siew CK (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 17(4):879–892

    Article  Google Scholar 

  28. Ortega JM (1987) Matrix theory. Plenum Press, New York

    Book  MATH  Google Scholar 

  29. Feng GR, Huang GB, Lin QP, Gay R (2009) Error minimized extreme learning machine with growth of hidden nodes and incremental learning. IEEE Trans Neural Netw 20(8):1352–1357

    Article  Google Scholar 

  30. Duchon J (1977) Splines minimizing rotation-invariant semi-norms in Sobolev spaces. In: Schempp W, Zeller K (eds) Constructive theory of functions of several variables, No. 571 in Lecture Notes in Mathematics. Springer, Berlin, pp 85–100

Download references

Acknowledgments

The research was supported by the National Natural Science Foundation of China(No. 61101240), the Zhejiang Provincial Natural Science Foundation of China (No. Y6110117), and the Science Foundation of Zhejiang Education Office (No. Y201122002).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fei Long Cao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, Z.H., Zhao, J.W. & Cao, F.L. Surface reconstruction based on extreme learning machine. Neural Comput & Applic 23, 283–292 (2013). https://doi.org/10.1007/s00521-012-0891-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-012-0891-8

Keywords

Navigation