Surface reconstruction based on extreme learning machine

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.

[1]  Guang-Bin Huang,et al.  Extreme learning machine: a new learning scheme of feedforward neural networks , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).

[2]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1992, VVS.

[3]  Chee Kheong Siew,et al.  Extreme learning machine: Theory and applications , 2006, Neurocomputing.

[4]  Robert K. L. Gay,et al.  Error Minimized Extreme Learning Machine With Growth of Hidden Nodes and Incremental Learning , 2009, IEEE Transactions on Neural Networks.

[5]  Jean-Daniel Boissonnat,et al.  Geometric structures for three-dimensional shape representation , 1984, TOGS.

[6]  Xiangxu Meng,et al.  Hermite variational implicit surface reconstruction , 2009, Science in China Series F: Information Sciences.

[7]  M. Floater,et al.  Multistep scattered data interpolation using compactly supported radial basis functions , 1996 .

[8]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[9]  Hong Chen,et al.  Approximation capability in C(R¯n) by multilayer feedforward networks and related problems , 1995, IEEE Trans. Neural Networks.

[10]  Hans-Peter Seidel,et al.  Surface and normal ensembles for surface reconstruction , 2007, Comput. Aided Des..

[11]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[12]  Seungyong Lee,et al.  Self-Organising Maps for Implicit Surface Reconstruction , 2008, TPCG.

[13]  Adrião Duarte Dória Neto,et al.  An Adaptive Learning Approach for 3-D Surface Reconstruction From Point Clouds , 2008, IEEE Trans. Neural Networks.

[14]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[15]  Hong Chen,et al.  Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems , 1995, IEEE Trans. Neural Networks.

[16]  David W. Lewis,et al.  Matrix theory , 1991 .

[17]  James F. O'Brien,et al.  Modelling with implicit surfaces that interpolate , 2005, SIGGRAPH Courses.

[18]  Gabriel Taubin,et al.  The ball-pivoting algorithm for surface reconstruction , 1999, IEEE Transactions on Visualization and Computer Graphics.

[19]  FengGuorui,et al.  Error minimized extreme learning machine with growth of hidden nodes and incremental learning , 2009 .

[20]  Bernhard Schölkopf,et al.  Implicit Surface Modelling with a Globally Regularised Basis of Compact Support , 2006, Comput. Graph. Forum.

[21]  James F. O'Brien,et al.  Spectral surface reconstruction from noisy point clouds , 2004, SGP '04.

[22]  Chandrajit L. Bajaj,et al.  Automatic reconstruction of surfaces and scalar fields from 3D scans , 1995, SIGGRAPH.

[23]  Shigeru Muraki,et al.  Volumetric shape description of range data using “Blobby Model” , 1991, SIGGRAPH.

[24]  Jean Duchon,et al.  Splines minimizing rotation-invariant semi-norms in Sobolev spaces , 1976, Constructive Theory of Functions of Several Variables.

[25]  Chee Kheong Siew,et al.  Universal Approximation using Incremental Constructive Feedforward Networks with Random Hidden Nodes , 2006, IEEE Transactions on Neural Networks.

[26]  Aluizio F. R. Araújo,et al.  Growing Self-Reconstruction Maps , 2010, IEEE Transactions on Neural Networks.

[27]  K. S. Banerjee Generalized Inverse of Matrices and Its Applications , 1973 .

[28]  Richard K. Beatson,et al.  Reconstruction and representation of 3D objects with radial basis functions , 2001, SIGGRAPH.

[29]  C. R. Rao,et al.  Generalized Inverse of Matrices and its Applications , 1972 .

[30]  Kurt Hornik,et al.  Some new results on neural network approximation , 1993, Neural Networks.

[31]  Feilong Cao,et al.  Interpolation and rates of convergence for a class of neural networks , 2009 .

[32]  Zongben Xu,et al.  The estimate for approximation error of neural networks: A constructive approach , 2008, Neurocomputing.

[33]  Marshall W. Bern,et al.  A new Voronoi-based surface reconstruction algorithm , 1998, SIGGRAPH.