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A novel approach for high dimension 3D object representation using Multi-Mother Wavelet Network

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Abstract

In this paper, we present a novel approach for 3D objects representation. Our idea is to prove that wavelet networks are capable for reconstruction and representing irregular 3D objects used in computer graphics. The major contribution consist to transform an input surface vertices into signals and to provide instantaneously an estimation of the output values for input values. To prove this, we will use a new structure of wavelet network founded on several mother wavelet families. This structure uses several mother wavelet, in order to maximize best wavelet selection probability. An algorithm to construct this structure is presented. First, Data is taken from 3D object. The vertices and their corresponding normal values of a 3D object are used to create a training set. To this stage, the training set can be expressed according to three functions, which interpolates all their vertices. Second we approximate each function using wavelet network. To achieve a better approximation, the network is trained several iterations to optimize wavelet selection for every mother. To guarantee a small error criterion, we adjust wavelet network parameters (weight, translation and dilation) by using an improved Orthogonal Least Squares method version. We consider our proposed approach on some 3D examples to prove that the new approach is able to approximate 3D objects with a good approximation ability.

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References

  1. Alimi AM (2003) The beta-based neuro-fuzzy system: Genesis and main properties. TASK Quarterly Journal, Special Issue on “Neural Networks” eds. W. Duch and D. Rutkowska 7(1):23–41

    Google Scholar 

  2. Aouiti C, Alimi AM, Karray F, Maalej A (2002) A hierarchical genetic algorithm for the design of beta basis function neural network. In: Proceedings of the international joint conference on neural networks, vol 2, pp 1246–1251

  3. Aouiti C, Alimi AM, Maalej A (2002) A genetic-designed beta basis function neural network for multi-variable functions approximation. Syst Anal Model Simul 42(7):975–1009

    MATH  Google Scholar 

  4. Bellil W, Ben Amar C, Alimi AM (2006) Comparison between beta wavelet neural networks, RBF neural networks and polynomial approximation for 1D, 2D functions approximation. International Journal of Applied Science, Engineering and Technology vol 13, pp 33–38

  5. Bellil W, Ben Amar C, Alimi AM (2006) Synthesis of wavelet filters using wavelet neural networks. Transactions on Engineering, Computation and Technology 13:108–111

    Google Scholar 

  6. Bellil W, Othmani M, Ben Amar C (2007) Initialization by Selection for multi library wavelet neural network training. In: Proceeding of the 3rd international workshop on artificial neural networks and intelligent information processing ANNIIP07, in conjunction with 4th international conference on informatics in control, automation and robotics, ICINCO, pp 30–37

  7. Bellil W, Othmani M, Ben Amar C, Alimi AM (2008) A new algorithm for initialization and training of beta multi-library wavelets neural network. In: Aramburo J, Ramirez Trevino A (eds) Advances in robotics, automation and control, I-Tech Education and Publishing, pp 199–220, October

  8. Blow T (2002) Spherical diffusion for 3d surface smoothing. In: 3DPVT’02: the first international symposium on 3D data processing visualization and transmission, Padova, Italy, pp 449

  9. Chen Y, Wu, BL Luk (1999) Combined genetic algorithm optimisation and regularised orthogonal least squares learning for radial basis function networks. IEEE Trans Neural Netw 10(5):1239–1243

    Article  Google Scholar 

  10. Chui CK (1992) An introduction to wavelets. Academic Press, New York, NY, U.S.A.

    MATH  Google Scholar 

  11. Clarenz U, Diewald U, Rumpf M (2000) Nonlinear anisotropic diffusion in surface processing. In: Ertl T, Hamann B, Varshney A (eds) Proceedings of IEEE Visualization 2000, pp 397–405

  12. Eck M, DeRose T, Duchamp T, Hoppe H, Lounsbery M, Stuetzle W (1995) Multiresolution analysis of arbitrary meshes. In: SIGGRAPH95: proceedings of the 22nd annual conference on computer graphics and interactive techniques, New York, NY, USA. ACM Press, pp 173–182

  13. Funkhouser T, Min P, et al (2003) A search engine for 3d models. ACM Trans Graph 22(1):83–105

    Article  Google Scholar 

  14. Golub GH, Van Loan CF (1989) Matrix computations, 2nd ed. Baltimore, MD: John Hopkins University Press

  15. Gomm JB, Yu DL (2000) Selecting radial basis function network centers with recursive orthogonal least squares training. IEEE Trans Neural Netw 11:06–314

    Article  Google Scholar 

  16. Hamdani TM, Alimi AM, Karray F (2006) Distributed genetic algorithm with bi-coded chromosomes and a new evaluation function for features selection. 2006 IEEE Congress on Evolutionary Computation, CEC 2006, Article number 1688362, pp 581–588

  17. Hartman J, Wernecke J (1996) VRML 2.0 handbook. Addison-Wesley

  18. Hassine R, Karray F, Alimi AM, Selmi M (2003) Approximation properties of fuzzy systems for smooth functions and their first-order derivative. IEEE Trans Syst Man Cybern, Part A, Syst Humans 33(2):160–168

    Article  Google Scholar 

  19. Hassine R, Karray F, Alimi AM, Selmi M (2006) Approximation properties of piece-wise parabolic functions fuzzy logic systems. Fuzzy Sets and Systems 157(4):501–515

    Article  MathSciNet  MATH  Google Scholar 

  20. Huang H, Shen L, et al (2005) Surface alignment of 3D spherical harmonic models: application to cardiac MRI analysis. In: MICCAI2005, LNCS 3749, pp 67–74

  21. Jemai O, Zaied M, Ben Amar C, Alimi AM (2010) FBWN: an architecture of Fast Beta Wavelet Networks for Image Classification. In: 2010 IEEE World Congress on Computational Intelligence, IJCNN 2010, International Joint Conference on Neural Networks, pp 1953–1960

  22. Jin J, Dai M, Bao H, Peng Q (2004) Watermarking on 3d mesh based on spherical wavelet transform. J Zhejiang Univ Sci 5(3):251–258

    Article  MATH  Google Scholar 

  23. Jun Z, Walter GG, Miao Y (1995) Wavelet neural networks for function learning. IEEE Trans Signal Process 43(6):1485–1496

    Article  Google Scholar 

  24. Kallel I, Jmaiel M, Alimi AM (2002) A multi-agent approach for genetic algorithm implementation. Proc IEEE Int Conf Syst Man Cybern 7:358–363

    Google Scholar 

  25. Kazhdan M, Funkhouser T, Rusinkiewicz S (2003) Rotation invariant spherical harmonic representation of 3d shape descriptors. In: SGP 03: proceedings of the eurographics/ ACM SIGGRAPH symposium on geometry processing. Eurographics Association, pp 156–164

  26. Lekutai G (1997) Adaptive self-tuning neuro wavelet network controllers. phD thesis, Virginia Polytechnic Institute and State University, The Electrical Engineering Department

  27. Levy B (2006) Laplace-beltrami eigenfunctions: towards an algorithm that understands geometry. In: IEEE international conference on shape modeling and applications

  28. Masmoudi M, Samet M, Alimi AM (2000) A bipolar implementation of the beta neuron. Int J Electron 87(6):675–682

    Article  Google Scholar 

  29. Min H, Baotong C (2005) A novel learning algorithm for wavelet neural networks. In: First international conference on natural computation, ICNC, Changsha, China, pp 1–7

  30. Othmani M, Bellil W, Ben Amar C, Alimi AM (2010) A new structure and training procedure of multi-mother wavelet network. International Journal of Wavelets, Multiresolution and Information Processing: World Scientific Publishing Company 8(1):149–175

    Article  MathSciNet  MATH  Google Scholar 

  31. Saupe D, Vranic DV (2001) 3d model retrieval with spherical harmonics and moments. In: Proceedings of the 23rd DAGMSymposium on pattern recognition, Springer-Verlag, pp 392–397

  32. Shen L, Ford J, Makedon F, Saykin A (2004) A surfacebased approach for classification of 3D neuroanatomic structures. Intelligent Data Analysis 8(6):519–542

    Google Scholar 

  33. Titsias MK, Likas AC (2001) Shared kernel model for class conditional density estimation. IEEE Trans Neural Netw 12(5):987–996

    Article  Google Scholar 

  34. Zaied M, Jemai O, Ben Amar C (2008) Training of the beta wavelet networks by the frame theory: application to face recognition. IEEE International Conference on Image Processing Theory, Tools and Applications, IPTA’2008, pp 165–170

  35. Zhang H, van Kaick O (2007) Spectral methods for mesh processing and analysis. In: Eurographics 2007, Prague, Czech Republic

  36. Zhang Q (1997) Using wavelet network in nonparameters estimation. IEEE Trans Neural Netw 8:227–236

    Article  Google Scholar 

  37. Zhang Q, Benveniste A (1992) Wavelet networks. IEEE Trans Neural Netw 3(6):889–898

    Article  Google Scholar 

  38. Zhou K, Bao H, Shi J (2004) 3d surface filtering using spherical harmonics. Comput Aided Des 36(4):363–375

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the financial support of this work by grants from General Direction of Scientific Research (DGRST), Tunisia, under the ARUB program.

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Authors and Affiliations

  1. Higher Institute for Applied Science and Technology, University of Gafsa, 2112, Gafsa, Tunisia

    Mohamed Othmani

  2. Faculty of Sciences, University of Gafsa, 2112, Gafsa, Tunisia

    Wajdi Bellil

  3. REGIM: REsearch Group on Intelligent Machines, University of Sfax, National School of Engineers (ENIS), BP 1173, Sfax, 3038, Tunisia

    Chokri Ben Amar & Adel M. Alimi

Authors
  1. Mohamed Othmani
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  2. Wajdi Bellil
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  3. Chokri Ben Amar
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  4. Adel M. Alimi
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Correspondence to Mohamed Othmani.

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Othmani, M., Bellil, W., Ben Amar, C. et al. A novel approach for high dimension 3D object representation using Multi-Mother Wavelet Network. Multimed Tools Appl 59, 7–24 (2012). https://doi.org/10.1007/s11042-010-0697-6

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