Abstract
We propose, in this paper, a novel technique for large Laplacian boundary deformations using estimated rotations. The introduced method is used in the domain of Region of Interest (ROI) to align features of mesh based on Multi Mother Wavelet Neural Network (MMWNN) structure found in several mother wavelet families. The wavelet network allows the alignment of the characteristic points of the original mesh towards the target mesh. The key component of our correspondence scheme is a deformation energy that penalizes geometric distortion, encourages structure preservation and simultaneously allows mesh topology changes. To ensure the design of wavelet neural network architecture, an optimization algorithm should be applied to estimate and optimize the network parameters. Therefore, we compare our approach of 3d mesh deformation using MMWNN architecture based on genetic algorithm and our approach relying on Levenberg-Marquardt Method. We also discuss the existing comparison metrics for static and deformed triangle meshes employing the two mentioned approaches. Besides, we enumerate their strengths, weaknesses and relative performance.
Similar content being viewed by others
References
Daubechies I (1992) Ten lectures on wavelets. In: CBMS-NSF regional conference series in applied mathematics, pp 1–350
Zhang Q, Benveniste A (1992) Wavelet Networks. IEEE Trans Neural Netw 3:889–898
Bouchrika T, Zaied M, Jemai O, Ben Amar C (2012) Ordering computers by hand gestures recognition based on wavelet networks. In: 2nd international conference on communications computing and control applications, CCCA12, pp 1–6
Echauz J, Vachtsevanos G (1995) Wavelet neural networks for EEG modeling and classification. Math J
Zhang J, Walter GG, Miao Y, Wayne Lee W (1995) Wavelet neural networks for function learning. IEEE Trans. Signal Process 43:1485–1496
Lin CJ (2009) Nonlinear systems control using self-constructing wavelet networks. Appl Soft Comput 9:71–79
Karimi H, Lohmann B, Moshiri B, Jabedar-Maralani P (2006) Wavelet-based identification and control design for a class of nonlinear systems. Int J Wavel Multiresol Inform Process 4:213–226
Billings SA, Wei HL (2005) A new class of wavelet networks for nonlinear system identiffication. IEEE Trans Neural Netw 16:862–874
Dhibi N, Elkefi A, Bellil W, Ben Amar C (2016) 3D high resolution mesh deformation based on multi library wavelet neural network architecture. 3D Res J 7:408–416
Oussar Y, Dreyfus G (2002) Initialization by selection for wavelet network training. Neurocomputin 34:131–143
Bodyanskiy Y, Lamonova N, Pliss I, Vynokurova O (2005) An adaptive learning algorithm for a wavelet neural network. Exp Syst 22:235–240
Jinhua X, Ho DWC (2005) A constructive algorithm for wavelet neural networks. In: International conference on natural computation. Changsha, China, pp 730–739
Qingmei S, Yongchao G (2003) A stepwise updating algorithm for multiresolution wavelet neural networks. In: Proceedings of the international conference on wavelet analysis and its applications (WAA). Chongqing, China, pp 633–638
Kai C, Yoshio H (2004) An adaptive hybrid wavelet neural network and its application. In: IEEE international conference on robotics and biomimetics, pp 73–86
Seong-Joo K, Yong-Taek K, Jae-Yong S, Hong-Tae J (2002) Design of the scaling-wavelet neural network using genetic algorithm. In: Proceedings of the international joint conference on neural networks. Honolulu, pp 2174–2179
ChangGyoon L, Kangchui K, Eungkon K (2004) Modeling for an adaptive wavelet network parameter learning using genetic algorithms. In: International conference on modeling and simulation, CA, USA, pp 55-5-9
Min H, Baotong C (2005) A novel learning algorithm for wavelet neural networks. In: International conference on natural computation. ICNC, Changsha, China, pp 1–7
Mehra M, Rathish Kumar BV (2007) Error estimates for time accurate wavelet based schemes for hyperbolic partial differential equations. Int J Wavel Multiresol Inform Process 5:657–678
Mallat SG (1989) A theory for multi-resolution signal decomposition: the wavelet representation. IEEE Trans Patt Anal Mach Int 11:674–693
Valette S, Prost R (2004) Wavelet-based multiresolution analysis of irregular surface meshes. IEEE Trans Vis Comput Graph 10:113–122
Wang YS, Lee CR (2009) Evaluation of nonstationary vehicle passing loudness based on an antinoise wavelet pre-processing neural network mode. Int J Wavel Multiresol Inform Process 7:459–480
Chen S, Wu Y, Luk BL (1999) Combined genetic algorithm optimization and regularized orthonormal least squares learning for radial basis function networks. IEEE Trans Neural Netw 10:1239–1243
Othmani M, Bellil W, Ben Amar C, Alimi AM (2012) A novel approach for high dimension 3D object representation using multi-mother wavelet network. Int J Multimed Tools Appl 59:7–24
Othmani M, Bellil W, Ben Amar C, Alimi AM (2010) A new structure and training procedure for multi-mother wavelet networks. Int J Wavelets Multiresolut Inf Process 8(1):149–175
Ruqiang Y, Gao Robert X (2009) Base wavelet selection for bearing vibration signal analysis. Int J Wavel Multiresol Inform Process 7:411–426
Oussar Y, Rivals I, Personnaz L, Dreyfus G (1998) Training wavelet networks for nonlinear dynamic input-output modeling. Neurocomputing 20:173–188
Kardanpour Z, Hemmateenejad B, Khayamian T (2005) Wavelet neural network-based QSPR for prediction of critical micelle concentration of Gemini surfactants. Analytica Chimica Acta 531:285–291
Cui WZ, Zhu Ch, Zhao H (2005) Prediction of thin film thickness of field emission using wavelet neural networks. Thin Solid Films 473:224–229
Chen Y, Yang B, Dong J (2006) Time-series prediction using a local linear wavelet neural network. Neurocomputing 69:449–465
Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Netw 5:989–993
Ni Ampazis, Perantonis SJ (2002) Two highly efficient second order algorithms for training feedforward networks. IEEE Trans Neural Netw 13:1064–1074
Titsias MK, Likas AC (2001) Shared kernel model for class Conditional density Estimation. IEEE Trans Neural Netw 12:987–996
Colla V, Reyneri LM, Sgarbi M (1999) Orthogonal least squares algorithm Applied to the initialization of multi-layer perceptrons. In: European symposium on artificial neural networks. Bruges, Belgium, pp 363–369
Dhibi N, Ben amar C (2019) Multi-mother wavelet neural network training using genetic algorithm-based approach to optimize and improves the robustness of gradient-descent algorithms: 3D mesh deformation application. In: IWANN,pp 98–108
Dhibi N, Ben Amar C (2019) Multi-mother wavelet neural network based on genetic algorithm and multiresoluion analysis for fast 3d mesh deformation. IET Image Process 13:2480–2486
Wang Y, Guiqing L, Zhichao Z, Huayun H (2016) Articulated-motionaware sparse localized decomposition. Comp Graph Forum 36:247–259
Florian B, Gemmar P, Hertel F, Goncalves J, Thunberg J(2016) Linear shape deformation models with local support using graph-based structured matrix factorisation. In: CVPR, pp 5629–5638
Tan Q, Gao L, Lai Y-K, Yang J, Xia S (2018) Mesh-based autoencoders for localized deformation component analysis. In: Thirty-second AAAI conference on artificial intelligence, vol 32, issue 1, pp 2452–2459
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Dhibi, N., Amar, C.B. Performance of Genetic Algorithm and Levenberg Marquardt Method on Multi-Mother Wavelet Neural Network Training for 3D Huge Meshes Deformation: A Comparative Study. Neural Process Lett 53, 2221–2241 (2021). https://doi.org/10.1007/s11063-021-10512-y
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-021-10512-y