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Symmetry 2018, 10(3), 58; https://doi.org/10.3390/sym10030058

Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering

1
Department of Information Science, Faculty of Sciences, Toho University, 2-2-1 Miyama, Funabashi 274-8510, Japan
2
Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros, s/n, E-39005 Santander, Spain
3
Department of Industrial Engineering and Management, College of Industrial Technology, Nihon University, 1-2-1 Izumi-cho Narashino, Chiba 275-8575, Japan
4
Department of Geographical Engineering and Graphical Expression Techniques, University of Cantabria, Avda. de los Castros, s/n, E-39005 Santander, Spain
*
Author to whom correspondence should be addressed.
Received: 26 December 2017 / Revised: 25 January 2018 / Accepted: 26 February 2018 / Published: 3 March 2018
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Abstract

This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark. View Full-Text
Keywords: shape reconstruction; surface approximation; reverse engineering; computer-aided design; global-support functions; Bézier surfaces; least-squares optimization; metaheuristics; cuckoo search algorithm; Lévy flights shape reconstruction; surface approximation; reverse engineering; computer-aided design; global-support functions; Bézier surfaces; least-squares optimization; metaheuristics; cuckoo search algorithm; Lévy flights
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Iglesias, A.; Gálvez, A.; Suárez, P.; Shinya, M.; Yoshida, N.; Otero, C.; Manchado, C.; Gomez-Jauregui, V. Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering. Symmetry 2018, 10, 58.

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