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dc.contributor.authorIglesias Prieto, Andrés 
dc.contributor.authorGálvez Tomida, Akemi 
dc.contributor.authorSuárez Cano, Patricia
dc.contributor.authorShinya, Mikio
dc.contributor.authorYoshida, Norimasa
dc.contributor.authorOtero González, César Antonio 
dc.contributor.authorManchado del Val, Cristina 
dc.contributor.authorGómez Jáuregui, Valentín 
dc.contributor.otherUniversidad de Cantabriaes_ES
dc.description.abstractThis 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.es_ES
dc.description.sponsorshipThis research work has received funding from the project PDE-GIR (Partial Differential Equations for Geometric modelling, Image processing, and shape Reconstruction) of the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant agreement No. 778035, the Spanish Ministry of Economy and Competitiveness (Computer Science National Program) under Grant #TIN2017-89275-R of the Agencia Estatal de Investigación and European Funds FEDER (AEI/FEDER, UE), and the project #JU12, jointly supported by public body SODERCAN of the Regional Government of Cantabria and European Funds FEDER (SODERCAN/FEDER UE). We also thank Toho University, Nihon University, and the Symmetry 2018, 10, 58 23 of 25 University of Cantabria for their support to conduct this research workes_ES
dc.format.extent25 p.es_ES
dc.publisherDepartment of Applied Research Institute of Mathematics of National Academy of Science of Ukrainees_ES
dc.rightsAttribution-ShareAlike 4.0 Internationales_ES
dc.sourceSymmetry 2018, 10, 58es_ES
dc.titleCuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineeringes_ES

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Attribution-ShareAlike 4.0 InternationalExcept where otherwise noted, this item's license is described as Attribution-ShareAlike 4.0 International