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.
Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria