Cuckoo Search Algorithm with Levy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering
Cuckoo Search Algorithm with Levy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering
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DOI：
10.3390/sym10030058
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发表时间：
2018-03-01
期刊：
影响因子：
2.7
通讯作者：
Gomez-Jauregui, Valentin
中科院分区：
文献类型：
--
作者：
Iglesias, Andres;Galvez, Akemi;Gomez-Jauregui, Valentin
本文涉及《对称》杂志的几个重要主题，即计算机辅助设计、计算几何、计算机图形学、可视化和模式识别。我们还利用了张量积曲面的对称结构，其中参数变量u和v在形状重建中起对称作用。本文讨论了逆向工程应用中基于数据点云的全局支持参数曲面逼近的一般问题。给定一组测量数据点，将其近似化为非线性连续最小二乘优化问题。然后，应用最近的一种称为杜鹃搜索算法（CSA）的元启发式算法计算该最小化问题的所有相关自由变量（即数据参数和表面极点）。该方法包括利用Levy飞行迭代生成新解，以促进解的多样性并防止停滞。该方法的一个关键优点是它的简单性：CSA只需要两个参数，比任何其他元启发式方法都少得多，因此参数调优成为一项非常容易的任务。该方法易于理解和实现。我们的方法已应用于三个说明性噪声数据点集合的基准，这些数据点对应于显示几个具有挑战性特征的表面。实验结果表明，即使在有噪声和无组织数据点的情况下，该方法也能取得很好的效果。因此，该方法可以直接用于实际应用的逆向工程，而无需进一步的预处理/后处理。与此问题的最经典数学技术的比较工作以及最近对CSA的修改称为改进CSA （ICSA）也被报道。两个非参数统计测试表明，我们的方法优于经典数学技术，并为基准测试中的所有实例提供与ICSA相同的结果。
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 Levy 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.