Iterative two-step genetic-algorithm-based method for efficient polynomial B-spline surface reconstruction

Gálvez, Antonio; Iglesias, Andrés; Puig-Pey, Jaime

doi:10.1016/j.ins.2010.09.031

Cited by 102 publications

(37 citation statements)

References 60 publications

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“…Unfortunately, this path has been barely explored so far. Remarkable exceptions are the surface approximation methods based on particle swarm optimization [39], genetic algorithms [40,41] and immune genetic algorithms [42]. However, these methods are designed for either local-support surfaces or explicit functions and, therefore, they are not applicable for the problem addressed in this paper.…”

Section: Previous Workmentioning

confidence: 99%

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

et al. 2018

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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.

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Section: Previous Workmentioning

confidence: 99%

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

et al. 2018

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“…However this approach is not well suited for complex shapes. Classical choices in this case are the freeform piecewise polynomial functions, such as Bézier and B-splines [14,18,19,33,65]. In general, B-splines are the most commonly used approximating functions because they are very flexible, widely available, have powerful mathematical properties and can represent well a large variety of shapes [15,50].…”

Section: Introductionmentioning

confidence: 99%

Elitist clonal selection algorithm for optimal choice of free knots in B-spline data fitting

Gálvez

Iglesias

Avila

et al. 2015

Applied Soft Computing

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“…Applications to this domain include the EA in [33,34], where genetic algorithms were introduced to computer graphics. Later on, other evolutionary algorithms were also applied [14,2], while the most recent studies include also genetic algorithms [18] for polynomial Bspline surface reconstruction, particle swarm optimization [16] for the same problem and particle swarm optimization for Bézier surface reconstruction [15]. For example, Gálvez and Iglesias [17] applied the firefly algorithm [10,11] for polynomial Bézier surface parameterization, which is a well known problem in computer graphics.…”

Section: Introductionmentioning

confidence: 99%

Particle swarm optimization for automatic creation of complex graphic characters

Perc

Ljubič

Kamal

et al. 2015

Chaos, Solitons & Fractals

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Iterative two-step genetic-algorithm-based method for efficient polynomial B-spline surface reconstruction

Cited by 102 publications

References 60 publications

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

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

Elitist clonal selection algorithm for optimal choice of free knots in B-spline data fitting

Particle swarm optimization for automatic creation of complex graphic characters

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