Automatic knot adjustment using an artificial immune system for B-spline curve approximation

ílker, Erkan; Arslan, Ahmet

doi:10.1016/j.ins.2008.11.037

Cited by 74 publications

(32 citation statements)

References 29 publications

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“…Curve approximation has been addressed with genetic algorithms [33,34], artificial immune systems [35,36], estimation of distribution algorithms [37], and hybrid techniques [38]. These works show that nature-inspired metaheuristic methods exhibit a very good performance for the case of curves, suggesting that they might also be very good candidates for the case of surfaces.…”

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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“…Roughly, they can be classified into two groups: discrete approaches [58,62,69] and continuous approaches [17,70,72]. Methods in the former group convert the original continuous problem into a discrete combinatorial optimization problem to be solved by either genetic algorithms [58,69] or artificial immune systems [62]. As expected, this conversion process introduces large discretization errors, making them both inaccurate and unreliable for real-world problems.…”

Section: Previous Workmentioning

confidence: 99%

“…Although these runtime values make the method not well-suited for real-time applications, it still outperforms the alternative metaheuristic techniques in this regard. For comparison, the methods in [58,62] require from tens of seconds to minutes even for simpler examples than those discussed in this paper (see Table 5 for details). Runtimes improve with the method in [70], but they are still in the range of tens of seconds, clearly slower than ours.…”

Section: Computation Timesmentioning

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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“…Sarfraz and Raza [13]; Yoshimoto et al [18]), artificial immune systems (cf. Gálvez et al [3]; Ülker and Arslan [16]) or estimation of distribution algorithms (cf. Zhao et al [19]).…”

Section: Introductionmentioning

confidence: 99%

Robust Spatial Approximation of Laser Scanner Point Clouds by Means of Free-form Curve Approaches in Deformation Analysis

Bureick

Alkhatib

Neumann

2016

Journal of Applied Geodesy

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Abstract:In many geodetic engineering applications it is necessary to solve the problem of describing a measured data point cloud, measured, e. g. by laser scanner, by means of free-form curves or surfaces, e. g., with B-Splines as basis functions. The state of the art approaches to determine B-Splines yields results which are seriously manipulated by the occurrence of data gaps and outliers.Optimal and robust B-Spline fitting depend, however, on optimal selection of the knot vector. Hence we combine in our approach Monte-Carlo methods and the location and curvature of the measured data in order to determine the knot vector of the B-Spline in such a way that no oscillating effects at the edges of data gaps occur. We introduce an optimized approach based on computed weights by means of resampling techniques. In order to minimize the effect of outliers, we apply robust M-estimators for the estimation of control points.The above mentioned approach will be applied to a multi-sensor system based on kinematic terrestrial laserscanning in the field of rail track inspection.

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Automatic knot adjustment using an artificial immune system for B-spline curve approximation

Cited by 74 publications

References 29 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

Robust Spatial Approximation of Laser Scanner Point Clouds by Means of Free-form Curve Approaches in Deformation Analysis

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