Bézier Curve and Surface Fitting of 3D Point Clouds Through Genetic Algorithms, Functional Networks and Least-Squares Approximation

Gálvez, Antonio; Iglesias, Andrés; Cobo, Ángel; Puig-Pey, Jaime; Espinola, Jesús

doi:10.1007/978-3-540-74477-1_62

Cited by 64 publications

(31 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Errors typically fall within the interval [0.9, 2.6] in our executions, although upper (and possibly lower) values can also be obtained. This means that the present method compares well with the genetic algorithms approach reported in [7], although the PSO seems to yield more scattered output throughout the output domain. Other remarkable feature is that the best and mean errors are very close each other for all cases, as opposed to the genetic algorithms case, where the differences are generally larger.…”

Section: Discussionsupporting

confidence: 63%

See 1 more Smart Citation

Particle Swarm Optimization for Bézier Surface Reconstruction

Gálvez

Cobo

Puig-Pey

et al. 2008

Computational Science – ICCS 2008

Self Cite

View full text Add to dashboard Cite

Abstract. This work concerns the issue of surface reconstruction, that is, the generation of a surface from a given cloud of data points. Our approach is based on a metaheuristic algorithm, the so-called Particle Swarm Optimization. The paper describes its application to the case of Bézier surface reconstruction, for which the problem of obtaining a suitable parameterization of the data points has to be properly addressed. A simple but illustrative example is used to discuss the performance of the proposed method. An empirical discussion about the choice of the social and cognitive parameters for the PSO algorithm is also given.

show abstract

Section: Discussionsupporting

confidence: 63%

“…The generalization to functional networks is also analyzed in [5,11,12]. A previous paper in [7] describes the application of genetic algorithms and functional networks yielding pretty good results for both curves and surfaces.…”

Section: Introductionmentioning

confidence: 99%

Particle Swarm Optimization for Bézier Surface Reconstruction

Gálvez

Cobo

Puig-Pey

et al. 2008

Computational Science – ICCS 2008

Self Cite

View full text Add to dashboard Cite

show abstract

“…A combination of genetic algorithms and neural networks is discussed in [27]. Some papers addressed this problem by using functional networks [28,29], a powerful generalization of neural networks. A more recent paper describes the application of a hybrid neural-functional network to NURBS surface reconstruction [30].…”

Section: Previous Workmentioning

confidence: 99%

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

et al. 2018

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Kodoma et al (2005) proposed the use of hybrid algorithms by combining matrix-based representation genetic algorithm and a simulated annealing algorithm to reduce the computing time; however, performance presented by this hybrid algorithm and the original proposal based only on genetic algorithms are similar. The work by Gálvez et al (2007) concerns to the problem of curve and surface fitting. They focus on the case of 3D point clouds fitted with Bézier curves and surfaces.…”

Section: Previous Workmentioning

confidence: 99%