Adaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximation

One of the key problems in using B-splines successfully to approximate an object contour is to determine good knots. In this paper, the knots of a parametric B-spline curve were treated as variables, and the initial location of every knot was generated using the Monte Carlo method in its solution do...

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Bibliographic Details
Published in:Computer aided design Vol. 43; no. 6; pp. 598 - 604
Main Authors: Zhao, Xiuyang, Zhang, Caiming, Yang, Bo, Li, Pingping
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.06.2011
Subjects:
Algorithms
Approximation
B-spline curve approximation
Contour
EDA
GMM
Knot placement
Knots
Mathematical analysis
Mathematical models
Optimization
Position (location)
Vectors (mathematics)
B-spline curve approximation
EDA
Contour
GMM
Knot placement
ISSN:0010-4485, 1879-2685
Online Access:Get full text
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Summary:One of the key problems in using B-splines successfully to approximate an object contour is to determine good knots. In this paper, the knots of a parametric B-spline curve were treated as variables, and the initial location of every knot was generated using the Monte Carlo method in its solution domain. The best km knot vectors among the initial candidates were searched according to the fitness. Based on the initial parameters estimated by an improved k -means algorithm, the Gaussian Mixture Model (GMM) for every knot was built according to the best km knot vectors. Then, the new generation of the population was generated according to the Gaussian mixture probabilistic models. An iterative procedure repeating these steps was carried out until a termination criterion was met. The GMM-based continuous optimization algorithm could determine the appropriate location of knots automatically. A set of experiments was then implemented to evaluate the performance of the new algorithm. The results show that the proposed method achieves better approximation accuracy than methods based on artificial immune system, genetic algorithm or squared distance minimization (SDM). ► The locations of the knots of a parametric B-spline curve are treated as variables. ► We develop a GMM-based EDA to determine the appropriate locations of the knots. ► We initialize the parameters of GMM using a data-mass-based k -means algorithm. ► A point cloud representing a closed curve can be approximated successfully.
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ISSN:0010-4485
1879-2685
DOI:10.1016/j.cad.2011.01.015