Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Artificial Immune Systems: A New Computational Intelligence Paradigm
Artificial Immune Systems: A New Computational Intelligence Paradigm
A Survey of Optimization by Building and Using Probabilistic Models
Computational Optimization and Applications
Expanding from Discrete to Continuous Estimation of Distribution Algorithms: The IDEA
PPSN VI Proceedings of the 6th International Conference on Parallel Problem Solving from Nature
Automatic Knot Placement by a Genetic Algorithm for Data Fitting with a Spline
SMI '99 Proceedings of the International Conference on Shape Modeling and Applications
Capturing Outline of Fonts Using Genetic Algorithm and Splines
IV '01 Proceedings of the Fifth International Conference on Information Visualisation
An error-bounded approximate method for representing planar curves in B-splines
Computer Aided Geometric Design
Spline curve approximation and design by optimal control over the knots
Computing - Geometric modelling dagstuhl 2002
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
B-spline curve fitting based on adaptive curve refinement using dominant points
Computer-Aided Design
Approximation by smoothing variational vector splines for noisy data
Journal of Computational and Applied Mathematics
Data gravitation based classification
Information Sciences: an International Journal
Automatic knot adjustment using an artificial immune system for B-spline curve approximation
Information Sciences: an International Journal
Adaptive knot placement in B-spline curve approximation
Computer-Aided Design
Efficient particle swarm optimization approach for data fitting with free knot B-splines
Computer-Aided Design
A new iterative mutually coupled hybrid GA-PSO approach for curve fitting in manufacturing
Applied Soft Computing
IGA-based point cloud fitting using B-spline surfaces for reverse engineering
Information Sciences: an International Journal
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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).