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Lévy Flight-Driven Simulated Annealing for B-spline Curve Fitting

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Nature-Inspired Algorithms and Applied Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 744))

Abstract

Point cloud approximation by spline models, also called curve and surface reconstruction, is an active research field in computer-aided design and manufacturing (CAD/CAM). Due to the physical and mechanical processes used to obtain the data, the measurements are often affected by noise and other distortions. Obtaining a suitable spline model to reconstruct the underlying shape of the data while maintaining a low design complexity leads to a multivariate and highly non-linear optimization problem, also known to be non-convex and multi-modal. In this work, we propose a method to fit a given point cloud by means of a B-spline curve model. Our approach to solve the optimization problem is based on a powerful thermodynamics-driven metaheuristic known as the Simulated Annealing. We compute the model parameters by combining traditional SA techniques with Lévy flights (random walks based on the Lévy distribution). The ability to perform such a flight allows the algorithm to escape from local minima and energy plateaus, a strong requirement when dealing with highly multi-modal problems. The performance and robustness of our algorithm is tested against three illustrative examples. Our experimental results show that our method is able to reconstruct the underlying shape of the data, even in the presence of noise, with acceptable accuracy and in a completely automated way.

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Acknowledgements

This research has been kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. #TIN2012-30768, Toho University (Funabashi, Japan), and the University of Cantabria (Santander, Spain). The authors are particularly grateful to the Department of Information Science of Toho University for all the facilities given to carry out this work. We also thank the anonymous reviewers who helped us to improve the chapter with their constructive comments and suggestions. A special recognition is also owe to our editor, Prof. Xin-She Yang, for his kind assistance and encouraging support during the process of writing this chapter.

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Authors and Affiliations

  1. Department of Communications Engineering, Universidad de Cantabria, Avda. de Los Castros, s/n, E-39005, Santander, Spain

    Carlos Loucera

  2. Faculty of Sciences, Department of Information Science, Toho University, 2-2-1 Miyama, Narashino Campus, Funabashi, 274-8510, Japan

    Andrés Iglesias & Akemi Gálvez

  3. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de Los Castros, s/n, 39005, Santander, Spain

    Andrés Iglesias & Akemi Gálvez

Authors
  1. Carlos Loucera
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  2. Andrés Iglesias
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  3. Akemi Gálvez
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Correspondence to Andrés Iglesias .

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Editors and Affiliations

  1. School of Science and Technology, Middlesex University, London, United Kingdom

    Xin-She Yang

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Loucera, C., Iglesias, A., Gálvez, A. (2018). Lévy Flight-Driven Simulated Annealing for B-spline Curve Fitting. In: Yang, XS. (eds) Nature-Inspired Algorithms and Applied Optimization. Studies in Computational Intelligence, vol 744. Springer, Cham. https://doi.org/10.1007/978-3-319-67669-2_7

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  • DOI: https://doi.org/10.1007/978-3-319-67669-2_7

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  • Online ISBN: 978-3-319-67669-2

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