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Immunological Approach for Data Parameterization in Curve Fitting of Noisy Points with Smooth Local-Support Splines

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Advances in Swarm Intelligence (ICSI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9712))

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Abstract

This paper addresses the problem of computing the parameterization of a smooth local-support spline curve for data fitting of noisy points by using an immunological approach. Given an initial set (not necessarily optimal) of breakpoints, our method applies a popular artificial immune systems technique called clonal selection algorithm to perform curve parameterization. The resulting optimal data parameters are then used for further refinement of the breakpoints via the deBoor method. In this way, the original non-convex optimization method is transformed into a convex one, subsequently solved by least-squares singular value decomposition. The method is applied to two illustrative examples (human hand and ski goggles, each comprised of three curves) of two-dimensional sets of noisy data points with very good experimental results.

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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, and the University of Cantabria.

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Authors and Affiliations

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

    Andrés Iglesias, Akemi Gálvez & Andreina Avila

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

    Andrés Iglesias & Akemi Gálvez

Authors
  1. Andrés Iglesias
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  2. Akemi Gálvez
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  3. Andreina Avila
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Corresponding author

Correspondence to Andrés Iglesias .

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Editors and Affiliations

  1. Peking University, Beijing, China

    Ying Tan

  2. Xi'an Jiaotong-Liverpool University, Suzhou, China

    Yuhui Shi

  3. Shenzhen University, Shenzhen, China

    Ben Niu

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Iglesias, A., Gálvez, A., Avila, A. (2016). Immunological Approach for Data Parameterization in Curve Fitting of Noisy Points with Smooth Local-Support Splines. In: Tan, Y., Shi, Y., Niu, B. (eds) Advances in Swarm Intelligence. ICSI 2016. Lecture Notes in Computer Science(), vol 9712. Springer, Cham. https://doi.org/10.1007/978-3-319-41000-5_11

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  • DOI: https://doi.org/10.1007/978-3-319-41000-5_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40999-3

  • Online ISBN: 978-3-319-41000-5

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