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Construction and Analysis of Zone-dependent Interpolatory/Non-interpolatory Stochastic Subdivision Schemes for Non-regular Data

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Mathematical Methods for Curves and Surfaces (MMCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8177))

Abstract

This work is devoted to the definition of stochastic subdivision schemes adapted to the reconstruction of non-regular data. These schemes are constructed in the framework of the Kriging theory. Thanks to the introduction of a zone-dependent error variance in the Kriging approach, they combine interpolatory and non interpolatory subdivision schemes according to a domain segmentation. Their originality relies on the introduction and coupling of three ingredients: a segmentation of the data, a local prediction according to the characteristics of the different zones and an adaption strategy near segmentation points. The convergence of the corresponding 4-point scheme is analyzed. Its behavior is compared with other subdivision schemes on various numerical experiments.

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Author information

Authors and Affiliations

  1. Centrale Marseille, LATP, UMR 7353, CNRS, Aix-Marseille univ., 13451, Marseille, France

    Xiaoyun Si & Jacques Liandrat

  2. PSN-RES/SEMIA/LIMAR, CE Cadarache, Institut de Radioprotection et de Sûreté Nucléaire(IRSN), 13115, Saint Paul Les Durance, France

    Jean Baccou

Authors
  1. Xiaoyun Si
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  2. Jean Baccou
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  3. Jacques Liandrat
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Editor information

Editors and Affiliations

  1. Department of Informatics and Centre of Mathematics for Applications, University of Oslo, Norway

    Michael Floater

  2. DMA, University of Oslo, P.O.Box 1053, 0316, Blindern, Oslo, Norway

    Tom Lyche

  3. Laboratoire LJK, Université Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

  4. University of Oslo, Norway

    Knut Mørken

  5. Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA

    Larry L. Schumaker

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Si, X., Baccou, J., Liandrat, J. (2014). Construction and Analysis of Zone-dependent Interpolatory/Non-interpolatory Stochastic Subdivision Schemes for Non-regular Data. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2012. Lecture Notes in Computer Science, vol 8177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54382-1_26

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  • DOI: https://doi.org/10.1007/978-3-642-54382-1_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54381-4

  • Online ISBN: 978-3-642-54382-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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