IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-387-92920-0_28.html
   My bibliography  Save this book chapter

Splines and Multiresolution Analysis

In: Handbook of Mathematical Methods in Imaging

Author

Listed:
  • Brigitte Forster

    (Technische Universität München)

Abstract

Splines and multiresolution are two independent concepts, which – consideredtogether – yield a vast variety of bases for image processing and image analysis.The idea of a multiresolution analysis is to construct a ladder of nested spacesthat operate as some sort of mathematical looking glass. It allows to separatecoarse parts in a signal or in an image from the details of various sizes.Spline functions are piecewise or domainwise polynomials in one dimension(1D) resp.nD.There is a variety of spline functions that generate multiresolution analyses. The viewpoint in this chapter is the modeling of such spline functions in frequency domain via Fourier decay to generate functions with specified smoothness in time domain resp. space domain. The mathematical foundations are presented and illustrated at the example of cardinal B-splines as generators of multiresolution analyses. Other spline models such as complex B-splines, polyharmonic splines, hexagonal splines, and others are considered. For all these spline families exist fast and stable multiresolution algorithms which can be elegantly implemented in frequency domain. The chapter closes with a look on open problems in the field.

Suggested Citation

  • Brigitte Forster, 2011. "Splines and Multiresolution Analysis," Springer Books, in: Otmar Scherzer (ed.), Handbook of Mathematical Methods in Imaging, chapter 28, pages 1231-1270, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-92920-0_28
    DOI: 10.1007/978-0-387-92920-0_28
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-0-387-92920-0_28. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.