IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-387-92920-0_35.html
   My bibliography  Save this book chapter

Differential Methods for Multi-Dimensional Visual Data Analysis

In: Handbook of Mathematical Methods in Imaging

Author

Listed:
  • Werner Benger

    (Center for Computation and Technology at Lousiana State University)

  • René Heinzl

    (Shenteq s.r.o)

  • Dietmar Hildenbrand

    (University of Technology Darmstadt)

  • Tino Weinkauf

    (New York University)

  • Holger Theisel

    (Institut fur Simulation und Graphik AG Visual Computing)

  • David Tschumperlé

    (GREYC (UMR-CNRS 6072))

Abstract

Images in scientific visualization are the end-product of data processing. Starting from higher-dimensional datasets, such as scalar-, vector-, tensor- fields given on 2D, 3D, 4D domains, the objective is to reduce this complexity to two-dimensional images comprehensible to the human visual system. Various mathematical fields such as in particular differential geometry, topology (theory of discretized manifolds), differential topology, linear algebra, Geometric Algebra, vectorfield and tensor analysis, and partial differential equations contribute to the data filtering and transformation algorithms used in scientific visualization. The application of differential methods is core to all these fields. The following chapter will provide examples from current research on the application of these mathematical domains to scientific visualization and ultimately generating of images for analysis of multi-dimensional datasets.

Suggested Citation

  • Werner Benger & René Heinzl & Dietmar Hildenbrand & Tino Weinkauf & Holger Theisel & David Tschumperlé, 2011. "Differential Methods for Multi-Dimensional Visual Data Analysis," Springer Books, in: Otmar Scherzer (ed.), Handbook of Mathematical Methods in Imaging, chapter 35, pages 1533-1595, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-92920-0_35
    DOI: 10.1007/978-0-387-92920-0_35
    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_35. 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.