IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-0159-5_9.html
   My bibliography  Save this book chapter

Bayesian Inference and Geometric Algebra: An Application to Camera Localization

In: Geometric Algebra with Applications in Science and Engineering

Author

Listed:
  • Chris Doran

Abstract

Geometric algebra is an extremely powerful language for solving complex geometric problems in engineering [ 4 , 8 ]. Its advantages are particularly clear in the treatment of rotations. Rotations of a vector are performed by the double-sided application of a rotor, which is formed from the geometric product of an even number of unit vectors. In three dimensions a rotor is simply a normalised element of the even subalgebra of G 3, the geometric algebra of three dimensional space. In this paper we are solely interested in rotations in space, and henceforth all reference to rotors can be assumed to refer to the 3-d case. Rotors have a number of useful features. They can be easily parameterised in terms of the bivector representing the plane of rotation. Their product is a very efficient way of computing the effect of compound rotations, and is numerically very stable.

Suggested Citation

  • Chris Doran, 2001. "Bayesian Inference and Geometric Algebra: An Application to Camera Localization," Springer Books, in: Eduardo Bayro Corrochano & Garret Sobczyk (ed.), Geometric Algebra with Applications in Science and Engineering, chapter 0, pages 170-189, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0159-5_9
    DOI: 10.1007/978-1-4612-0159-5_9
    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:978-1-4612-0159-5_9. 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.