On Averaging Rotations

Claus Gramkow

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    Abstract

    In this article two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very offten the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong to a non-linear manifold and renromalization or orthogonalization must be applied to obtain proper rotations. These latter steps have been viewed as ad hoc corrections for the errors introduced by assuming a vector space. The article shows that the two approximative methods can be derived from natural approximations to the Riemannian metric, and that the subsequent corrections are inherient in the least squares estimation. Keywords: averaging rotations, Riemannian metric, matrix, quaternion
    Original languageEnglish
    Title of host publicationProceedings from The 11th. Scandinavian Conference on Image Analysis
    Place of PublicationLyngby
    Publication date1999
    Pages615-620
    Publication statusPublished - 1999
    Event11th Scandinavian Conference on Image Analysis (SCIA) - Kangerlussuaq, Greenland
    Duration: 7 Jun 199911 Jun 1999
    Conference number: 11

    Conference

    Conference11th Scandinavian Conference on Image Analysis (SCIA)
    Number11
    CountryGreenland
    CityKangerlussuaq
    Period07/06/199911/06/1999

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