Determining rigid body transformation parameters from ill-conditioned spatial marker co-ordinates

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Title Determining rigid body transformation parameters from ill-conditioned spatial marker co-ordinates
Author Carman, A.B.; Milburn, P.D.
Journal Name Journal of Biomechanics
Year Published 2006
Place of publication United Kingdom
Publisher Elsevier
Abstract The three-dimensional location of a body-fixed axis system is described by position and orientation parameters that can be calculated knowing local and global coordinates of three or more body-fixed markers. However, marker distribution can become ill-conditioned when marker placement is symmetrical with respect to the mean of the markers. As symmetry and ill-conditioning increases, random errors in marker locations can affect the stability of orientation parameters as a result of the mathematical approach adopted. The present study investigates the methods of Veldpaus et al. [1988; Journal of Biomechanics 21, 45], Challis [1995; Biomechanics 28, 733] and Andriacchi et al. [1998; Journal of Biomedical Engineering 120, 743] for obtaining segment orientation parameters when segment markers ranged from well-defined to highly ill-conditioned depending on the symmetry of segment markers. A novel fourth approach is also presented that enabled comparisons of the root mean square error of reconstructed marker coordinates to verify that an optimal solution was obtained. No single method produced optimal results for all axis orientation parameters when reconstructing movement trials. The best performed was the method of Veldpaus et al. [1988; Journal of Biomechanics 21, 45] based on consistent results and ease of implementation. The fourth approach presented provided a reliable method in all but the highly ill-conditioned markers, however implementation was computationally difficult. The method of Challis [1995; Biomechanics 28, 733] was only suited to well-conditioned marker sets which avoided markers lying in a single plane with symmetries in marker distribution relative to the mean. The method of Andriacchi et al. [1998; Journal of Biomedical Engineering 120, 743] produced, at best, orientation parameters that approximated the results obtained by least squares methods.
Peer Reviewed Yes
Published Yes
Alternative URI http://dx.doi.org/10.1016/j.jbiomech.2005.05.028
Volume 39
Issue Number 10
Page from 1778
Page to 1786
ISSN 0021-9290
Date Accessioned 2008-08-28
Date Available 2009-11-10T05:56:16Z
Language en_AU
Research Centre Griffith Health Institute; Centre for Musculoskeletal Research
Faculty Griffith Health Faculty
Subject PRE2009-Biomechanics
URI http://hdl.handle.net/10072/26550
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1x

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