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Reply to Michael's question of determination of R

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  • Reply to Michael's question of determination of R

    Objectif: Reply to Michael's question concerning the determination of
    kinematic parameters from noisy landmarkers,

    Dear Michael and to those who are concerned,

    If I understand your question, you want to determine the rotation matrix R
    and the translation vector V from noisy landmarker measurements. This is a
    difficult problem.

    Two main errors are involved: incertainty in determinationof tha landmark
    coordinates by your opto-electrical system and error due to relative skin
    movement. Generally, an opto-electrical system now can give a very acurate
    measurement if the system is correctly calibrated and the cameras are
    carefully positionned. Skin movement in some case is the most important
    source of errors.

    The bone movement itself can be considered as a rigid-body movement, which
    can be described by R and V. But due to measurement errors, the bone movement
    is no more a rigid-body movement. If you suppose that all measurement errors
    are independent and normally distributed with constant standard deviation,
    Veldpaus et al (1988) [A least square algorithm transfromation from spatial
    marker coordinates, J. Biomch, 21, 45-54] proposed a very efficient algorithme
    for the calculation of R. With my colleagues, we proposed also an algorithme
    [WANG et al (1993), Using the polar decomposition theory to determine the
    rotation matrix from noisy landmark measurements in the study of human joint
    kinematics, 2nd Int Sym. of 3D analysis of human movement, Poitier,
    July,France]. The advantage of our method is that it can theoretically seperate
    the rotation from an orthotropic deformation. It provides also a tool to
    quantify the deformation caused by measurement errors. But application of our
    method needs a deep understanding of deformation nature, especially due to skin
    movement. I don't think the skin movement can be simplified as a random
    measurement error. Of cause, If the deformation nature is not known,
    the algorithme proposed by Veldpaus is better, because it provides a solution
    in a least-square sense.

    >From this reply, I want to know if there exists a group who works on
    this specific question (skin movement). If yes, I would like to know who
    work in this group. If not, why we don't create such a group to share

    Xuguang WANG, PhD