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DLT background information

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  • DLT background information

    Dear Biomch-L readers,

    After my posting regarding the 2-D DLT method, one subscriber suggested
    that it might be useful to provide some background information about
    the DLT procedure, for those who are not familiar with it. Biomch-L
    is not the place for a complete course on kinematic analysis, but I
    can provide a short explanation and a few references.

    DLT stands for "Direct Linear Transform" and is a mathematical
    transformation between raw 2D camera data (u,v) and the actual 3D
    coordinates (X,Y,Z) of a point. The transformation depends on
    the position and orientation of the camera, and is characterized
    by eleven constants (camera parameters). The method is commonly
    used to obtain 3D coordinates from two or more cameras. The
    DLT equations are:

    Code:
        aX + bY + cZ + d
    u = ----------------
        iX + jY + kZ + 1
    
        eX + fY + gZ + h
    v = ----------------
        iX + jY + kZ + 1
    If you have six or more calibration points with known (X,Y,Z), and
    corresponding raw camera coordinates (u,v), the camera parameters
    a,b,c...k can be solved because you have twelve or more equations
    (two for each calibration landmark) with eleven unknowns. This is
    done for each camera. When the camera parameters are known, the
    unknown (X,Y,Z) coordinates of other landmarks can be solved from
    the (u,v) data of two or more cameras because there are four or more
    equations for the three unknowns (X,Y,Z).

    An overview of various 3D measuring techniques (DLT being one of them)
    can be found in:
    Woltring, H.J. and R. Huiskes (1990) "Stereophotogrammetry", in:
    Biomechanics of Human Movement, edited by N. Berme and A. Capozzo,
    pp. 108-127, Bertec Corporation, Worthington, Ohio.

    The original publication about the DLT method is:
    Abdel-Aziz, Y.I and H.M. Karara (1971) "Direct linear transformation
    from comparator coordinates into object-space coordinates", in:
    Proceedings ASP/UI Symposium on Close-Range Photogrammetry, pp.1-18,
    American Society of Photogrammetry, Falls Church, VA.

    There are many publications in which the DLT method is used, evaluated,
    or improved. Example:
    Wood, G.A. and R.N. Marshall (1986) "The accuracy of DLT extrapolation
    in three-dimensional film analysis". J. Biomech. 19, pp. 781-785.

    -- Ton van den Bogert
    Human Performance Laboratory
    University of Calgary, Canada
    Last edited by Ton van den Bogert; August 4th, 2011, 09:57 AM. Reason: equation was not formatted correctly
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