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    Dear All,

    three weeks ago I posted a question regarding source codes for 3D
    reconstruction, in particular for MDLT (see below original question for more
    details). I received two valuable replies, mostly dealing with Tsai
    algorithm (camera model), for which I am sincerely grateful about. Since my
    primary need is still not satisfied, exchanging and/or just sending my
    version of MDLT source code (Matlab) to anyone who is interested (for which
    I would like to receive confirmation that it works fine, thus I can not give
    any guarantee for it yet) will hopefully encourage someone to do the same.
    Nevertheless I am thankful for those replays bringing to my awareness the
    existence of Tsai algorithm. Therefore I would like to ask couple questions
    about it.

    1. Looking at a Tsai camera model and for instance camera model represented
    in a paper: Hatze H. HIGH-PRECISION THREE-DIMENSIONAL PHOTOGRAMMETRIC
    CALIBRATION AND OBJECT SPACE RECONSTRUCTION USING A MODIFIED DLT-APPROACH.
    J. Biomechanics, 1988, 21, 533-538 are quite similar. The only noticeable
    difference is Tsai camera model takes into account transformation between
    true (distorted) position of the point's image on the sensor plane and its
    coordinates in the camera's frame buffer and Hatze model stops right before.
    If I am right, does it mean that real improvement of Tsai model upon Hatze
    model, if any, lies in the fact that it is really necessary to take into
    account errors during digitizing process and is sufficient to incorporate
    only one coefficient for lens distortion - radial distortion?

    2. Hatze model suggests three coefficients for symmetrical lens distortion
    and two for asymmetrical lens distortion. But his paper is from ten years
    back. Are today's camera optics so good that there is no need to take
    anything more than a coefficient of radial distortion? How many of those
    coefficient incorporate today's commercial 3D systems? 3. Is Tsai camera
    model the best (or at least one of) optimum for today's reconstruction
    algorithms (camera models) or it is just one among many others (which are
    they besides traditional DLT) in every day practical use?

    Thank you all in advance. Any additional comments concerning specially the
    original question or the new ones will be posted.

    Sincerely, Tomislav.

    ORIGINAL QUESTION****************************************** ***************:

    I am post-graduate student in biomechanics. My work is primarily concerned
    with algorithms for 3D reconstruction such as DLT and its variations. I
    wrote in MATLAB function for DLT and moved on towards the MDLT, accounting
    for a fact that we have 10 independent unknown parameters rather than 11,
    and also the non-linear (M)DLT taking into account additional parameters due
    to optical distortion and decentring distortion (five additional ones).
    However I have been experiencing some difficulties with convergence of sets
    of solution and a fact that those improved algorithms do not always yield
    better (solution) reconstruction accuracy. Rather than going in more details
    with a whole list of questions (linearization, Taylor series, local minimum
    etc.) I would kindly ask you if you could provide me with (or tell me where
    I can find it; Up to this time I have located only one site giving the full
    DLT source code from Kinemat) a source code for MDLT and non linear DLT
    preferably in MATLAB, but C is all right too. Therefore I can compare it
    with mine since I believe I am pretty much clear on theory (Hatze, H.
    (1988). High-precision three-dimensional photogrammetric calibration and
    object space reconstruction using a modified DLT approach). J. Biomechanics
    28,1219-1224; Miller R., Norman et al.(1980). A technique for obtaining
    spatial kinematic parameters of segments of biomechanical systems from
    cinematographic data J. Biomechanics 13, 535-547 etc.), but I might be doing
    something wrong in implementation itself - writing a code.

    I would be glad to post summary of replies of all those who can give me some
    advice and/or are willing to share their source codes of any variation of
    DLT (or any other approach for 3D reconstruction) written in any language
    (tool).

    END OF ORIGINAL QUESTION
    REPLIES******************************************* **************************
    *******:

    Dear Tomislav,

    I can probably save you some time. Here are a number of sites that have the
    latest or most developed codes for camera calibration and reconstruction.

    Have a look.

    Janne Heikkila

    University of Oulu, Finland

    (MATLAB Toolbox - linearization/calibration very accurate -better than
    TSAI!)

    email: jth@ee.oulu.fi

    web: http://ee.oulu.fi/~jth

    Hynek Bakstein

    http://terezka.ufa.cas.cz/hynek/toolbox.html

    MATLAB toolbox and thesis (see thesis for comparison of methods!)

    Peter Corke - CSIRO (Australia) Machine Vision Toolbox (MATLAB) (Tsai
    algorithm in matlab)

    http://www.cat.csiro.au/cmst/programs/autom/pic/download.html

    Tsai Camera Calibration Software (Tsai software in C code)

    http://www.cs.cmu.edu/~rgw/TsaiCode.html

    Regards,

    Alan Morris

    Research Engineer - Gait Laboratory

    Bloorview MacMillan Centre

    350 Rumsey Road

    Toronto, Ontario

    CANADA

    M4G-1R8

    Tel (416) 425-6220 x3508Fax (416) 425-1634

    ortcam@oise.utoronto.ca

    Tomislav,

    Just a note... a very handy book for photogrammetric reconstruction

    techniques, especially when using non-linear distortion parameters and

    multiple images (rather than just 2) is called:

    Close range photogrammetry and machine vision. Edited by K.B. Atkinson,
    1996. Whittles Publishing, Scotland, UK. ISBN 1-870325-46-X

    I think you might find it useful. Sorry, I don't have any code.

    Sincerely,

    Steve

    Steven Boyd, M.Sc., Ph.D. Candidate

    Department of Mechanical Engineering

    University of Calgary

    2500 University Dr., N.W.

    Calgary, Alberta, Canada

    T2N 1N4

    phone: 403-220-2802

    fax: 403-284-3553

    email: boyd@kin.ucalgary.ca

    END OF REPLIES

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