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  • Camera positioning - Update

    Below is my original question, responses from BIOMCH-L and finally our own
    findings (very briefly) relating to camera positioning. I would like to
    thank everyone for their response.

    ===============Original Question==========================================

    We are doing some 3D video work using two cameras that requires the cameras
    to be unusually close together; i.e. about 30 degrees apart. I can find
    plenty of literature and manuals that state that the cameras should be 90
    degrees apart or between 60 and 120 degrees apart, but all of these appear
    to be rule of thumb. I can't find any literature that has scientifically
    monitored what happens at various angles and how far you can go as the sine
    of angle between the cameras approaches zero.

    While we are testing our specific 30 degree problem, if anyone has any
    experimental information relating to this topic or can lead me to some
    articles I'd be grateful if you could contact me.

    I will put useful responses on BIOMCH-L for your perusal.



    ===============BIOMCH-L Response==========================================

    >From Tue Nov 1 03:23:14 1994

    When we were testing a special DLT procedure with panning cameras (J.
    Biomechanics, 26: 741-751, 1993), the angle between two cameras was about
    15 degrees, and the mean calibration errors were lower than 20 mm. In our
    application of this procedure, we tried to maximize the the angle between
    the two cameras. The maximum angle we had might be about 30 degrees and the
    mean calibration errors were about 10 mm. If you are going to use DLT
    procedure for stationary cameras, the mean calibration error could be well
    below 10 mm if the angle between the two cameras is no less than 30 degrees.
    Good luck.

    Bing Yu, Ph.D.
    Orthopedic Biomechanics Laboratory
    Mayo Clinic
    Rochester, MN 55905


    >From Tue Nov 1 03:23:27 1994

    I am a Ph. D. student and I have quite alarge experience with 3D data
    collection (my masters degree is in biomechanics). We are currently
    collecting data with cameras at about 50 degrees. The main problem is
    that the error in the "depth" direction is twice as large as the other
    two directions. My guess is that as you close more and more the angle
    the error in the "depth" direction becomes larger and larger.
    In our case, the "depth" direction has little relevance for the type of
    data we will be looking at. However, if that is also your case, you may
    want to consider to collect 2D data instead.
    Rosa M. Angulo-Kinzler


    >From Tue Nov 1 07:33:10 1994

    I do not have any references, but I used cameras that were rather close
    in my dissertation experiments last year. The main problem (using Motion
    Analysis sistem) was that the algorithms for identifying the 3-d position
    of some points in space got confused by the two cameras that were the

    One posible solution (it worked for me): consider not only the angles
    among cameras on the horizontal plane, but on other planes as well (i.e.,
    use one camera higher than others, pointing at a different vertical angle
    to the target).

    Luis Fernando Aragon-Vargas, PhD Phone & Fax +506-227-9392
    School of Physical Education e-mail:
    Universidad de Costa Rica


    >From @QUCDN.QueensU.CA:anglin@conn.ME.QueensU.CA Tue Nov 1 07:35:04 1994

    We worked with two cameras about 50 degrees apart to monitor arm motions
    for daily-living activities. We were also constrained in our angle in
    order to keep the markers in view at all times for the 22 different
    actions (although there was some provision for missed markers on each
    frame). For the larger angles, the cosine is still reasonably close to
    one; as you said this gets worse for the smaller angles. However, all
    you are really concerned about is the accuracy, so if you can demonstrate
    through calibration tests that your accuracy is sufficient for your
    purposes, then 30 degrees should be fine. The other solution could be to
    add a third (overhead) camera.

    Best of luck,

    Carolyn Anglin
    (P.S. The work was done at the University of British Columbia, Mechanical


    >From Tue Nov 1 07:56:31 1994

    Hi Russell,
    There is a paper in 'Photogrammetic Engineering' by Y.I. Abdel-Aziz,
    1974,p1341-1346 called 'Expected Accuracy of Convergent Photos'. In it,
    he discusses your problem. If you consider the axes to be Y vertical, X
    horizontal, and Z toward the camera, Y accuracy stays pretty much the
    same with angle (you'd expect that). Z accuracy degrades to about 1/4 of
    the Y accuracy at 30 degrees between the two cameras. X accuracy is
    about the same as the Y accuracy. As the angle increases, you must
    compromise between X and Z accuracy.
    Since the depth measurement is determined by the difference between
    the images of the two cameras, it is intuitive that the more identical
    the two images are (ie, smaller angle), the more difficult it is to
    extract the differences accurately. With ideal cameras there's no
    problem....but with video cameras and their shortcomings there will be a
    lot of trouble when you look at the difference signals.
    Another paper is : 'N.A. Borghese and G. Ferrigno',"an Algorithm for
    3-D Automatic Movement Detection by Means of Standard TV Cameras",IEEE
    Transactions on Biomedical Engineering",Vol 37,No.12,p1221-1225,Dec.
    1990. Their data suggests about 3 times the error you would get at the
    optimum 90 degrees.
    I would think that there should be a fair number of papers out there
    by now, as this subject has pretty well been beaten to death.


    Paul J Guy work phone:519-885-1211 ext 6371 home/FAX/:519-576-3090 64 Mt.Hope St.,Kitchener,Ontario,Canada


    >From Tue Nov 1 09:27:46 1994

    Dear Russell

    Ian Stokes at Vermont should be able to help.
    I think Manohar Panjabi published something in J Biomech a few years ago.
    I've only just moved to Flinders and haven't got all my papers here with me
    yet but there is something in the literature on this subject that shows that
    accuracy drops off if you have an angle below 60 degrees. Good luck in your
    search. Please let me know what you find out.

    Mark Pearcy
    Associate Professor of Biomedical Engineering


    School of Engineering
    Flinders University of South Australia
    GPO Box 2100
    South Australia 5001

    Phone: (+61) 8 201 3612
    Fax: (+61) 8 201 3618


    >From Tue Nov 1 10:00:01 1994

    I would say that you don't need experimental data about your
    specific problem. All what you need is an estimate (based on the
    literature, of course) of the error you can have on each of the
    two separate 2D views. Also, you need to determine how large
    your field of view will be, for each camera (in degrees). In fact,
    in your case the error will be larger for points located farther
    away from both cameras than the intersection of the two optical
    axes (I hope I was clear enough).
    Knowing the above data, it is quite easy to calculate the
    statistical probability of a given error, or the amount of error
    associated with a given probaility level (for example, 5%). The
    problem should be solved, in my opinion, calculating the error
    on the horizontal plane (assuming that both your cameras are
    oriented with their optical axes horizontally).
    I was not explicit, but you can probably guess what I mean.
    Please let me know if you agree, or if you want more details.


    Paolo de Leva
    Istituto Superiore di Educazione Fisica
    Biomechanics Lab
    Via di Villa Pepoli, 4
    00153 ROME

    Tel: 39-6-575.40.81
    FAX: 39-6-575.40.81 (or 39-6-361.30.65)

    e-mail address:


    >From Tue Nov 1 23:24:01 1994

    Dear Russell

    Suggest you contact Harvey Mitchell at E-mail:

    He lives in your part of the world and is an expert on
    Stereo video technology, (sometimes called digital photogrammetry).


    Barbara van Geems
    Department of Biomedical Engineering
    University of Cape Town Medical School
    Observatory 7925
    South Africa
    Tel: (021) 406-6547
    Fax: (021) 448-3291


    >From CRISCO@BIOMED.MED.YALE.EDU Tue Nov 1 23:30:56 1994

    For two camera systems I am pretty sure that the optimal angle is close to
    30 degrees when using such code as DLT for 3D reconstruction. I can not
    rember where I read this but you might try: Marzan and Karara (1975) A
    computer program for direct linear transformation of the colinearity
    condition, Symposium on close range photogrammetric systems, july28-aug1,
    Champaign, Illinois.

    Trey Crisco


    >From Wed Nov 2 15:31:48 1994


    I spent 7 years conducting 3D analyses with video and optoelectric
    cameras. If your cameras are only 30 degrees apart, you may
    have a large error in the depth dimension. The two cameras
    will track horizontal and vertical spacial coordinates fairly
    accurately, however, look closely at the third coordianate.

    Good Luck



    >From Thu Nov 3 02:58:45 1994

    please, give a look of our paper:

    Borghese NA, Ferrigno G - An Algorithm for 3-D Automatic Movement Detection by
    Means of Standard TVCAmeras - IEEE Trans. of BME vol. 37, NO.12, 1990.

    At pag. 1224 we report what happen varying the angle bwteen the cameras by
    numerical simulations, at 30 degrees you should expect a decrease in depth accuracy of a
    factor of 2.

    Nunzio Alberto Borghese


    >From KOLLJO1@VM.AKH-WIEN.AC.AT Fri Nov 4 19:13:31 1994

    Hallo from Vinna-Austria

    We are a group running a Gaitlab with videometry 6 camera system.
    There is no way out for dealing with rule over the thumb for cameraposition.
    It means much more trials with experience than a theoretical approach. If you
    deal with two cameras the theoretical optimum is 90 degrees between the
    lensaxis. This would give you least 3D errors because of digitalisation error
    or lens distortion.
    But you should have in mind that the most difficult thing to manage with two
    cameras are covered or merging markers which results in loosing the track.
    So the best cameraposition depends on your marker set. If you are
    flexible with the marker set you should choose one where no hiding or merging
    occours for camera postions that are as near to 90 degrees as possible.
    If, for some other reason, you are restricted to 30 degrees between the
    cameraaxes, you have to deal with doubled 3D location errors for markers in the
    depth (i.e. the direction your cameras look and oposit).

    VIDEOMETRY AND FORCEPLATES; Proc. Third International Symposium on 3-D Analyis
    of Human Movement, Stockholm Sweden 1994:49


    >From Mon Dec 12 18:39:00 1994


    I adressed the topic in my doctoral dissertation ...

    Walton, James S. "Close-Range Cine-Photogrammetry: A Generalized
    Technique for Quantifying Gross Human Motion. Doctor's Dissertation,
    The Pennsylvania State University, 1981.

    Jim WALTON

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    * 4D VIDEO * Jim.Walton@Forsythe.Stanford.Edu *
    * 3136 Pauline Drive * *
    * SEBASTOPOL, CA 95472 * BITNET : Jim.Walton@Stanford.Bitnet *
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    ===============Our Findings (in brief)====================================

    We tried to break down where the errors were coming from, ie. small angle
    between cameras, digitiser repeatability, camera resolution, calibration

    Our greatest error came initially from the calibration frame. We were using
    an open ended frame (sometimes called a Christmas tree or sputnik) that we
    bought from a motion analysis company about two years ago. The frame was
    factory measured to millimetre accuracy. When we re-measured the frame, we
    found that some coordinates of some points were out by up to 10mm. This,
    resulted (when combined with all other errors) in marker accuracies after
    3D reconstruction of up to 20-30mm (3D distance). The markers we used were
    a fixed distance apart (700mm), auto-digitised and the field of view was 2m.

    Rather than re-measuring our calibration frame, we decided to build our own,
    closed (cuboid) calibration. We did this for three reasons. First, because the
    open frame would continue to deteriorate over time and the closed system was
    less likely to change over time. Second, building our own ended up being
    cheaper and quicker than getting surveyors to remeasure the open frame.
    Third, a closed system would be easier to remeasure at a later date and easier
    for us to control placement of makers in whatever orientation we needed.

    We got very satisfactory results from our cuboid (we didn't compare the cuboid
    with the open frame because we didn't have accurate measurements for this
    system). We had a field of view of about 1.5m (about 3mm per pixel), manually
    digitised, markers were fixed distances apart and were 3mm diameter ball
    bearings covered with 3M reflective tape. The reflection from the bearing was
    obviously much greater than one pixel and the centroid calculation actually
    improved the resolution of the system. The errors were often around 2-3mm and
    never greater than 6mm. This 6mm error occurred along the depth direction,
    which was always worse, while the other directions amounted to a maximum error
    of 4mm. This is more than satisfactory and we decided not to take it any
    further at this stage.

    A colleague of mine, Rezaul Begg (, did most of this
    work and is currently conducting more detailed experiments relating to camera
    angles and distances from the centre of field view. We are currently getting
    our open calibration frame remeasured because the cuboid is not easily
    transportable (it is one piece).