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Stereophotogrammetric error sources

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  • Stereophotogrammetric error sources

    Dear subscribers,

    I believe that this is a topic that can be explored in detail only on a
    mailing list. The phenomenon is assumed to be known, but actually it is
    quite complex and, as far as I know, nobody described it in detail and
    thoroughly (if I am wrong, please let me know). Examples of sources of error
    affecting simpler measurement instruments are given in engineering
    textbooks. There’s no space in a scientific paper for an in-depth analysis
    of a phenomenon which is assumed to be known. I attached below a list of
    papers each of which briefly summarizes the sources of stereophotogrammetric
    error. I will give you my analysis in the next paragraphs. Is there anybody
    who would like to discuss it?

    IMPORTANT NOTE: this posting is not about the “soft tissue artifact”, which
    is an error in the estimated position of anatomical landmarks and bones. The
    STA has been already discussed on BIOMCH-L, and the literature about it is
    profuse and exhaustive.

    The stereophotogrammetric error is defined herein as the error in the
    reconstructed three-dimensional (3-D) position of a single retroreflective
    or light-emitting marker. The sources contributing to this error vary with
    the adopted technology. In the most widely used systems, which use
    retroreflective markers and multiple cameras endowed with CCD or CMOS image
    sensors, the stereophotogrammetric error is mainly due to these sources
    (sorted by order of appearance in the data collection and processing flow):

    1. Non-uniform reflectivity of the marker surface. The information about
    marker position is initially transmitted to the cameras by reflected light.
    A non-uniform marker reflectivity may deform the optical image of the marker
    projected on the surface of an image sensor, or cause an unexpected
    distribution of the photons forming the image. Note that the circle-fitting
    algorithms used to locate the marker image centroid typically assume that
    the image is circular, and in some cases (Vicon MX® systems) also assume
    that the intensity of the light decreases as the distance from image center

    2. Partial or total occlusion of the marker with respect to one or more
    video-cameras. Occlusions are defined as situations in which a marker is
    partially or totally hidden by parts of the subject’s body, or objects in
    the environment, or other markers. Partial occlusion, by deforming the
    marker image, causes an inaccurate determination of the marker center
    position on the image plane (this error is reduced but not eliminated by
    systems ignoring non-circular marker images or using pixel grey level values
    to locate the marker center). Total occlusion reduces 3-D reconstruction
    precision by reducing the number of video-cameras which can provide raw 2-D
    coordinates. Total occlusion is often preceded by partial occlusion. These
    sources may occasionally produce very large error peaks (“wild points”) or
    discontinuities in the reconstructed marker trajectory. These errors may
    have an absolute value by one order of magnitude larger than the standard
    deviation of the stereophotogrammetric error estimated in ideal conditions
    of marker visibility.

    3. Spatial quantization error. An image sensor contains an array of
    photodetectors, and its finite spatial resolution entails a quantization of
    the spatial information transmitted by the light. When a cloud of photons
    strikes a photodetector, during an exposure interval, the photodetector
    measures its energy, independently of the distribution of the photons on the
    photodetector surface. Thus, while the optoelectronic transduction performed
    by the sensor involves a natural quantization with negligible error (photons
    and electrons are very small quanta), the position of the photons is
    non-negligibly quantized. Typically, the light reflected by a marker hits
    more than one photodetector. In this case, the spatial quantization error is
    partly compensated by the more or less sophisticated circle-fitting
    algorithms used to locate the marker image centroid. These algorithms
    exploit a priori information about the image to achieve an apparent
    sub-pixel resolution (Furneé, 1997). For instance, the shape of the image is
    typically assumed to be circular. However, this produces an error when the
    marker is partially occluded, or non-spherical, or non-uniformly reflective.

    4. Resonance of video-camera support (wall brackets, tripods, etc.) to
    possible environmental vibration produced, for instance, by vehicles. This
    source of error is assumed herein to be negligible, because vibration, if it
    exists, is not likely to persist and be stationary for all trials in a
    motion capture session.

    5. Motion blur. When the marker moves relative to a camera its recorded
    image appears stretched in the direction of its relative motion. When the
    velocity of the relative motion is not constant, the centroid of this
    stretched image does not coincide with the mean position of the centroid of
    the optical image, during the exposure interval. This error is correlated
    with exposure time, which in turn can be minimized provided that the image
    sensors are highly sensitive and the markers are properly illuminated
    (typically by stroboscopic light projectors).

    6. Electronic noise, which produces flickering of the marker image produced
    by each video-camera, even when the marker is motionless relative to the

    7. Quantization error in the analog-to-digital conversion of the signal
    associated with each pixel.

    8. Inaccuracy of the system calibration parameters, for instance due to
    inaccuracy of the reference measures or limitations of the optimization
    algorithm used for calibration.

    9. Unavoidable limitations of the system calibration model; for instance,
    discrepancies between the structural imperfections of the video-cameras
    (such as lens aberrations or geometric irregularities of lenses and image
    sensors, or misalignment of lenses relative to image sensors), and the
    mathematical model used to represent them; in most systems, the calibration
    model is designed to partly compensate for the image distortion produced by
    these imperfections. A complete compensation is impossible.


    Cappozzo A, Della Croce U, Catani F, Leardini A, Fioretti S, Maurizi M, et
    al. Stereometric system accuracy tests. In: Measurement and data processing
    methodology in clinical movement analysis-preliminary. CAMARC II Internal
    Report; 1993.

    Cappozzo, A., Della Croce, U., Fioretti, S., Leardini, A., Leo, T., Maurizi,
    M., 1994. Assessment and testing of movement analysis systems: spot checks.
    Gait and Posture 3, 172.

    Della Croce U, Cappozzo A. A spot check for estimating stereophotogrammetric
    errors. Med Biol Eng Comp 2000;38:260–6.

    DeLuzio KJ, Wyss UP, Li J, Costigan PA. A procedure to validate
    three-dimensional motion assessment systems. J Biomech 1993;26:753–9.

    Ehara Y, Fujimoto H, Miyazaky S, Tanaka S, Yamamoto S. Comparison of the
    performance of 3-D camera systems. Gait Posture 1995;3:166–9.

    Ehara Y, Fujimoto H, Miyazaky S, Mochimaru M, Tanaka S, Yamamoto S.
    Comparison of the performance of 3-D camera systems II. Gait Posture

    Furnée H. Real-time motion capture systems. In: Allard P, Cappozzo A,
    Lumberg A, Vaughan K, editors. Three-dimensional analysis of human
    locomotion. New York: Wiley; 1997. p. 85–108.

    Holden JP, Selbie S, Stanhope SJ. A proposed test to support the clinical
    movement analysis laboratory accreditation process. Gait Posture

    Morris JRW, MacLeod A. An investigation of the sources and characteristics
    of noise in a video-based kinematic measurement system. In: Models,
    connections with experimental apparatus and relevant DSP techniques for
    functional movement analysis. CAMARC II Internal Report; 1990.


    Cappello A, Leardini A, Benedetti MG, Liguori R, Bertani A. Application of
    stereophotogrammetry to total body three-dimensional human tremor. IEEE
    Trans Rehabil Eng 1997;5(4):388–93.

    Everaert DG, Spaepen AJ, Wouters MJ, Stappaerts KH, Oostendorp RA. Measuring
    small linear displacements with a three-dimensional video motion analysis
    system: determining its accuracy and precision. Arch Phys Med Rehabil

    Haggard P, Wing AM. Assessing and reporting the accuracy of position
    measurements made with the optical tracking systems. J Motor Behav

    Klein PJ, DeHaven JJ. Accuracy of three-dimensional linear and angular
    estimates obtained with the Ariel performance analysis system. Arch Phys Med
    Rehabil 1995;76:183–9.

    Richards JG. The measurement of human motion: a comparison of commercially
    available systems. Hum Mov Sci 1999;18:589–602.

    Thornton MJ, Morissey MC, Coutts FJ. Some effects of camera placement on the
    accuracy of the kinemetrix three-dimensional motion analysis system. Clin
    Biomech 1998;13:452–4.

    Vander Linden DW, Carlson SJ, Hubbard RL. Reproducibility and accuracy of
    angle measurements obtained under static conditions with the motion analysis
    video system. Phys Ther 1992;72:300–5.

    With kind regards,

    Paolo de Leva

    Department of Human Movement and Sport Sciences,

    Istituto Universitario di Scienze Motorie

    Rome, Italy