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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
increases.
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
camera.
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.
REFERENCES
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
1997;5:251–5.
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
2003;17:205–13.
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.
REFERENCES ABOUT ACCURACY OF SPECIFIC SYSTEMS
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
1999;80(9):1082–9.
Haggard P, Wing AM. Assessing and reporting the accuracy of position
measurements made with the optical tracking systems. J Motor Behav
1990;22:315–21.
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
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
increases.
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
camera.
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.
REFERENCES
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
1997;5:251–5.
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
2003;17:205–13.
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.
REFERENCES ABOUT ACCURACY OF SPECIFIC SYSTEMS
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
1999;80(9):1082–9.
Haggard P, Wing AM. Assessing and reporting the accuracy of position
measurements made with the optical tracking systems. J Motor Behav
1990;22:315–21.
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