Photogrammetric Method
By : Muharil S.Pd
These methods are the one most often used in occupational
biomechanics. One camera can be utilized when a motion is performed in one
plane , while for three dimensional analysis, two or more cameras are employed.
Figure 5.4 depicts an orthogonal arrangement for two cameras. when
the cameras
are positioned with perpendicular optical axes, accurate three dimensional coordinates of a point in space can be obtained by applying the formula (Martin and Pongratz 1974 Nigg Herzog (1994)
(54)
(5 5)
(5 6)
where
x,y,z are the actual value i of the coordinate of a given point space, XYx is the x-coordinate,
measured in the XY film plan; Zyy is the y-
coordinate measured in the Zyz is the distance from
film plane 2 to the origin along the x axis and Dz is the distance from film
plane I to the origin along the z axis A nonpependicular photographic
system,using cameras is the same plane but separated by a given distance ,has
been advocated by ayoub and ramsey (1970).
The
foregoing techniques assume optically
perfect cameras. Since optical distortion exissts, various techniques have been devised to reduce errors from those, one
method involves the use of a third camera in an orthogonal arrangement (along
the y axis in figure ) this providesa means of checking the estimates, by using
the data from the cameras in pairs that is , cameras1 and 2, 2 and 3, and 1 and
3 in the equations to yield three separate estimates of the x, y and z
coordinates.this overdetermined system is the resolved by using the mean of the with an estimated
mean error of approximately 1.0 cm.
Asecond technique for corecting for optical distortion has been suggested by
andriacchi et al (1979). A grid of known calibration points in used to define a
“ correction” polynomial are determined for the calibration grid, the
polynomial is used the “correct” the estimate obtained from equations 5.4, 5.5
and 5.6. A cluster of 10,19, and 29 calibration point was use to test this
tecnique and resulted in an average resolution of 0,57 cm for 10 points
0.56 cm for 19 points, and a0.45 cm for 29 points , which andriachi and
collegues believe would be sufficient for human motion analysis. Correction for
distortion in photogrametric method is discussed by Miller and Nelson (1976) and Nigg and Herzog (1994).
Another
requirement of a photogrammetric systemis the ability to accurately locate a
moving target. This can be accomplished by using a strobe light set close to
the optical axes of the cameras . Reflective markers are taped either directly
over the joint center on the skin or on tight-fitting clothing. The result is a
set of discrete points on a film frame
that, when joined , from a linkage movement diagram, as illustrated in figure
5.5 for a lifting activity. The strobe rate depends on the velocity of motion.
In high velocity motions of the arm such
as when one throws a ball, a strobe rate of
80-100 flashes/sec may be required to have enough data to accurately
estimate peak accelarations. In handling heavy load where in slower movements
ocur. Too fast a strobe rate results in adjacent reference markers being
optically indistinguishable . thus, an analysis of lifting may require a strobe
rate of only 20-40 flashes/sec. In general, the rule is the use the highest
strobe rate that allows point to be easily distinguished during a specific
motion.
The
problem of over lapping reference point is eliminated by using motion picture
film or video tape methods.in doing so. However. A set of at least three
stationary reference markers must be include in each frame. The coordinate of
each marker are than measured relative to thesee stationary points in each
frame analysis. Thios procedure avoids any depedence on the frame alignment
capabilty of the film or videotape transport mechanisms in the camera and the
playback unit. A discussion of marker location method and errors is presented
in deluzio et al (1993) errors of 2 4 can expected estimating joint angles. The
estimatoin of
The angular
velocity and accelaration values can be
accomplished by a number of methods, given accurate locations of joint center
for specified time intervals. A graphical methods is describes by plagenhoef
(1971). Pearson and Mcginley (1961) and fisher (1967) used the first two terms
in a taylor series expansion of the angular data from the frame at each time t. This yields, as
estimates of angular velocity and accelaration,
Where is the angular velocity of joint at time (t)
is the angular acceleration of joint at
time is the angular displacement of joint t plus a small interval with
dependent on the strobe or movie film rate, and is the angular displacement of
joint at time minus a small interval.
The
use of a taylor series expansion as the basis for deriving the proceding
equations provides some data smothing capability, since additional terms can be
added to the series. The reduces the sometimes large acceleration. Other
mathematical smothing techniques have been devised as well, some require the
statistical fitting of polynomial function to displacement curves,using a mean
least squared eror criterion . The first and second derivatives of the
resulting polynomial prediction equation represent the velocity and
accelerations functions (jackson 1979) A slightly different approachhas been to
fit spline functions to the displacement data (Zernicke et al 1976; Wood and
Jenings (1981). All of these technique computerized
analysis of the data and all depend on the user deciding how much smothing in
necessary. The peak acceleration will be under estimate and shifted in time if
the smothing is too great. To litle smothing . if the acceleration values occur
at aproximately the same in the motions, if they are of the same relative
magnitudes and if the accelerations and regular
when plotted-that is, if they have very little variance from trial to
trial then the data are probably providing good motion estimates and can be
used in subsequent biomechanical analysis.
5.2.14 Video
Spot Locator Systems
Clearly , if a fast sampling rate can be obtained without the extra
cost of film
or video data
coding, (then a major improve ment in motion analysis is possible. This concept
has led to the development of various
video systems for locating contrasting sport against a given background. Reflective
markers can be used. along with a strobe light, to provide point images for traditional
television-based video systems Contemporary systems rely on rapidly pulsed
light-emitting diodes (LEDt) or passive reflective markers
attached to the person The light rays from these spots are detected by a
special camera with a dual axis photosensitive diode, instead of with a film or
conventional videotape system When a single spot of light hits the
photosensitive diode, tt outputs the sport two dimensional
location to a digital computer.
Video sport locator systems such as Selspot™, Vicon™, Ripen
™,Vision™, MacRefkx™, and others are commercially available.
These systems can track up to 30 markers, and for one marker they
track at more than 300 Hz .Woltring and Marsolais (1980) and
Fwretti et al (1985 ) have evaluated the utility of such sysaerm and believe that, with careful calibration of
the cameras to reduce optica! and diode signal
distortion errors, the tyatems are quite accurate
for normal motion studies One
of the biggest concern in all of these spot locator systems
is the time required
To accurately track sequence of markers from multiple cameras Recall from equations 5 4-5 6, that three-dimensional spot location requires data from several
cameras to be synchronized so that the pairwise estimates of a spot's location for each interval A/ be of the same marker (i e . each marker must be
uniquely identified and not mixed up throughout the sampling period) This requires sophisticated software that automatically tracks the diserete
marker motions, even when some marker drop out (e g , when a marker is in the shadow of a body segment) or
when the trajectories of two markers merge together for several intervals
Again, a
variety of mathematical techniques are used to track digitized spot motions today. One technique,
described by Muijtjens et al (1997), showed that even when 40% of the markers
were missing tn the middle of a sequence, 70% of the remaining markers were correctly
located Still, if a minimum number of cameras are employed (i.e , duplicate
estimates are not provided), the user may have to visually inspect each camera’s
spot sequence and fiil in" missing
data before any kinematic parameters can be estimated
Chao’s (1978) examination of both photographic and videographic systems still appears to be relevant TV. The advantages of these methods are as
follows
1.
They
produce estimateof motions in an
absolute universal reference frame and
thus are easily used in biomechanical studies.
2.
Joint center can be accurately located by projecting in
intersection of the long axes of segmet (three or more ) body reference marker
placed on each segment (rather than over an estimated joint center)
3. Body
reference markers are smaller and lower in mass than those of either an
axoskeleton oraccelerometer-type of system; thus interference with normal
motion will be minimal.
4. Since multiple camera system allow the
determination of motions in three dimensions over time , diverse activities can
be studied.
5. The resulting data directly produce stick
diagram of postures and motions that
are important in describing specific motor behaviors Also, the system provides graphical feedback on the spatial positions of body segments over time.
The limitations of such systems can also be summarized This is perhaps best done
separately for each system For photogrammetric systems, the disadvantages are
as follows :
1. The film data must be manually decoded, which can be quite time
consuming and prone to human
error
2. The use of two cameras requires additional care in maintaining
alignments and frame synchrony, resulting in additional time in data
reduction In fact, Paul and Douwes (l993) have
devised estimate?, of the error caused by cameras not being aligned normal to
the plane of motion
3. If still cameras are used, reference
points cluster together it the sampling rate (is too low, making it difficult to synchronized the reference
point from different cameras.
4.
Reference points can be obscured from the camera by other body segments
5.
The additional calculations
required to estimate relative motions may produce cumulative error
Videographic
systems also have disadvantages that
must be recognized :
1. To acquaire high resolution and fast sampling with
multiple cameras, complex
and expensive electronic equipment is necessary
2.
I
Lighting condition! need to be controlled (There must be no point light
source the background )
3.
Large
amounts of data that need to be stored in a digital computer are quickiy acquired, usually requiring direct data transfer and storage when high sampling
rate« are used
4.
These
systems use a relatively new technology that requires advanced expertise
tn computer and electronic to maintain and adapt the system to specific application.
In addition to video based spot locator systems. Sonic and electromagnetic system have been developed In contrast to current video based systems, these technologis
have the advantage that the marker positions can be
tracked in real time, making them attractive for virtual reality applications With
sonic systems, the subject wears active emmiters. such as park gap devices or miniature
speakers, that transmit an inaudible (> 20 khz) tone for a
fraction of a second Multiple microphones placed at known location aound the subjeci are wad lo triangulate the location
oi the emitters, simply by measuring the time necessary for the sound to travel to each microphone Although sonic system are in expensive to build and their accuracy can be quite good, sampling rale« are restricted because of the relatively low velocity of sound waves and eminer cross talk (Raaehke et el, 1993) In electromagnetic systems an electromagnetic field is created by a centrally located transmitter
and is used by aenaors ««ached to the pervm in order to detect all sixpositional and rotational degrees of freedom (An et al, 1987) One major limitation on the use of electromagnetic «ystems tn the workplace is that they are sensitive to ferrous and conductive metal« in the environment, which can severely warp the magnetic field and cause inaccuracies However, they have the benefit that they do not have marker occlusion problems In terms of cost, these
systems, such as the Flock of Birds from Ascension Technology (Bur I ingion, Vermont), «re
comparable to video-based systems P; r ac- < lit hi y also ii comparable, with
a positional accuracy of I.I6® and t rotational avcu 'at y of I ()% of normal range of motions (Milne el
aK. 19%) An additional factor to be considered in the selection of a
motion tracking technology is the control wires required for the markers worn by the subject. In contrast to video based passive marker,both
eloctromagnetic and ultrasonic sytem require the device tobe powered via wires
, which may cut motion of the subjecti
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