RESULTS
Point estimation. Mean error
was calculated for each coordinate axis (table 2). There was little difference in the size
of the mean absolute point estimation error between the 22 calibration points and the 12
extra marker points. Estimation errors observed for reconstruction of calibration points
did not appreciably differ from those encountered in the reconstruction of the extra
marker points. The average mean error associated with absolute point reconstruction was
less than 3.5mm. The relative error, which represents a grand mean of the standard
deviations of the values for the absolute error, was smaller (
Points -Y (SD) Y (SD) Z (SD)
Calibration (ii22) 3.9 (3.6) 4.3 (2.3) 2.1 (1.3)
Extra (ii = 12) 4.4 (4.2) 3.9 (3.5) 2.3 (2.9)
Grand Mean: 3.48 (absolute error).
Mean of SDs: 2.97 (relative error).
Table 2: Mean Error in Millimeters of
Point Estimates Along the x-, y- and z-Coordinate Axes
Absolute and relative point estimates for reconstruction of
the center point demonstrated similar accuracy. Mean errors for absolute reconstruction of
point estimate on repeated measures (n =10) were 1.3mm, 4.6mm, and 3.I mm along the x-, -
v-, and z-axes, respectively. Relative point estimation showed comparable variability (x =
2.7mm, v 3.7mm, z = 1.6mm).
Length test I (primary camera placement). The
mean estimate (n = 27) for a 50cm length was found to be 49.87cm (SD 0.35). Estimates for
cells located in the center of the data acquisition region were consistently
overestimated. Estimates for cells located in the periphery were consistently
underestimated. However, upon analysis of variance (ANOVA) of length versus distance from
the centerline of the acquisition region, the differences were found not to be
statistically significant.
the error value for each rotational placement was
transformed into an absolute value and a mean error was then calculated. The size of mean
error (0.71 deg, SD 0.47) was larger than those observed in previous angular tests
reported in this study. Although the pattern of error associated with the degree of
rotation was difficult to characterize, a sign bias was observed. Twenty-five of the 30
angular estimates underestimated the reference angle (fig 4).
Fig 4-Angular rotation results. The estimate by the
Ariel system of the angle defined by the goniometer arms is plotted against the rotation
placement angle, the angle between the xz plane, and the plane defined by the goniometer.
In each case, the true value of the angle is the value label on the y-axis (goniometer
angle axis). The second set of axis labels to the right of the drawing shows the deviation
of the system estimate in degrees from the true value of the goniometer angle.
Table 4: Angular Consistency Measured
Across the Data Acquisition Region (in Degrees)
Goniometer Setting Mean Deviation 50
30 0.09 0.25
60 0.05 0.52
90 0.00 0.25
120 0.41 0.61
150 0.34 0.44
Angular rotation. The six rotation placements
were used to calculate a composite mean error. In data analysis,
Table 3: Mean and SD of 10 Trials of
Angles Calculated by Ariel System (in Degrees) for Reference Angles 10 deg to 180 deg
Goniometer Reference Estimate Average
Setting Angle Mean Deviation 50
10 10.1 10.1 0.0 0.409
20 20.2 20.0 0.2 0.225
30 30.1 30.0 0.1 0.297
40 40.3 40.0 0.3 0.369
50 50.7 50.0 0.7 0.254
60 60.6 60.7 0.1 0.307
70 70.8 70.6 0.2 0.384
80 80.7 80.3 0.4 0.312
90 90.8 90.4 0.4 0.489
100 100.9 100.9 0.0 0.203
110 111.1 110.8 0.3 0.368
120 121.1 120.7 0.4 0.438
130 131.1 130.9 0.2 0.521
140 140.8 140.8 0.0 0.241
150 150.9 150.8 0.1 0.469
160 160.9 160.4 0.5 0.402
170 170.5 169.9 0.6 0.503
180 180 178.6 1.4 0.596
180* 180 180.0 0.0 0.542
Derived from segment angles.
Angular consistency. A mean angle value was
calculated by averaging angle reconstruction data observed across the data acquisition
region. The absolute magnitude of the difference between the known reference angle and its
mean estimate defined the measurement error. Measurement errors observed for the reference
angles (n = 5) were all less than 0.5 deg (table 4). Accuracy and consistency of angular
estimates for references angles corresponding to goniometer settings 30 deg through 90 deg
were found to be excellent; the difference between the reference angle and its mean
estimate was consistently found to be less than 0.1 deg across the data acquisition field.
Increased variability for larger angles (goniometer settings 120 deg and 150 deg) may be
meaningful or may reflect procedural artifact. Some vibration of the movable arm was noted
on film as the cart was wheeled along the data acquisition path that may have contributed
to the random error represented by the standard deviations. A systematic pattern of error
dependent on position in the data acquisition field was also observed. Data collected at
one end of the filming region exhibited a consistent overestimation of the reference
angle, whereas data collected at the other end of the filming region exhibited a
consistent underestimation of the reference angle. This phenomenon was observed
independent of camera placement, calibration frame orientation, or direction of motion
sequence. Although the size of this error may not be clinically significant in human gait
studies, these latter two observations require further study.
Angular
accuracy. The mean (n = 10) value for each reference angle is presented in table
3. The mean of the average deviations (n = 17) derived for goniometer settings 10 deg to
170 deg was found to be 0.26 deg (SD 0.21). The average mean within trial variability
(0.36 deg, SD 0.10) was derived by averaging the SD for each of the reference angles.
Angular estimates of reference angle 180 deg showed a much larger error (1.4 deg, SD
0.59). Recalculation of estimates for 180 deg using the segment angle analysis option
corrected this error (0.13 deg, SD 0.54). This option corrects for errors in angle
estimation caused by the behavior of the cosine function in the neighborhood of 180 deg.
The mean estimate (n = 27) for a 50cm length was found to be
49.95cm (SD 0.78). As in length test 1, there was a clear pattern of overestimation of
model length in the center cells and underestimation of model length for cells located in
the periphery. In contrast to test 1, however, a test of ANOVA of length versus distance
from the centerline of the acquisition region showed a significant (p
Length test 2 (secondary camera placement, wide-angle
lens conformation).