## 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.

**Length test 2 (secondary camera placement, wide-angle lens conformation).**