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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 (<3mm) than the absolute error.

        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.

Length test 2 (secondary camera placement, wide-angle lens conformation). 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 <.000) field dependent bias. The error band of variability defined as standard deviation suggests that the size of this bias may have implications in human gait studies.

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.

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.

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.

Table 3: Mean and SD of 10 Trials of Angles Calculated by Ariel System (in Degrees) for Reference Angles 10 deg to 180 deg

Angular rotation. The six rotation placements were used to calculate a composite mean error. In data analysis,

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

Table 4: Angular Consistency Measured Across the Data Acquisition Region (in Degrees)

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.

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).

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