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Technical Reports |
DJ Wilson, PhD, is Clinical Assistant Professor, Gait Laboratory, Department of Physical Medicine and Rehabilitation–DC 0046.00, Howard A Rusk Rehabilitation Center, University of Missouri–Columbia, One Hospital Dr, Columbia, MO 65212 (USA) (dan_wilson{at}pmr.missouri.edu). Address all correspondence to Dr Wilson
BK Smith, JK Gibson, PT, OCS, BK Choe, BC Gaba, and JT Voelz were graduate students, Department of Health and Exercise Sciences, University of Missouri–Columbia, at the time this study was conducted
Submitted July 28, 1998;
Accepted February 24, 1999
 | Abstract |
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Key Words: Accuracy • Digitization • Kinematics • Videotape analysis
| Introduction |
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One measure of a system's accuracy is the degree of agreement between a reference standard and the estimates of that standard made by use of the system. There has been general agreement among researchers that system users should determine the limits of their system's accuracy in order to provide a basis for making inferences based on the data. To provide system users with suggestions and bases of comparison, several authors1–3,5,6 have published accuracy limits for a variety of kinematic systems (Tab. 1). The common method in these studies is the use of automated digitization.
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and the Peak Performance Technologies System,
record the images directly on videotape. A computer frame-grabbing board is then used to convert the images to digital information so that they may be scanned for light-intensity contrasts. The light intensity of each pixel is determined, and those light intensities above a user-defined level are used to calculate coordinate positions. The use of the videotaped images makes the portability of such systems possible, allowing the videotape data to be collected in a variety of settings. These settings, however, may not always provide the conditions necessary for automated digitization. For example, in our gait laboratory, we often film patients outdoors on a variety of walking surfaces to evaluate their gait. The process of obtaining videotaped images and digitizing them manually off-line creates a number of potential sources of error. Among these sources of error are digitizer (observer) error, calibration error, marker error, and skin movement or artifact error.7 Digitizer error affects both the accuracy and the reliability of measurements obtained with a motion measurement system.4 Digitizer error often arises from improper manual alignment of the superimposed crosshairs with the landmark of interest. The crosshairs, provided by the software to aid in locating the landmarks, must be positioned exactly for accurate position determination.
Tracking errors occur when the object of interest cannot be located accurately during motion. These errors most often occur due to movement that is too rapid for the hardware capabilities of the system. The Nyquist theorem states that the frame rate must be twice the motion rate for accurate measurement. For example, a 60-Hz camera records every 0.017 second. Movement that occurs repeatedly during this time frame at a higher rate than 30 Hz cannot be tracked accurately. In this study, we chose to investigate the effects of both digitizer error and tracking error on the accuracy of a motion measurement system.
The purposes of this study were (1) to determine the limits of accuracy in determining intersegmental angles during pendular motion at varying speeds and (2) to determine changes in accuracy introduced by autodigitization and digitization by experienced manual raters. To create the most realistic scenario possible for both clinical gait laboratory and research, multiple raters participated. Each digitizer performed a manual reduction of the same images to allow for interdigitizer comparisons.
| Method |
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TopAbstractIntroductionMethodResultsDiscussionConclusionReferences |
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were placed at 30-degree angles relative to the plane of activity for filming (Fig. 1). The camcorders were equipped with 12:1 variable-speed control power zoom lenses with digital focus. Film speed was 60 Hz, with a shutter speed of 1/500 second. A single 300-W floodlight was positioned to the outside of each camera to illuminate the retroreflective markers. Each camera was placed at a height of 101.6 cm.
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was used for the analysis of videotapes. Ariel software, version 6.92, was used on an AST IBM 386 computer, with videotaped images converted to digital information before digitizing using a frame-grabbing board. A calibration structure was constructed of 5.08-cm polyvinyl chloride piping. Thirty calibration points (system maximum) were inserted over 8 threaded 1.27-cm metal calibration rods. Each calibration point consisted of a 2.54-cm-diameter spherical wooden ball wrapped in retroreflective tape. The calibration balls, which had holes through their centers, were inserted over the calibration rods at 30.48, 60.96, 91.44, 121.92, and 152.42 cm from ground level. This placement of calibration balls formed a rectangular calibration area 182.88 cm wide (x direction), 152.40 cm high (y direction), and 60.96 cm deep (z direction). The position of each of the 30 balls was verified prior to data collection by 3 independent observers using a metal tape measure until all observers' measurements agreed.
The testing equipment consisted of a rigid T-shaped pendulum suspended by the bottom edge (Fig. 2). The pendulum was fastened to a piece of plywood, which served as the background, by a metal bolt. The bolt served as the axis of rotation, and nonplanar movement about the bolt was minimized. Eight spherical 1.90-cm-diameter polystyrene balls wrapped in retroreflective tape were secured to the pendulum with double-sided tape. The background plywood and pendulum were painted black in an effort to minimize reflection.
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To provide a common spatial orientation for comparison, 10 frames on either side of the vertical downward position were digitized for each angular speed. The angular speed changed across these 20 frames, except for the zero-movement condition. The variability due to this change in angular speed on a frame-to-frame basis is hereafter referred to as "frame." The data collection procedure thus produced 120 reconstructed angular estimates (12 angles x 10 trials) for each of the 4 angular speeds.
Data Reduction
The 80 independent film clips (4 angular speeds x 10 trials x 2 views) were manually digitized across the 20 frames by 5 experienced raters. Each rater had a minimum of 16 weeks (an academic semester) of experience in manual digitization. Data produced by each person's digitization were compared with autodigitized data to verify their accuracy. The data were transformed to 3-D coordinates using direct linear transformation (DLT) and smoothed with a Butterworth second-order, low-pass recursive filter. The filter's cutoff frequency (fc) was chosen on the basis of the point of linearization of the filtered and unfiltered displacement, using successive increments in the fc.8 The fc chosen (6 Hz) agreed well with values for fc in published human gait analysis studies.9 Three-dimensional coordinates generated by the DLT were used to compute reconstructed estimates of the 12 reference angles across the 20 frames at each angular speed.
Data Analysis
Variability scores (error) for each angle were calculated by subtracting the reconstructed 3-D angle from the calculated reference angle. Independent variables included the pendulum's release position (angle), the angles formed by the markers attached to the pendulum (angle), the 20 frames digitized for each trial (frame), and the 6 raters (including autodigitization) (rater). A 4-factor (position x angle x frame x rater) analysis of variance (ANOVA) for repeated measures on each variable was used to evaluate accuracy. Angle and frame were treated as blocking variables to eliminate any interactions with position or rater. This statistical treatment does not include the variability due to these 2 variables in the main effects (rater and position) ANOVA.
Intraclass correlation coefficients (ICCs) were used to estimate the variability within release positions (across frames). The ICCs were calculated for each rater within each release position. The ICC is a measure of the similarity among the angle estimates within a given angular speed relative to the differences among the angular speeds.10 The ICCs were calculated as a percentage of variation among groups as follows:
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| Results |
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TopAbstractIntroductionMethodResultsDiscussionConclusionReferences |
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Results of the overall ANOVA for the general linear model are shown in Table 3. Each of the main effects and the position x rater interaction were significant (effects discussed individually in next section). We tested for differences due to rater within each position and for differences due to position for each rater.
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The overall ANOVA for each of the 4 release positions was significant (F=16.28; df=3,37; P <.0001) (Tab. 3). The results of the ANOVA for the rater effects by position are summarized in Table 4. A Tukey multiple-comparison test for each release position revealed the mean error for the autodigitized trials (0.255°) to be larger (P <.01) than the mean error for most of the manual raters (range=0.080°–0.203°). The results of the Dunnett test confirmed that the mean error for the autodigitized trials was larger (P <.0001) than the mean error for all of the manual raters (except rater 3 for the zero-movement trials) for each of the 4 release positions (Tab. 4).
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The 90-degree release position produced the least consistency for each rater, except for rater 2. The range of ICCs for this release position was .703 to .883. Despite the greater angular speed (relative to the 90° release position), the 120-degree release position produced ICCs ranging from .884 to .939.
| Discussion |
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TopAbstractIntroductionMethodResultsDiscussionConclusionReferences |
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The autodigitized trials contained greater error (
°=0.223°) than the manually digitized trials (=0.153°). The reason for the greater error within the autodigitized trials was unclear; however, we believe that lighting conditions may have produced digitizing error specific to autodigitization. While filming an object imotion, lighting conditions may produce errors in centroid identification.7 Centroid calculations are based on the mathematical center of all pixels identified above a threshold light level. In our laboratory, we have identified varying pixel configurations as lighting conditions are altered due to the motion of the object being videotaped. In contrast, manual raters have the advantage of a spherical presentation of markers even if shading conditions of the marker are inconsistent. The center of the marker may be identified regardless of uneven lighting of the marker. A number of other potential sources of error will be discussed later in this section.
Despite the largest error values, the measurements obtained in the autodigitized trials had the best reliability. This result seems to indicate that errors in the autodigitized trials were consistent, perhaps indicating a nonrandom (systematic) error component. Whether this nonrandom error was specific to our data collection setting or system is unclear. Similar studies performed in other laboratories may help answer this question.
The results of this investigation may be deceiving, given the various statistically significant differences reported. The statistically significant differences in error reported do not imply a lack of clinical utility of the kinematic data. The range of errors for the 12 angles was 0.028 to 0.556 degree. We believe these values are clinically acceptable, in agreement with error ranges reported by other authors.1,2,5 Statistical interpretation of the results is relevant only to the degree that it may help find ways to reduce error by improving instrumentation or data collection methods.
The generalizability of our results is limited with respect to clinical applications. The idealized data collection setting used to evaluate the limits of the system's accuracy does not reflect all of the sources of error that may exist in clinical settings. One important source of error in clinical videotape settings is the placement of external markers on the body to estimate joint rotational centers or the mechanical axis of a body segment. There is some question as to whether these markers can be placed in the correct locations and whether these placements can be reproduced. It is generally difficult to locate a good estimate of the instantaneous center of rotation.11 Due to the idealized setting used here, instantaneous centers of rotation were not estimated. In clinical practice, however, at least 3 markers are necessary to calculate 3-D angles between 2 rigid bodies: one on the instantaneous center of rotation and one on each body (segment). The use of 2 markers on each body segment allows for the calculation of the angular change between the lines (vectors) connecting the markers on the respective segments. Error in the placement of markers at any of the 3 points will produce error in the angle calculated from these markers.
Schamhardt et al7 contended that the size of the markers is the main determinant of the obtainable accuracy in a kinematic system. For a high resolution (1,000 x 800 pixels) image system, covering a field of view of 5 x 4m, 5 pixels or image lines in height and width was reported to be needed for acceptable accuracy. Dividing the screen resolution (1,000 pixels) by the field of view (500 cm) gives the conversion factor (2 pixels/cm) for finding the needed marker size. Subsequently dividing the required image lines (5 pixels) by the conversion factor gives the marker size (2.5 cm diameter) needed to obtain the required accuracy.
In our study, the APAS' image resolution is governed by the frame-grabbing board. The board has an image resolution of 640 x 480 pixels. The 1.83 m (width) x 1.52 m (height) field of view used in this study, therefore, would require 1.43-cm-diameter markers (5.0 pixels/3.50 pixels/cm) for acceptable accuracy. The 1.90-cm-diameter markers used should not have created unacceptable errors in accuracy.
One source of error that was not present in our study was the possibility of miscalibration. Calibration must be performed in order to determine the positions of the camera(s) in the laboratory space. The accuracy of the 3-D coordinates is determined mainly by the accuracy of the calibration process. Estimates of the distance between the D and H markers (59.8 cm) on the pendulum (Fig. 2) obtained by the APAS were exact.
| Conclusion |
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| Footnotes |
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This study was funded, in part, by the National Institute of Child Health and Human Development, National Institutes of Health (grant 5 T32 HD07460–05).
The opinions contained in this article are those of the grantee and do not necessarily reflect those of the National Institutes of Health.
* Motion Analysis Corp, 3617 Westwind Blvd, Santa Rosa, CA 95403. 
Ariel Dynamics Inc, 7887 Dunbrook Rd, Suite B, San Diego, CA 92126.
Peak Performance Technologies Inc, 7388 S Revere Pkwy, Suite 601, Englewood, CO 80112.
Panasonic Corp, One Panasonic Way, Secaucus, NJ 07094.
|| Johnson Level and Tool Manufacturing Co Inc, 6333 W Donges Bay, Mequon, WI 53092.
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This article has been cited by other articles:
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  R. Dickstein, A. Dunsky, and E. Marcovitz Motor Imagery for Gait Rehabilitation in Post-Stroke Hemiparesis Physical Therapy, December 1, 2004; 84(12): 1167 - 1177. [Abstract] [Full Text] [PDF]
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