POST PROCESSING TECHNIQUE FOR APPROXIMATING PROJECTILE TRAJECTORY IN 3D SPACE 1
C.M. Pfeifer, 1,3 J.M. Burnfield, 2 M.H. Twedt, 1 J.A. Hawks, 3 R.M. Hasenkamp, 3 G.M. Cesar University of Nebraska-Lincoln 1 Dept. of Mechanical & Materials Engineering, Dept. of Biological Systems Engineering. 3 Nebraska Athletic Performance Lab Email:
[email protected]
2
INTRODUCTION Understanding the three-dimensional (3D) trajectory of ball flight and its relationship to environmental (wind, humidity, temperature) and human factors (kinematics and EMG) is essential to optimizing elite athlete performance. Unfortunately, existing technology is often too expensive ($15,000$100,000), has limited accuracy, and/or lacks the versatility required to track diverse objects (e.g., soccer ball vs. football vs. baseball). The purpose of this study was to develop and validate an affordable post-processing method that uses computer-vision to track the 3D trajectory of a ball. METHODS A golf ball was selected as the initial object for algorithm development. One camera (Panasonic HC-V100, 1080p, 24 Hz), oriented perpendicular to the x-axis (Figure 1), produced data relevant to the projectile's motion along the x and z-axis (longitudinal and vertical position). A second similar camera, oriented parallel to the x-axis, produced data relevant to the projectile's motion along the y-axis (lateral position). To create a "sight triangle" which was subsequently used to evaluate the projectile’s movement in the y-direction, a set of calibration lines (40x10 mm) was affixed to the ground 0.762 m apart in the expected direction of projectile motion (x-axis) to calibrate the video data in the x-z plane. A second equidistant set (in the xdirection) was placed 0.305 m apart in the ydirection for calibration of the camera directed down the x-axis. An uncompensated 2D motion trajectory of the golf ball’s flight was calculated for each camera by measuring position with a pixel to distance ratio (Tracker software) [1]. Data from the two cameras
were time-synched through identification of the ball to ground impact.
Figure 1 - Data Collection Set-Up/Explanation of Variables
To accommodate for the distortion arising from outof-plane motion for each camera, coordinate data were adjusted using the following methodology. The y-position was adjusted using equations 1-3: {Eq. 1} {Eq. 2}
{Eq. 3} where is the uncompensated y-position, and are the distance between the two calibration markers in pixels from the view of the parallel camera (see Figure 1), is the correcting y-factor, is the distance from the origin of the reference frame to the furthest set of calibration markers, is the distance in pixels from the view of the parallel camera, is the uncompensated x-position, is the position in pixels, is the distance between the two sets of calibration markers, is the distance in pixels from the view of the parallel camera, and is the compensated y-position.
traveled by the projectile. Calibration markers must be accurately positioned and the cameras needs to be directed to clearly view the x-z and y-z planes to obtain the most accurate position measurements.
Next, was used to calculate the compensated z and x-positions, and respectively. These compensated positions were calculated using equations 4 and 5: {Eq. 4} {Eq. 5} where h was the viewing height of the camera, was the distance from the perpendicular camera to the x-z plane (see Figure 1), was the longitudinal distance the perpendicular camera was from the coordinate origin, and is the uncompensated zposition. Algorithm validation was performed using a “gold standard” 3D motion analysis system (3 Qualisys Oqus 300 series cameras, 200 Hz, calibration residuals < 1mm). A golf ball (42.67 mm in diameter), covered with retro-reflective tape, was simultaneously tracked during flight through a 3x3x3 m capture volume by the 2D Panasonic cameras and the 3D motion capture technology. Ten repetitions were performed (Table 1).
Figure 2 - Example result displaying the Gold Standard, Uncompensated, and Compensated trajectories. (Trial 05)
The low frame rate (24 Hz) of the 2D cameras used in the current study resulted projectile blurring in a number of frames. In these instances the center of the blurred projectile was approximated and assessed as the data point. Cameras recording at a higher frequency would be expected to reduce the amount of error resulting from video processing and time-based compiling.
RESULTS AND DISCUSSION The uncompensated coordinate data resulted in an average percent deviation from the gold standard 3D trajectory of 10.37 ± 3.88%. After applying the presented geometrical adjustment technique, the average percent deviation of the compensated from the gold standard trajectory was reduced to 4.20 ± 1.35%. These findings demonstrate that the compensated technique was over 240% more accurate than the uncompensated approach at golf ball trajectory tracking.
In summary, this work developed and validated an affordable (estimated at $400), accurate (<5% average error) technology for tracking 3D ball flight. Current work is aimed at validating range and versatility of use with other projectiles (e.g., a football). REFERENCES
The error presented relates to the average overall error in the system with respect to the distance
1.
D. Brown. Tracker-Video Analysis and Modeling Tool, www.cabrillo.edu/~dbrown/tracker
Table 1 - Average resultant deviation from the control for uncompensated and compensated position. Trial 01
Trial 02
Trial 03
Trial 04
Trial 05
Trial 06
Trial 07
Trial 08
Trial 09
Trial 10
Average*
Uncompensated Position
Error (mm)
62.6
253.8
325.9
254.9
109.8
61.6
192.5
169.2
201.2
243.1
172.1
77.4
Error (%)
6.77%
14.40%
19.30%
12.08%
10.12%
3.21%
9.61%
8.97%
15.99%
12.14%
10.37%
3.88%
Compensated Position
Error (mm)
39
88
314.8
140.3
47.2
50.1
40.8
70
60.9
88.6
69.4
32.4
Error (%)
4.22%
4.99%
16.11%
6.65%
4.34%
2.61%
2.04%
3.71%
4.84%
4.43%
4.20%
1.35%
*Trial 03 was determined an outlier and is not included in the average and standard deviation calculations.
STDEV*
