Khadem et al. Poster
Comparative Tracking Error Analysis of Five Different Optical Tracking Systems
Rasool Khadem, Ph.D., Clement C. Yeh, M.S., Mohammad Sadeghi-Tehrani, M.S., Michael R. Bax, M.S., Jeremy A. Johnson, M.S.,
Jacqueline Nerney Welch, M.S., Eric P. Wilkinson, B.S.E., Ramin Shahidi, Ph.D.
California Institute of Computer-Assisted Surgery, Stanford University School of Medicine, Stanford, CA
The positional and angular precision of five different optical tracking system (OTS) configurations are measured. The dependence of the two precision measurements on position and within the digitizing volume and angle between the dynamic reference frame (DRF) and camera are examined. The maximum positional and angular error for all measurements and for 95% of all measurements are also presented.
The OTS is responsible for reporting the location and orientation of a dynamic reference frame (DRF) in a three-dimensional space. Ideally, the OTS would report the true location and orientation of the DRF and would be constant for multiple readings of a stationary DRF. However, errors do arise in OTS measurements for several reasons, including quantization due to a finite number of the pixels in the image sensor, imperfect optics, and inaccuracies due to triangulating the position of each emitter. If the average of multiple readings does not converge to the correct location and orientation, the system is biased; if multiple readings are not closely grouped, the system is imprecise. This study measures the precision of OTS position and angle measurements. Since precision is a qualitative term, jitter is used to quantify the deviation of repeated measurements from the mean. Jitter is defined to be the standard deviation of a series of OTS measurements of a stationary DRF about their sample mean. Positional jitter is a measure of the precision of the DRF position measurement, and angular jitter measures the precision of the orientation measurement.
Materials and Methods
Optical Tracking Systems (OTS): Four cameras from two manufacturers were tested: the FlashPoint (Image Guided Technology, Boulder, Colorado) and the Polaris (Northern Digital Inc., Ontario, Canada). Three different sizes of FlashPoint cameras were tested, and the Polaris camera was tested in both active and passive configurations. Table 1 lists the five system configurations tested in this experiment, and the cameras and DRFs are pictured in Figure 3.
Linear Testing Apparatus (LTA): A precision-machined assembly consisting of a movable, vertical plate with uniformly-spaced holes on which the DRF was mounted (Figure 1).
Stepper Motor Assembly: The assembly allowed the DRF to be mounted to the LTA and be rotated about the vertical axis (Figure 2).
Jitter is defined as the standard deviation of a sequence of measurements about the mean of the measurements.
Positional jitter measurements were obtained at positions uniformly spaced throughout a three-dimensional volume for each OTS. The camera viewing volumes and the testing volume dimensions are given in Table 2. The spatial x, y and z coordinates were consecutively sampled 100 times at each sensor position.
Angular jitter was measured throughout a subset of the volume, and for angles between 0 degrees and the maximum viewable angle. The angle step size was determined by the minimum rotation of the stepper motor, 1.8 degrees. For each position and angle, 100 angle measurements were taken and the jitter calculated.
Positional jitter for all systems
Angular jitter for all systems
Differences between systems
Table 1. Optical tracking system configurations tested.
Table 2. Dimensions of the vendor specified digitizing volume and of the volume tested in this study.
Table 3. Positional jitter value ranges.
Table 4. Angular jitter value ranges.
The precision of position and angle measurements made by five commercially available optical tracking systems has been quantified throughout a volume. The easiest way to reduce both positional and angular jitter of measurements made by an optical tracking system is to minimize the distance between the camera and the tracked instrument while staying in the camera's digitizing volume.
The method presented for jitter measurement and analysis is independent of the tracking technology, and can be used for investigating the precision of future tracking systems.
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