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

 

Abstract

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.

 

Introduction

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.

 

Results

For the following results summary, refer to Figure 3, Figure 4, and Figure 5 and Tables 3-4.

Positional jitter for all systems

• Dominated by the z component (camera look direction).
• Relatively constant over single z-plane (independent of x, y, and q).
• Increases with increasing z.
• Relatively constant for varying angles up to some cutoff angle.
• Best jitter obtained with 300 mm FlashPoint due to proximity of digitizing volume to OTS camera.

Angular jitter for all systems

• Relatively constant over single z-plane (independent of x, y, and q).
• Relatively constant for a given depth up to some angle (60 degrees for active configurations, 40 degrees for passive).

Differences between systems

• For IGT systems, positional jitter increases with z; for NDI systems, it remains relatively constant over a given range of z and q.
• Both passive and active configurations of the Polaris camera have much larger outliers for both positional and angular measurements than do any of the FlashPoint systems (Figure 5).
• When considering all data, the maximum error for the NDI cameras is far larger than the error for any of the IGT configurations; when the worst 5% of outliers are ignored, the performance of the NDI configurations significantly improve and nearly reach that of the IGT systems.
• Both positional and angular jitter of the IGT systems were more predictable and well-behaved than that of either NDI configuration.
• Passive NDI behaves differently than the four active OTS configurations. Positional and angular jitters increase dramatically for orientations larger than 40 degrees. The variation in jitter for the NDI passive configuration is also much larger than for the active configurations.

 

 

Table 1. Optical tracking system configurations tested.

 

System	DRF Used	Image Sensor Distance [mm]
IGT 300 mm FlashPoint	3 LED 50 mm active IGT	200
IGT 580 mm FlashPoint	3 LED 50 mm active IGT	480
IGT 1 m FlashPoint	3 LED 50 mm active IGT	1000
NDI Polaris	4 LED Active TRAXTAL	480
NDI Polaris (passive)	4 LED Passive TRAXTAL	480

 

 

Table 2. Dimensions of the vendor specified digitizing volume and of the volume tested in this study.

Camera	Max X Spec [mm]	Max X Tested [mm]	Max Y Spec [mm]	Max Y Tested [mm]	Min Z Spec [mm]	Min Z Tested [mm]	Max Z Spec [mm]	Max Z Tested [mm]
300mm Flashpoint	150	300	150	400	600	600	900	900
580mm Flashpoint	500	430	500	650	1000	1060	2000	2160
1m Flashpoint	500	800	500	650	1000	1060	2000	2160
Polaris	500	410	500	620	1400	1400	2400	2400
Polaris (passive)	500	350	500	620	1400	1400	2400	2400

 

 

Table 3. Positional jitter value ranges.

Camera	mJ[mm]	D+ [mm]	D-[mm]	Jcenter [mm]	D[mm]
300mm Flashpoint	0.028	0.012	-0.012	0.028	0.012
580mm Flashpoint	0.046	0.044	-0.033	0.051	0.038
1m Flashpoint	0.047	0.059	-0.035	0.059	0.047
Polaris	0.053	0.042	-0.032	0.058	0.037
Polaris (passive)	0.109	0.082	-0.068	0.115	0.075

 

Table 4. Angular jitter value ranges.

Camera	mJq [degrees]	Dq+ [degrees]	Dq- [degrees]	Jqcenter [degrees]	Dq [degrees]
300mm Flashpoint	0.0339	0.0441	0.0339	0.0390	0.0390
580mm Flashpoint	0.0434	0.1595	0.0434	0.1015	0.1015
1m Flashpoint	0.0424	0.1914	0.0424	0.1169	0.1169
Polaris	0.0464	0.4909	0.0377	0.2730	0.2643
Polaris (passive)	0.0575	1.7355	0.0478	0.9014	0.8917

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Conclusion

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.