Results and Discussion
where the standard deviation is below a 25% increase above the minimum. Outside this region the standard deviations are at least 25% higher than the minimum. The majority of the results obtained are within 50% of the minimum standard deviation regardless of their position in the FOV. The trend curves indicate that at the extremes of the FOV the standard deviations are approximately 0.02 pixels. For comparison, a marker intensity of 10 could result in a standard deviation of approximately 0.1 pixels.
Using the curves fitted to the results in this chapter, a model of the overall standard devi-
ation can be constructed using a combination of each curve.
ssuming that the effects are
uncorrelated, the model of standard deviation in X can be written
q σ 2 X ( I ) + σ 2 X ( D ) + σ 2 X ( X ) .
n equation can similarly be written for σY.
The performance of the modules were also measured over long periods. The drifts mea- sured indicate that it would be preferable for the system to recalibrate often. Over a period of 2 minutes, the mean standard deviation of a marker near the centre of the FOV was 0.0061 pixels in X and 0.0074 pixels in Y as measured by Module 4. These results corre- spond to 12.2 µm in X and 14.8 µm in Y at 2 m and agree with Trinder  (as reported by Shortis et al. 1995 ) who concluded from simulations that subpixel precision of 0.01
pixels or better can be obtained.
The pose algorithm was tested with synthetic data. Under some initial conditions the algo- rithm converges well. case is shown where the position error was 0.5 mm. However, un- der other initial conditions convergence is poorer, at approximately 30 mm. It is concluded that a more robust minimisation algorithm is required to allow the pose to be calculated from a broader range of initial conditions. Lourakis and rgyros  note that Levenberg- Marquardt  algorithm is used as a minimisation algorithm in structure and motion
problems and this suggests it could be of use in the pose estimation algorithm designed.
The Black Spot modules have excellent stationary performance as shown by the results in this chapter and the pose algorithm has potential given a suitable minimisation algo- rithm. Further testing should be undertaken to reveal the Black Spot modules’ dynamic performance. It is apparent that the Blackfin DSP is well suited to marker tracking given the firmware’s ability to track 27 markers concurrently. Further testing could investigate how high this number can be increased and incorporate more computational intensive al- gorithms.