Results and Discussion
Figure 8.3 (a)The shape of a 3D histogram plot of centroid positions indicates that the X and Y co-ordinates of the centroids are approximately Gaussian distributed. (b) The spread of centroids are shown falling within a 0.05 by 0.05 pixel region.
demonstrating how small the variation in position can be.
Variation due to marker intensity
Clarke et al note that “The standard deviation of a centroid co-ordinate is approximately inversely proportional to the maximum intensity level.” . This relationship is tested in this section. It should be noted that the observed intensity is dependent on the shutter period of the camera which was set to 300 µs in this test. Three markers were fixed near the centre of a Black Spot module’s FOV. The markers’ intensities were varied in discrete steps while the centroids of the marker were recorded over time. The data set was analysed and the spread of the centroids over time were calculated for each intensity. The resulting graph in Figure
8.4a shows the effect of intensity on the spread of the centroids for 1 marker. by Clarke et al. , the graph has a hyperbolic shape.
The data were analysed again using all three LEDs and plotted in Figure 8.4b. duced a plot with the same shape and a similar curve was fitted to the data.
This pro- s shown,
increasing the maximum intensity value of a marker above a value of approximately 80 makes little improvement to the spread of centroids. Consequently, a lower weighting should be given to makers of intensity less than this value. Shortis et al. 1994  note that in their simulations, the location accuracy of the centroid calculation degrades with an increase in saturation of the image. In this case, saturation is present when the maximum