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A Prototype Optical Tracking System Investigation and Development - page 119 / 170

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8.2 Black Spot module testing (2D testing)

105

Standard Deviation (pixels)

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

Standard Deviation (pixels)

Std. dev. X

0.5

Std. dev. Y

0.4

0.3

0.2

Std. dev. X Std. dev. Y

0.1

0.05

00

50

100 Intensity Value

150

200

00

50

100

150 Intensity Value

200

250

300

(a)

(b)

Figure 8.4 The spread of the centroids is approximately inversely proportional to the maximum intensity of a marker. (a) Data collected using one marker. (b) Data collected using three markers. Both plots have the same shape and curves were fitted to each of them. There is little improvement in centroid variation for markers with intensity greater than approximately 80 for a shutter period of 300 µs.

intensity is 255. It is concluded that markers with intensities between 80 and below 255 can be treated equally.

The fitted curves have the form

σ=

p1I + p2 I + q1

,

(8.1)

where I is the intensity, p1, p2, q1 are constants and σ is the standard deviation. For the plot in Figure 8.4b, the fit for the standard deviation in X is

3I + 0.468 3.56

,

3I + 0.417 4.07

.

σX(I) =

4.65 × 10 I

and the fit for the standard deviation in Y is

σY(I) =

7.41 × 10 I

(8.2)

(8.3)

8.2.3

Variation due to viewing angle

This section attempts to determine whether there is a dependence between the variation in centroid positions and the position of a marker image in the camera’s FOV. To test this the rotation turret was used to vary the camera angle. This varied the positions of the visible markers in the camera’s FOV. Rotating the camera corresponds to a change in θ1 as d e fi n e d i n F i g u r e 8 . 5 . I n t h i s t e s t i t i s a s s u m e d θ 2 d o e s n o t a f f e c t t h e v a r i a t i o n i n c e n t r o i d measured from this marker, rather that this angle only affects the apparent intensity of the s

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