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A Prototype Optical Tracking System Investigation and Development - page 43 / 170

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3.2 Black Spot module analysis

29

v

v

v

Image plane

f

z

Figure 3.6 A translation of the camera and its corresponding effect on an image. The two green circles represent a marker in two different frames. For simplicity the marker is shown moving with respect to the camera, however in reality, the opposite is true as shown by the arrow at the origin in the diagram. By determining the maximum velocity during a sweep the maximum tracking speed required of the Black Spot firmware can be determined.

an approximate increase of 50% in the maximum sweep velocity1 (0.52 + 50

0.8 m/s),

the equivalent image velocity is

0 v=

0.8 × 6 × 10 60 × 0.5 × 6 × 10 3

6

27 pixels/frame.

(3.20)

Using a similar method the linear acceleration was analysed. The maximum linear accel- eration was approximately 9.1 m/s2 and this is approximately 14 m/s2 when increased by 50% leading to a value of

0 a=

a f T zk 2 r

=

14 × 6 × 10 602 × 0.5 × 6 × 10 3

6

= 8 pixels/frame2.

(3.21)

These values are used in the design of the firmware as described in Chapter 4.

3.2.5

Marker tracking

To track the movement of an image from one frame to the next the marker’s ROI must follow the marker. This is achieved by centring the ROI around the centroid of the marker after each frame (Figure 3.7). The translation of a marker across the camera’s image plane

can be estimated using the distance in pixels between the centroid of the ROI in the previ- ous frame and the centroid in the current frame. The system’s ability to track the movement of a marker is related to the magnitude of this image translation per frame and the size of the ROI. There is a trade-off between maximum image tracking speed that can be tracked

150% is used as a safety margin to account for the possibility that the scanned data represents a slower than average scan.

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