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4.2

# lgorithm design

43

s

max

p preal predicted

Figure 4.8 Using the linear prediction scheme, the ROI is positioned around the predicted point, ppredicted. The maximum deviation of the marker from the predicted point is shown and this is re- ferred to as smax.

frames can be calculated by

v n = p n

p n

1

,

(4.3)

where vn is the velocity in pixels / frame and pn, pn

1

are the pixel positions at time n

and n

1 respectively. The average acceleration can also be calculated by

a n = v n

v n

1.

(4.4)

ssuming that there are not any higher order terms then using kinematic equations the marker position in future frames can be calculated by

pn

N

= N 2 a n + N v n + p n ,

(4.5)

where N is the number of frames in the future to predict. In the implementation of this algorithm N is always set to one as there is no need to predict the position of the marker image further than one frame into the future. This reduces Equation 4.5 to

pn

1

= an + vn + pn.

(4.6)

The algorithm is designed to predict the position in the next frame assuming constant velocity so takes the form

ppredicted

= vn + pn.

(4.7)

The ROI is centred around ppredicted

after each frame. Figure 4.8 shows the maximum

deviation from the predicted position (smax) that can be tolerated for a given ROI size. This is described in terms of the minimum ROI size required by

ROI Size

2smax

• +

D.

(4.8)

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