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# 30

Theory and Design

nalysis

and ROI size.

larger ROI leads to a greater speed that may be tracked but large ROIs are

undesirable as they require a greater number of pixels to be analysed per frame. If the ROI size is too small then the marker cannot be tracked as the marker could move outside the

ROI within one frame period.

The required tracking speed affects the size of the ROIs used. The arrow in Figure 3.7 illustrates marker movement. For the marker to continue to be tracked, the magnitude of this movement must be small enough so that the marker remains within the ROI. This leads to a formula that describes the relationship between marker movement and minimum ROI Size, i.e.,

ROI Size

2smax

• +

D.

(3.22)

Here ROI Size refers to one of the dimensions of the ROI. Over one frame the maximum

m a r k e r m o v e m e n t i s e q u a l t o t h e m a x i m u m m a r k e r v e l o c i t y v 0 m a x

. This gives

ROI Size

2 v 0 m a x

• +

D,

(3.23)

where D is the marker diameter. The marker diameter is a function of distance between the camera’s origin and the marker. The maximum ROI size can be calculated by substituting D for the marker diameter when viewed at the closest tracking distance of 0.5 m. Using the green 8 mm diameter LEDs and optics described in Chapter 5 and using a pinhole camera model described in Section 3.1.1 this diameter is

Dmax

= 16 pixels.

(3.24)

Therefore, the ROI size required to track the maximum speed of 27 pixels / frame at 0.5 m is

Max. ROI Size

2 × 27 + 16 = 70 pixels.

(3.25)

This corresponds to a ROI of 70 by 70 pixels. The maximum ROI size can be reduced to 32 by 32 pixels using an algorithm in Chapter 4 that compensates for the velocity of the

marker and alters Equation 3.23 to depend on the maximum acceleration a

0 max

.

3.3

# Pose estimation

The second major function of the system is the estimation of pose from the 2D data pro- vided by the camera modules. There is a vast body of literature covering techniques to solve this type of problem. Solutions were first published by the photogrammetric com- munity and rediscovered by the computer vision community. Consequently, there are a number of names that are used to describe the class of problem. Relevant areas in the lit- erature have names such as multiview geometry [49], structure from motion [50], bundle

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