# 26

Theory and Design

nalysis

3.2.3

# Marker position calculation

# Shortis et al. 1994 [47] investigate a number of techniques for precisely locating a target. In

their paper they analyse the performance of centroids, Gaussian shape fitting, and ellipse fitting using a simulated environment. Their simulations show that the centroid performs well for precisely locating a target under a variety of conditions. This research uses the cen- troid of a marker to estimate position within the ROI. Shortis et al. 1995 [48] investigated

centroid and ellipse fitting algorithms using real data from video sequences and concluded that, in general, centroid algorithms are robust and insensitive to threshold level changes. The intensity weighted centroid is used in this research to precisely locate a marker within a ROI.

The calculation of the centroid of an image [47] is analogous to finding the centre of mass of an object where the intensity of an image is equivalent to mass. The centroid of an image is the intensity weighted sum of the points that make up that image and is therefore a vector- valued function. The calculations of the X, and Y components of the centroid with respect to the ROI position are

C_{ROI }

=

# X

ï£°

Y

ï£¹ ï£»

=

ï£° P m j = P j = P m j = P m m j =

P n P P P i= n i = n i= n i=

I(i,j)i I(i,j) I(i,j)j I(i,j)

ï£¹

ï£»

,

(3.17)

where I(i, j) denotes the intensity of the pixel at position [i, j] within the ROI of dimensions

n by m.

binary centroid calculation is also possible with I(i, j) set to 1 for all marker pix-

els. However, Shortis et al. [47,48] show that this has lower performance than the intensity weighted centroid.

fter calculating the location of a marker within its ROI, the location of the marker within the image can be calculated by

P_{Marker }

= P_{ROI }

+

C

_{ROI},

(3.18)

where P_{ROI }is the position of one of the corners of the ROI within the image. The corner chosen is the one with the lowest X and Y coordinates.

3.2.4

# Tracking speed calculations

The use of camera modules to calculate the positions of markers introduces a complication which is not an issue with the Fastrak. n electromagnetic tracker can determine the pose of a target regardless of the motion that the target is undergoing. This is not the case for the optical tracker proposed in this thesis due to the method used to track markers. s noted, a ROI is used to surround a marker image. When a marker moves between two consecutive