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# Chapter 3

Theory and Design Analysis

This chapter analyses the design of the optical tracking system described in Chapter 2. The major functions of the system are the tracking of markers within captured images, the calculation of the positions of the markers, and the estimation of the pose from this data. Firstly, supporting theory for this analysis is introduced in Section 3.1. Following this, the Black Spot design is analysed in Section 3.2. brief review of the pose estimation literature is given in Section 3.3. Finally, a possible beacon configuration is described in Section 3.4.

3.1

## Supporting theory

This section introduces quaternions, coordinate frames, and a basic camera model required by the hub’s pose estimation algorithm. coordinate frame describes the orientation and position of a 3D Cartesian coordinate system with respect to another coordinate system. The tracking system requires mathematical modeling of a camera and a coordinate frame to describe the pose of the camera. Quaternions are used to describe the rotation of a set of axes with respect to another. Firstly, the camera model is introduced. This is followed by quaternions and finally coordinate frames are introduced. It is assumed that the reader is

familiar with basic vector operations described in many mathematical texts [36, 37].

3.1.1

## Camera model

pinhole camera model [38] is used by the software to form a projection that maps 3D

scene coordinates to 2D camera coordinates.

pinhole camera has an infinitely small

aperture (pinhole) and an image plane (Figure 3.1a). Light rays pass through this pinhole and form an image on the image plane. The mapping or perspective transform relates the coordinates [x, y, z] of a point in 3D space to the 2D coordinates [u, v] of the point on the

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