Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--Stellenbosch University, 2008. / The medical radiation treatment facility at iThemba Labs requires a precise and robust patient positioning system. The current system makes use of an accurately calibrated multi-camera stereophotogrammetry (SPG) setup that is vulnerable to physical disruptions that invalidate system calibration. The task in this thesis is to design a vision system that can be used to verify the correct operation of the SPG system. We propose an unscented Kalman filter (UKF) based structure from motion (SFM) system for this purpose. Our SFM system does not rely on calibration information used by the SPG system and provides accurate reconstruction for verification purposes. The system is critically evaluated against a set of synthetic and real motion sequences.