# Metric reconstruction of multiple rigid objects

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2009.

Thesis

Engineers struggle to replicate the capabilities of the sophisticated human visual system. This thesis sets out to recover motion and 3D structure of multiple rigid objects up to a similarity. The motion of these objects are either recorded in a single video sequence, or images of the objects are recorded on multiple, di erent cameras. We assume a perspective camera model with optional provision for calibration information. The Structure from Motion (SfM) problem is addressed from a matrix factorization point of view. This leads to a reconstruction correct up to a projectivity of little use in itself. Using techniques from camera autocalibration the projectivity is upgraded to a similarity. This reconstruction is also applied to multiple objects through motion segmentation. The SfM system developed in this thesis is a batch-processing algorithm, requiring few frames for a solution and readily accepts images from very di erent viewpoints. Since a solution can be obtained with just a few frames, it can be used to initialize sequential methods with slower convergence rates, such as the Kalman lter. The SfM system is critically evaluated against an extensive set of motion sequences.