Monocular pose determination from lines: critical sets and maximum number of solutions

A subpart of the following problem is considered. It is assumed that a set of known three-dimensional lines with an unknown pose and orientation are observed with a camera. The problem is to recover the position and orientation of the camera from the observed image lines, assuming that a correspondence has been established between the 2-D and the 3-D lines. It is shown that there exist infinite sets of three-dimensional lines such that no matter how many lines are observed in these sets the solution to the orientation or pose determination problem is not unique. The maximum number of possible solutions is given. These results clearly define the domain of validity of algorithms which solve the orientation or pose determination problem