A Note on the P5P Problem with An Uncalibrated Camera

The P5P problem with an uncalibrated camera is systematically investigated in this paper. It is proved that if no 4 control points among the 5 control points are coplanar, or if no 3 image points are collinear in case the 4 control points are coplanar, the P5P problem could have the following 2 possible cases: (1) It has at most 4 solutions, and this upper bound is also attainable; (2) It has an infinite number of solutions. In addition, algebraic conditions are provided for the above two cases. Finally, we also present some practical algorithms to compute admissible solutions.