Finding all the solutions of PnP problem

PnP (perspective-n-point) problem is a classical problem in computer vision and photogrammetry. According to the number of corresponding points, PnP problem can be resolved linearly or nonlinearly. When the number of corresponding points is greater than or equal to 6, PnP problem can be formulated as an linear least squares problem and solution is unique in most cases; however, when the number of corresponding points is smaller than 6, resolving PnP problem is nonlinear in essence and there are usually multiple feasible solutions. In spite of intense study of PnP problem in the last few decades, finding all the solutions of PnP efficiently and numerically stably still remains an open problem. In this work, we attack this problem from a new perspective and propose a method for finding all the solutions of PnP problem when one of the solutions is given a priori. We also show experimentally that our method is numerically stable and efficient, even under severely noisy conditions.