An analytic solution for the perspective 4-point problem

The perspective n-point (PnP) problem is the problem of finding the position and orientation of a camera with respect to a scene object from n correspondence points. The authors propose an analytic solution for the perspective 4-point problem. The solution is found by replacing the four points with a pencil of three lines and by exploring the geometric constraints available with the perspective camera model. The P4P problem is cast into the problem of solving a biquadratic polynomial equation in one unknown