Global Optimal PnP Algorithm with Reverse Projection Error

A non-iterative global optimal PnP (perspective-n-point) algorithm with time complexity O(n) is proposed. The basic idea is to use camera internal parameters to reverse project 2D points into space, use the relationship between 3D points in world coordinates and 2D points to transform PnP problem into minimization problem, and use non-unit quaternion parameterization rotation matrix to transform PnP problems into unconstrained minimization problem, and finally solve the polynomial equation system composed of its first-order partial derivative. And the proposed method can deal with the minimization problem of PnP problem, P3P problem. Experimental results show that the proposed method can accurately process the all configuration of 3D points, and compared with the state-of-the-art PnP algorithm, the proposed method can provide comparable or better accuracy, and the computational efficiency is higher.