A direct solution for the central projection camera pose estimation by four control points

The Perspective $n$-point Problem (PnP) is the problem of finding the position and orientation of a central projection camera model by given spatial coordinates of the points and by their corresponding coordinates on the image. Due to the existing robotics and machine vision applications direct non-iterative methods of solution are of interest. The known general method to the direct non-iterative solution for the PnP problem in the case of four control points ($n=4$) uses the relinearization and seems to be rather complex. This paper presents an alternative more simple solution for the problem in the case $n=4$. The proposed method reduces computing requirements for the problem solution. In the case of more control points the solution obtained for four points can be used as an initial approximation for Gauss–Newton iterations or in RANSAC calculation scheme.