A simple solution for the non perspective three point pose problem

Non-Perspective Three Point Pose (NP3P) problem is a generalization of the classical three point pose problem for the case of multi-camera that have no common projection center. In this paper, we develop a simple, minimal algebraic solution to the NP3P problem where the projection rays of three points may have arbitrary but known directions. This problem is known to have a maximum of eight solutions. The problem is formulated mathematically as the solution of three multivariate polynomials. The technique of Sylvester matrix resultants of two equations is used to obtain an eighth order polynomial that can be solved to yield the pose parameters. The accuracy and computational cost of the new method is compared to other methods reported in the literature and it was found to have comparable accuracy with less computational cost.