Given a set of correspondences between 3D reference points and their images, pose estimation consists of determining the position and orientation of the calibrated camera with respect to the known reference points. The problem is called space resection in the photogrammetry community.
It is well known that there are closed-form solutions for 3 points, but there are multiple solutions with 3 points. Additional information is required to guarantee uniqueness. Four points generically suffice for uniqueness outside of certain critical configurations in space. Unfortunately, most of the approaches proposed for redundant data case rely either on iterative methods, or on applying closed form solutions to minimal subsets of the redundant data.
A family of linear unique-solution algorithms for 4, 5 and n-point pose estimation will be developed in this note. We therefore avoid iteration while taking advantage of data redundancy. We establish that the pose is uniquely determined and can be linearly estimated with at least 4 corresponding points provided that the reference points together with the perspective center do not lie on a critical surface of the configuration.