Nearly Analytical Pose Estimation

This paper develops a new, nearly analytical method for pose estimation. Two steps are required: (1) solution of a least squares matrix problem, followed by projection of the solution onto the nearest scaled subunitary matrix, and (2) solution of a least squares vector problem, followed by projection onto the three dimensional special orthogonal group, SO(3). Although the method can be iterated when necessary, it achieves accuracy to standard stopping criteria with on average only one iteration; thus it can be considered nearly analytical. The method is compared to numerical methods and is shown to be much faster than earlier iterative methods. Both perspective and affine cameras models are treated.