Object pose: links between paraperspective and perspective

D.F. Dementhon and L.S. Davis (1995) proposed a method for determining the pose of a 3D object with respect to a camera from 3D to 2D point correspondences. The method consists of iteratively improving the pose computed with a weak perspective camera model to converge at the limit, to a pose estimation computed with a perspective camera model. We show that the method of Dementhon and Davis can be extended to paraperspective. The iterative paraperspective pose algorithm that we describe in detail has interesting properties both in terms of speed and rate of convergence. Moreover, we introduce a simple way of taking into account the orthogonality constraint associated with the rotation matrix and we define the optimal experimental setup to be used in the presence of camera calibration errors