Closed Form Monocular Re-Projective Pose Estimation

In this article we introduce a closed form estimation of the pose determination problem. Unlike most other approaches our method minimizes a Euclidean error to re-projected image points. If we know the distances between these point we can reconstruct the 3D position of the points completely. If the exact distance is unknown the reconstruction is correct up to a scale factor. We compare our approach to several methods to estimate the pose and orientation of a planar pattern observed by a calibrated camera. All compared approaches are closed form solutions and take only one image for the pose estimation. The gain of the proposed method is not only a better starting value for non-linear optimizations but also its applicability for mobile solutions on constrained hardware. Therefore, we compare the error of the estimated pose to the ground truth for the investigated methods.