A Closed form Solution for Monocular Re-Projective 3D Pose Estimation of Regular Planar Patterns

In this article we present a method to estimate the pose and orientation of a planar pattern observed by a calibrated camera. The method takes advantage of the re-projective part of the camera mapping and presents a closed form solution assuming three equidistant collinear points. Only one image is used for the pose estimation. 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. The proposed algorithm has no iterations, no hidden non-linear parts, and uses no trigonometric functions.