Pose estimation from four corresponding points with a single camera

Finding the position and orientation between a camera and a target with respect to a scene object from n correspondence points is crucial for many computer and robot vision tasks. With a limited number of correspondence points, the closed-from solution is applied to solve the pose estimation problem. To estimate the pose between the camera and the target from the four reference point, a pose estimate model is built with the four projection line between the 3D space point and 2D image point, under the full perspective projection of the camera. The transformation matrix is determined by the coordinates of four reference points in camera coordinate system and the target coordinate system respectively. To figure out the transformation matrix, the distance factor of the four reference points in camera system must be calculated. Considering the quality of the triangle, the pose estimate model with is simplified, which avoid the iteration, as while as taking the advantage of the data redundancy. Considering the specific relationship of the four reference points, the Levenberg-Marquardt algorithm is used to figure out the unknown parameters in the pose estimate model. Then the position and orientation between the camera and the target is obtained with respect to the coordinate transformation matrix from the camera coordinates to the target coordinates. In the experiment, both synthetic and real data are used to examine the accuracy and stability of the pose estimate algorithms with four points. Experiment result shows the distance measurement precision better than 0.03mm, and the angle measurement precision better than 0.2°.