A two-step method for pose estimation based on five co-planar reference points is studied. In the first step, the pose of the object is estimated by a simple analytical solving process. The pixel coordinates of reference points on the image plane are extracted through image processing. Then, using affine invariants of the reference points with certain distances between each other, the coordinates of reference points in the camera coordinate system are solved. In the second step, the results obtained in the first step are used as initial values of an iterative solving process for gathering the exact solution. In such a solution, an unconstrained nonlinear optimization objective function is established through the objective functions produced by the depth estimation and the co-planarity of the five reference points to ensure the accuracy and convergence rate of the non-linear algorithm. The Levenberg-Marquardt optimization method is utilized to refine the initial values. The coordinates of the reference points in the camera coordinate system are obtained and transformed into the pose of the object. Experimental results show that the RMS of the azimuth angle reaches 0.076o in the measurement range of 0o-90o; the root mean square (RMS) of the pitch angle reaches 0.035o in the measurement range of 0o-60o; and the RMS of the roll angle reaches 0.036o in the measurement range of 0o-60o.

The pose estimation method based on geometric constraints is studied. The coordinates of the five feature points in the camera coordinate system are calculated to obtain the pose of an object on the basis of the geometric constraints formed by the connective lines of the feature points and the coordinates of the feature points on the CCD image plane; during the solution process, the scaling and orthography projection model is used to approximate the perspective projection model. The initial values of the coordinates of the five feature points in the camera coordinate system are obtained to ensure the accuracy and convergence rate of the non-linear algorithm. In accordance with the perspective projection characteristics of the circular feature landmarks, we propose an approach that enables the iterative acquisition of accurate target poses through the correction of the perspective projection coordinates of the circular feature landmark centers. Experimental results show that the translation positioning accuracy reaches ±0.05 mm in the measurement range of 0–40 mm, and the rotation positioning accuracy reaches ±0.06o in the measurement range of 4o–60o.

In order to estimate the position and orientation of an object with a single camera, a novel measurement method based on pinhole camera model with five reference points is presented. Taking the specially designed planar target with the monocular vision system, the projection line of the reference points is built. According to the projection model, the coordinates of the reference points in the camera coordinate system are estimated with the least-squares algorithm. Thus the position and orientation of the target are worked out. Experimental result shows that the measurement precision of angle is less than 0.2°, and that of displacement is less than 0.1 mm.