Three-dimensional location estimation of circular features for machine vision

AbstructEstimation of 3-D information from 2-D image coordinates is a fundamental problem both in machine vision and computer vision. Circular features are the most common quadratic-curved features that have been addressed for 3-D location estimation. In this paper, a closed-form analytical solution to the problem of 3-D location estimation of circular features is presented. Two different cases are considered: 1) 3-D orientation and 3-D position estimation of a circular feature when its radius is known, and 2) 3-D orientation and 3-D position estimation of a circular feature when its radius is not known. As well, extension of the developed method to 3-D quadratic features is addressed. Specifically, a closed-form analytical solution is derived for 3-D position estimation of spherical features. For experimentation purposes, simulated as well as real setups were employed. Simulated experimental results obtained for all three cases mentioned above verified the analytical method developed in this paper. In the case of real experiments, a set of circles located on a calibration plate, whose locations were known with respect to a reference frame, were used for camera calibration as well as for the application of the developed method. Since various distortion factors had to be compensated in order to obtain accurate estimates of the parameters of the imaged circle-an ellipse-with respect to the camera's image frame, a sequential compensation procedure was applied to the input grey-level image. The experimental results obtained once more showed the validity of the total process involved in the 3-D location estimation of circular features in general and the applicability of the analytical method developed in this paper in particular.