An analytical method for the 3D-location estimation of circular features for an active-vision system

A closed-form analytical solution to the circular-feature problem, which arose in the context of a 3-D object recognition system, is presented. Compared to previous methods, it is mathematically simpler, provides a solution for the case in which there does not exist a priori knowledge concerning the radius of a marker, and can be extended and applied to general quadratic surfaces. In addition, the method is clearer from a geometrical viewpoint. The method was applied to a set of circles, located on a calibration plate, whose locations were known with respect to a reference frame. The camera was calibrated prior to the application of the 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. Experimental results showing the validity of the method are reported