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Estimation 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. I. INTRODUCTION STIMATION of 3-D information from 2-D image coor-E dinates is a fundamental problem in both machine vision and computer vision. This problem exists in two forms: the direct and the inverse. When the camera parameters (the intrinsic: effective focal length, lens distortion factors, etc., and the extrinsic: 3-D position and 3-D orientation of the camera frame) are given in addition to the 2-D image coordinates, the problem is of the direct type. On the other hand, if

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SUMMARY Focusing and correcting the astigmatism of an electron microscope can be time consuming and difficult to achieve accurately. An automatic method of performing these tasks using an on‐line computer system and a digital framestore has been developed. The method is applicable to noisy images in both scanning and conventional transmission electron microscopes. It is capable of setting focus and correcting astigmatism at least as accurately as can be achieved by an experienced operator.