Three-dimensional location estimation of circular features for machine vision

Abstract

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

Natural interaction with virtual objects using vision-based six DOF sphere tracking

“…The concept of finding circular objects and curves in images has been studied for many years. In general, there are two different types of algorithms for curve detection (typically circles and ellipses) in images, those that are based on the Hough transform [3,15,16], and those that aren't [2,10,11,12,13]. It should be noted that this is not an exhaustive list of circle detection methods, since the main focus of this paper is not the circle detection technique.…”

A Sphere-Based Calibration Method for Line Structured Light Vision Sensor

“…the coordinate of the sphere center [ 0 0 0 ] under CCS can be expressed by the following equation [13,14]:…”

A real-time tracker for markerless augmented reality

“…The most common geometric features used in pose computation which are suitable for AR applications include indoor fiducial/marker based [3,19,25,32,33] and outdoor fiducial/marker based [26], the latter shows how the size of the marker contributes to robustness and ease of use. In the related computer vision literature geometric primitives considered for the estimation are often points [13,7], segments [9], lines [20], contours or points on the contours [21,24,10], conics [28,6], cylindrical objects [8] or a combination of these different features [25]. Another important issue is the registration problem.…”