A closed-form solution to eye-to-hand calibration towards visual grasping

Purpose – The purpose of this paper is to propose a method that calibrates the hand-eye relationship for eye-to-hand configuration and afterwards a rectification to improve the accuracy of general calibration. Design/methodology/approach – The hand-eye calibration of eye-to-hand configuration is summarized as a equation AX = XB which is the same as in eye-in-hand calibration. A closed-form solution is derived. To abate the impact of noise, a rectification is conducted after the general calibration. Findings – Simulation and actual experiments confirm that the accuracy of calibration is obviously improved. Originality/value – Only a calibration plane is required for the hand-eye calibration. Taking the impact of noise into account, a rectification is carried out after the general calibration and, as a result, that the accuracy is obviously improved. The method can be applied in many actual applications.

A novel camera calibration method for fish-eye lenses using line features

In this paper, a novel method for the fish-eye lens calibration is presented. The method required only a 2D calibration plane containing straight lines i.e., checker board pattern without a priori knowing the poses of camera with respect to the calibration plane. The image of a line obtained from fish-eye lenses is a conic section. The proposed calibration method uses raw edges, which are pixels of the image line segments, in stead of using curves obtained from fitting conic to image edges. Using raw edges is more flexible and reliable than using conic section because the result from conic fitting can be unstable. The camera model used in this work is radially symmetric model i.e., bivariate non-linear function. However, this approach can use other single view point camera models. The geometric constraint used for calibrating the camera is based on the coincidence between point and line on calibration plane. The performance of the proposed calibration algorithm was assessed using simulated and real data.

The Technology of Circular Parts Precise Measurement Based on Binocular Calibration

A method of measuring the radius of circular parts by binocular stereo vision technology is proposed. First of all the interior and exterior parameters of cameras are acquired by the camera calibration technology. Then the epipolar constraint can be calculated which contains the calibrated information. The image matching which uses the epipolar constraint is done to find the matching points. The three dimensional (3D) coordinates of edges points are reconstructed through trigonometry reconstruction. At last the analytic expression of the plane in which the circle lies and the circles radius are calculated in two steps by Levenberg-Marquardt (LM) algorithm. The proposed method does not require the prior knowledge of position between the measuring plane and the calibration plane which monocular measurement needs. Experimental results show that the measurement has high precision.

3-D Graphing of XRF Matrix Correction Equations

The Lachance-Traill, and Lucas-Tooth-Price matrix correction equations/functions for XRF determined concentrations can be graphically interpreted with the help of three dimensional graphics. Statistically derived Lachance-Traill and Lucas-Tooth-Price matrix correction equations can be represented as follows: 1 where: Ci -elemental concentration of element “i” Ij -X-Ray intensity representing element “i” Ai0 -regression intercept for element “i” Ai -regression coefficient Zj -correction term defined below 2 Ai0, Aj , and Zi together represent the results of a multi-dimensional contribution. li, Ci, and Zi can be represented in three dimensional Cartesian space by X, Y and Z. These three variables are connected by a matrix correction equation that can be graphed as the function Y = F(X, Z), which represents a plane in three dimensional space. It can be seen that each chemical element will deliver a different set of coefficients in the equation of a plane that is called here a calibration plane. The commonly known and used two dimensional calibration plot is a “shadow” of the three dimensional real calibration points. These real (not shadow) points reside on a regression calibration plane in this three dimensional space. Lachance-Traill and Lucas-Tooth-Price matrix correction equations introduce the additional dimension(s) to the two dimensional flat image of uncorrected data. Illustrative examples generated by three dimensional graphics will be presented.