Equation construction of a laser plane demonstrates a remarkable importance for vision measurement systems based on the structured light. Here we create a simple 1D target with a cone at the bottom and a checkered pattern on the top to calibrate the equation of the laser plane in the view field of a camera. A group of 2D coordinates of the intersection points are extracted from the images with the 1D target at different positions. The objective function is constructed to optimize the coefficients of the laser plane by minimizing the difference between the distance from the feature point to the the origin point and the length of the 1D target. The projective lines of the optimized laser plane on the 3D calibration board overlap the real intersection lines in the experimental images. Finally, the comparison work about the influences of the non-Gaussian noise and point number is investigated experimentally. The experiments show that the method of the distance optimal object from the feature point to the origin point provides an accurate and robust calibration for the laser plane in structured light measurement.

We demonstrate a global calibration method for the laser plane using a 3D calibration board to generate the two horizontal coordinates and a height gauge to generate the height coordinate of the point in the laser plane. A sigmoid-Gaussian function for the candidate centers is employed to normalize the eigenvalues of the Hessian matrix to prevent centers missing or muti-centers. Then camera calibration and laser plane calibration are accomplished at the same time. Finally the reconstructed 3D points are transformed to the horizontal plane by the forward process that involves one translation and two rotations. The parametric equation of the 3D curve is reconstructed by the inverse process that performs on the 2D fitting curve.

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We develop a new method to globally calibrate the feature points that are derived from the binocular systems at different positions. A three-DOF (degree of freedom) global calibration system is established to move and rotate the 3D calibration board to an arbitrary position. A three-DOF global calibration model is constructed for the binocular systems at different positions. The three-DOF calibration model unifies the 3D coordinates of the feature points from different binocular systems into a unique world coordinate system that is determined by the initial position of the calibration board. Experiments are conducted on the binocular systems at the coaxial and diagonal positions. The experimental root-mean-square errors between the true and reconstructed 3D coordinates of the feature points are 0.573 mm, 0.520 mm and 0.528 mm at the coaxial positions. The experimental root-mean-square errors between the true and reconstructed 3D coordinates of the feature points are 0.495 mm, 0.556 mm and 0.627 mm at the diagonal positions. This method provides a global and accurate calibration to unity the measurement points of different binocular vision systems into the same world coordinate system.