Global calibration and equation reconstruction methods of a three dimensional curve generated from a laser plane in vision 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.