Solution approach of a laser plane based on Plücker matrices of the projective lines on a flexible 2D target

A calibration method adopting Plücker matrices is proposed to explore the laser plane in a structured light measurement. The calibration model establishes the geometrical relationship among the camera, 2D target, and laser plane. The laser plane is constructed by multiple Plücker matrices of the dual 3D crossing lines between the laser plane and target planes in the camera coordinate system. Moreover, the validity of this calibration method is experimentally analyzed through the impact factors of noise magnitude and number of images. The mean errors of three directional angles of the normal vector to the laser plane are -0.174°, 0.170°, and -0.022°, respectively. The variances of the errors of three directional angles are 0.069°, 0.046°, and 0.160°, respectively. The maximal absolute errors of three directional angles are 1.362°, 1.351°, and 1.347°, respectively. The experiments prove that the calibration method is available to provide an accurate calibration for the laser plane.