Vision-based reconstruction of laser projection with invariant composed of points and circle on 2D reference

A vision-based reconstruction method is conducted by the point-circle invariant and the planar laser. The planar laser is coplanar to the two-dimensional (2D) reference. The combination of a circle on the 2D reference, a point on the 2D reference and a random point on the laser stripe is considered as the invariant, which is impervious to the projection from the laser plane to the image. Therefore, the reconstruction model is achieved by the invariant, which is generated from the projections of the above geometric features. The experiments are performed to verify the performance and reconstruction error of the method. The minimum error is 0.473 mm for the camera-reference distance of 600 mm, the scaleplate-projector distance of 100 mm and the reference length of 30 mm. Besides, the maximum error is 4.960 mm, for the camera-reference distance of 900 mm, the scaleplate-projector distance of 400 mm and the reference length of 120 mm. The reconstruction error means of 0.891 mm, 1.365 mm, 2.578 mm and 3.767 mm are observed with respect to the test conditions of 600–900 mm, which proves the applicability of the reconstruction method with the point-circle invariant.