Geometry-invariant-based reconstruction generated from planar laser and metrical rectification with conic dual to...

3D point reconstruction is a crucial component in optical inspection. A direct reconstruction process is proposed by combining two similarity invariants in active vision. A planar reference with an isosceles-right-angle pattern and a coplanar laser are adopted to generate the laser projective point on the measured object. The first invariant is the image of the conic dual to the circular points (ICDCP), which is derived from the lines in two pairs of perpendicular directions on the reference pattern. The invariant provides the transform from the projection space to the similarity space. Then, the ratio of the line segments consisting of the laser projection points and reference points is constructed as the other similarity invariant, by which the laser projection point in the similarity space is converted to Euclidean space. The solution of the laser point is modeled by the ratio invariant of the line segments and improved by a special point selection to avoid nonlinear equations. Finally, the benchmark-camera distance, the benchmark-generator distance, the benchmark length, image noise, and the number of orthogonal lines are experimentally investigated to explore the effectiveness and reconstruction error of the method. The reconstruction error averages of 0.94, 1.22, 1.77, and 2.15 mm are observed from the experiment results with the benchmark-camera distances from 600 mm to 750 mm with a 50 mm interval. This proves the validity and practicability of the reconstruction method.