Optimization reconstruction of projective point of laser line coordinated by orthogonal reference

A 3D reconstruction method is presented for the laser projective point of a laser line, which is located by an orthogonal reference. The laser line is initially expressed by the Plücker matrix generated from two random points on the line and then transformed to the dual Plücker matrix representation. The initial solution of the 3D laser point is obtained by the non-homogeneous linear equations, which are derived from the projection geometry of the 3D feature point on the reference and the 3D laser point on the laser line represented by the dual Plücker matrix. The optimization function is constructed by minimizing the sums of the re-projection errors of the reference points and the laser point. The average absolute error of the initial solution is 1.07 mm while the one of the optimization solution is 1.01 mm. The average relative error of the initial solution is 4.14% while the one of the optimization solution is 3.86%. Thus, the optimization reconstruction of the projective point contributes the accuracy and the prospect in the vision-based inspection fields.