3D reconstruction of laser projective point with projection invariant generated from five points on 2D target

Guan Xu,Jian Su,Xiaotao Li,Jing Yuan

doi:10.1038/s41598-017-07410-6

Abstract

Vision measurement on the basis of structured light plays a significant role in the optical inspection research. The 2D target fixed with a line laser projector is designed to realize the transformations among the world coordinate system, the camera coordinate system and the image coordinate system. The laser projective point and five non-collinear points that are randomly selected from the target are adopted to construct a projection invariant. The closed form solutions of the 3D laser points are solved by the homogeneous linear equations generated from the projection invariants. The optimization function is created by the parameterized re-projection errors of the laser points and the target points in the image coordinate system. Furthermore, the nonlinear optimization solutions of the world coordinates of the projection points, the camera parameters and the lens distortion coefficients are contributed by minimizing the optimization function. The accuracy of the 3D reconstruction is evaluated by comparing the displacements of the reconstructed laser points with the actual displacements. The effects of the image quantity, the lens distortion and the noises are investigated in the experiments, which demonstrate that the reconstruction approach is effective to contribute the accurate test in the measurement system.

Highlights

We focus on the second component, to construct the projection invariant according to the laser projective point and five target points
The optimization function is constructed by the differences between the re-projection points and the ideal points of the 2D target points and the laser points that are extracted in the image coordinate system
A reconstruction method for a laser projective point is discussed by the invariant determined by the five points on a 2D target

Summary

Methods

The reconstruction method of the projective point of the laser line includes two main components. In the camera-laser-line-based measurement system, a 2D target is employed to perform the two aims, the camera calibration and the projective point reconstruction of a laser line. The laser line of the projector lies on the O(W)-X(W)Y(W) plane that is the identical one of the target. The projective invariant in the world coordinate system is identical to the projective invariant of the laser projective point and the five mapping target points in the image coordinate system. The laser projective points and the mapping target feature points are extracted by the Harris method[25]

Results

Discussion

Conclusion