Abstract
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.
Highlights
Active vision with the structured light is considered as one of the most promising approach for the optical detection and profile reconstruction, where the line-structured light is attractive due to the high accuracy and efficiency[1,2,3,4,5,6,7,8]
The measurement aims to reconstruct the 3D coordinates of the projective point of the laser line coordinated by the orthogonal reference
In order to evaluate the initial solutions and the optimization solutions of the 3D laser points, the 3D laser points are projected to the feature points on the planar ruler with the check board pattern
Summary
Active vision with the structured light is considered as one of the most promising approach for the optical detection and profile reconstruction, where the line-structured light is attractive due to the high accuracy and efficiency[1,2,3,4,5,6,7,8]. The 1D-reference-based calibration is performed by rotating the reference around a fixed point. Xu12 introduces a simple calibration method by using the Plücker matrices with the help of the 2D target images. Fathi[15] proposes a conversion method to calibrate the camera for the application in the 3D reconstruction. The 1D reference method adopts at least six images to perform the camera calibration. The camera parameters are solved by the homograph from the 3D points on the reference to the 2D points on the image. A new camera calibration method of the laser plane is presented by Xu18 with a 3D reference and a 1D reference. The 2D coordinates of the intersection points between the laser plane and the 1D reference are extracted for the laser plane calibration.
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