Position and orientation measurement adopting camera calibrated by projection geometry of Pl\xfccker matrices of three-dimensional lines

Guan Xu,Anqi Zheng,Xiaotao Li,Jian Su

doi:10.1038/srep44092

Abstract

A position and orientation measurement method is investigated by adopting a camera calibrated by the projection geometry of the skew-symmetric Plücker matrices of 3D lines. The relationship between the Plücker matrices of the dual 3D lines and the 2D projective lines is provided in two vertical world coordinate planes. The transform matrix is generated from the projections of the 3D lines. The differences between the coordinates of the reprojective lines and the coordinates of extracted lines are employed to verify the calibration validity. Moreover, the differences between the standard movement distance of the target and the measurement distance are also presented to compare the calibration accuracy of the 3D line to 2D line method and the point-based method. Furthermore, we also explore the noise immunity of the two methods by adding Gaussian noises. Finally, an example to measure the position and orientation of a cart is performed as an application case of this method. The results are tabled for the reproduction by the readers. The results demonstrate that the line to line method contributes higher calibration accuracy and better noise immunity. The position and orientation measurement adopting the line to line method is valid for the future applications.

Highlights

A position and orientation measurement method is investigated by adopting a camera calibrated by the projection geometry of the skew-symmetric Plücker matrices of 3D lines
As the transformation matrix of the camera contains the position and orientation information of a measured object in a captured image, we focus on the position and orientation measurement technique using a calibrated camera by the projection geometry of Plücker matrices of three-dimensional lines
According to the 3D line to 2D line method, the transformation matrix P is generated from n 3D lines Li and n 2D projective lines li

Summary

Introduction

A position and orientation measurement method is investigated by adopting a camera calibrated by the projection geometry of the skew-symmetric Plücker matrices of 3D lines. As the transformation matrix of the camera contains the position and orientation information of a measured object in a captured image, we focus on the position and orientation measurement technique using a calibrated camera by the projection geometry of Plücker matrices of three-dimensional lines. Point-based calibration method achieves the advantages of high speed and easy operation It is affected by the image noises. The line-pattern-based calibration method is selected in this paper considering the moderate speed of extracting lines and good noises immunity. We firstly explore the camera calibration method adopting the projection geometry from the Plücker matrices of 3D lines to the 2D projective lines. The position and orientation of the measured cart is generated from the translation vector and the rotation matrix, and verified by the absolute and relative errors of the reconstructed displacements

Methods

Results

Conclusion