A Complete, Accurate and Efficient Solution for the Perspective-n-Line Problem

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“A Complete, Accurate and Efficient Solution for the Perspective-n-Line Problem” by L. Zhou, D. Koppel, and M. Kaess. IEEE Robotics and Automation Letters, RA-L, vol. 6, no. 2, Apr. 2021. Presented at ICRA 2021.

Abstract

This paper presents a complete, accurate, and efficient solution for the Perspective-n-Line (PnL) problem. Generally, the camera pose can be determined from N>=3 2D-3D line correspondences. The minimal problem (N=3) and the least-squares problem (N>3) are generally solved in different ways. This paper shows that a least-squares PnL problem can be transformed into a quadratic equation system that has the same form as the minimal problem. This leads to a unified solution for the minimal and least-squares PnL problems. We adopt the Gram-Schmidt process and a novel hidden variable polynomial solver to increase the numerical stability of our algorithm. Experimental results show that our algorithm is more accurate and robust than the state-of-the-art least-squares algorithms [1]-[4] and is significantly faster. Moreover, our algorithm is more stable than previous minimal solutions [3], [5], [6] with comparable runtime.

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BibTeX entry:

@article{Zhou21ral,
   author = {L. Zhou and D. Koppel and M. Kaess},
   title = {A Complete, Accurate and Efficient Solution for the
	Perspective-n-Line Problem},
   journal = {IEEE Robotics and Automation Letters, RA-L},
   volume = {6},
   number = {2},
   month = apr,
   year = {2021},
   note = {Presented at ICRA 2021.}
}
Last updated: March 26, 2021