# 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.

**Download:**
PDF.

**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: November 7, 2021