# Camera Pose Estimation from Lines using Pl"ucker Coordinates

arXiv: https://arxiv.org/abs/1608.02824 · HTML: https://mlsanity.com/paper/1608.02824/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2016.

## Built on by (most cited first, 7 of 7)

- [Towards Light-weight and Real-time Line Segment Detection](https://mlsanity.com/paper/2106.00186/) (2021)
- [Uncertainty-Aware Camera Pose Estimation from Points and Lines](https://mlsanity.com/paper/2107.03890/) (2021)
- [CPA: Camera-pose-awareness Diffusion Transformer for Video Generation](https://mlsanity.com/paper/2412.01429/) (2024)
- [PAPL-SLAM: Principal Axis-Anchored Monocular Point-Line SLAM](https://mlsanity.com/paper/2410.12324/) (2024)
- [PeLiCal: Targetless Extrinsic Calibration via Penetrating Lines for RGB-D Cameras with Limited Co-visibility](https://mlsanity.com/paper/2404.13949/) (2024)
- [PoseGravity: Pose Estimation from Points and Lines with Axis Prior](https://mlsanity.com/paper/2405.12646/) (2024)
- [A Geometric Framework for Absolute Pose and Velocity Estimation with Event Cameras](https://mlsanity.com/paper/2606.09139/) (2026)

## Abstract (arXiv)

Correspondences between 3D lines and their 2D images captured by a camera are often used to determine position and orientation of the camera in space. In this work, we propose a novel algebraic algorithm to estimate the camera pose. We parameterize 3D lines using Pl"ucker coordinates that allow linear projection of the lines into the image. A line projection matrix is estimated using Linear Least Squares and the camera pose is then extracted from the matrix. An algebraic approach to handle mismatched line correspondences is also included. The proposed algorithm is an order of magnitude faster yet comparably accurate and robust to the state-of-the-art, it does not require initialization, and it yields only one solution. The described method requires at least 9 lines and is particularly suitable for scenarios with 25 and more lines, as also shown in the results.