# CvxPnPL: A Unified Convex Solution to the Absolute Pose Estimation Problem from Point and Line Correspondences

arXiv: https://arxiv.org/abs/1907.10545 · HTML: https://mlsanity.com/paper/1907.10545/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2019.

## Built on by (most cited first, 12 of 12)

- [3D Line Mapping Revisited](https://mlsanity.com/paper/2303.17504/) (2023)
- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [Line as a Visual Sentence: Context-aware Line Descriptor for Visual Localization](https://mlsanity.com/paper/2109.04753/) (2021)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Fully Geometric Panoramic Localization](https://mlsanity.com/paper/2403.19904/) (2024)
- [Dynamical Pose Estimation](https://mlsanity.com/paper/2103.06182/) (2021)
- [Towards Understanding The Semidefinite Relaxations of Truncated Least-Squares in Robust Rotation Search](https://mlsanity.com/paper/2207.08350/) (2022)
- [LightGlueStick: a Fast and Robust Glue for Joint Point-Line Matching](https://mlsanity.com/paper/2510.16438/) (2025)
- [Efficient Solution of Point-Line Absolute Pose](https://mlsanity.com/paper/2404.16552/) (2024)
- [Registration beyond Points: General Affine Subspace Alignment via Geodesic Distance on Grassmann Manifold](https://mlsanity.com/paper/2507.17998/) (2025)
- [ARC-Calib: Autonomous Markerless Camera-to-Robot Calibration via Exploratory Robot Motions](https://mlsanity.com/paper/2503.14701/) (2025)
- [Unified and Efficient Point-Line Local Features](https://mlsanity.com/paper/2608.19894/) (2026)

## Abstract (arXiv)

We present a new convex method to estimate 3D pose from mixed combinations of 2D-3D point and line correspondences, the Perspective-n-Points-and-Lines problem (PnPL). We merge the contributions of each point and line into a unified Quadratic Constrained Quadratic Problem (QCQP) and then relax it into a Semi Definite Program (SDP) through Shor's relaxation. This makes it possible to gracefully handle mixed configurations of points and lines. Furthermore, the proposed relaxation allows us to recover a finite number of solutions under ambiguous configurations. In such cases, the 3D pose candidates are found by further enforcing geometric constraints on the solution space and then retrieving such poses from the intersections of multiple quadrics. Experiments provide results in line with the best performing state of the art methods while providing the flexibility of solving for an arbitrary number of points and lines.