# MLPnP - A Real-Time Maximum Likelihood Solution to the Perspective-n-Point Problem

arXiv: https://arxiv.org/abs/1607.08112 · HTML: https://mlsanity.com/paper/1607.08112/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2016.

## Built on by (most cited first, 13 of 13)

- [Uncertainty-Aware Camera Pose Estimation from Points and Lines](https://mlsanity.com/paper/2107.03890/) (2021)
- [CheckerPose: Progressive Dense Keypoint Localization for Object Pose Estimation with Graph Neural Network](https://mlsanity.com/paper/2303.16874/) (2023)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [CPnP: Consistent Pose Estimator for Perspective-n-Point Problem with Bias Elimination](https://mlsanity.com/paper/2209.05824/) (2022)
- [DAC: Detector-Agnostic Spatial Covariances for Deep Local Features](https://mlsanity.com/paper/2305.12250/) (2023)
- [Generalized Maximum Likelihood Estimation for Perspective-n-Point Problem](https://mlsanity.com/paper/2408.01945/) (2024)
- [Optimal DLT-based Solutions for the Perspective-n-Point](https://mlsanity.com/paper/2410.14164/) (2024)
- [Exploring the Adjugate Matrix Approach to Quaternion Pose Extraction](https://mlsanity.com/paper/2205.09116/) (2022)
- [Consistent and Optimal Solution to Camera Motion Estimation](https://mlsanity.com/paper/2403.01174/) (2024)
- [Neural Real-Time Recalibration for Infrared Multi-Camera Systems](https://mlsanity.com/paper/2410.14505/) (2024)
- [LOSTU: Fast, Scalable, and Uncertainty-Aware Triangulation](https://mlsanity.com/paper/2311.11171/) (2023)
- [A PnP Algorithm for Two-Dimensional Pose Estimation](https://mlsanity.com/paper/2312.08488/) (2023)
- [Solving Short-Term Relocalization Problems In Monocular Keyframe Visual SLAM Using Spatial And Semantic Data](https://mlsanity.com/paper/2407.19518/) (2024)

## Abstract (arXiv)

In this paper, a statistically optimal solution to the Perspective-n-Point (PnP) problem is presented. Many solutions to the PnP problem are geometrically optimal, but do not consider the uncertainties of the observations. In addition, it would be desirable to have an internal estimation of the accuracy of the estimated rotation and translation parameters of the camera pose. Thus, we propose a novel maximum likelihood solution to the PnP problem, that incorporates image observation uncertainties and remains real-time capable at the same time. Further, the presented method is general, as is works with 3D direction vectors instead of 2D image points and is thus able to cope with arbitrary central camera models. This is achieved by projecting (and thus reducing) the covariance matrices of the observations to the corresponding vector tangent space.