# CPnP: Consistent Pose Estimator for Perspective-n-Point Problem with Bias Elimination

arXiv: https://arxiv.org/abs/2209.05824 · HTML: https://mlsanity.com/paper/2209.05824/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 13 Sep 2022.

## Builds on (most cited first, 6 of 6)

- [VINS-Mono: A Robust and Versatile Monocular Visual-Inertial State Estimator](https://mlsanity.com/paper/1708.03852/) (2017)
- [6-DoF Object Pose from Semantic Keypoints](https://mlsanity.com/paper/1703.04670/) (2017)
- [Camera-to-Robot Pose Estimation from a Single Image](https://mlsanity.com/paper/1911.09231/) (2019)
- [Uncertainty-Aware Camera Pose Estimation from Points and Lines](https://mlsanity.com/paper/2107.03890/) (2021)
- [MLPnP - A Real-Time Maximum Likelihood Solution to the Perspective-n-Point Problem](https://mlsanity.com/paper/1607.08112/) (2016)
- [Backtracking Regression Forests for Accurate Camera Relocalization](https://mlsanity.com/paper/1710.07965/) (2017)

## Built on by (most cited first, 3 of 3)

- [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)
- [Differential 6-DOF Pose Estimation with Provable First-Order Immunity to Camera Calibration Errors](https://mlsanity.com/paper/2608.04673/) (2026)

## Abstract (arXiv)

The Perspective-n-Point (PnP) problem has been widely studied in both computer vision and photogrammetry societies. With the development of feature extraction techniques, a large number of feature points might be available in a single shot. It is promising to devise a consistent estimator, i.e., the estimate can converge to the true camera pose as the number of points increases. To this end, we propose a consistent PnP solver, named CPnP, with bias elimination. Specifically, linear equations are constructed from the original projection model via measurement model modification and variable elimination, based on which a closed-form least-squares solution is obtained. We then analyze and subtract the asymptotic bias of this solution, resulting in a consistent estimate. Additionally, Gauss-Newton (GN) iterations are executed to refine the consistent solution. Our proposed estimator is efficient in terms of computations -- it has O(n) computational complexity. Experimental tests on both synthetic data and real images show that our proposed estimator is superior to some well-known ones for images with dense visual features, in terms of estimation precision and computing time.