# A Conic Transformation Approach for Solving the Perspective-Three-Point Problem

arXiv: https://arxiv.org/abs/2504.01620 · HTML: https://mlsanity.com/paper/2504.01620/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Builds on (most cited first, 2 of 2)

- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [An Efficient Algebraic Solution to the Perspective-Three-Point Problem](https://mlsanity.com/paper/1701.08237/) (2017)

## Built on by (most cited first, 2 of 2)

- [P3P Made Easy](https://mlsanity.com/paper/2508.01312/) (2025)
- [Solving Minimal Problems Without Matrix Inversion Using FFT-Based Interpolation](https://mlsanity.com/paper/2605.06572/) (2026)

## Abstract (arXiv)

We propose a conic transformation method to solve the Perspective-Three-Point (P3P) problem. In contrast to the current state-of-the-art solvers, which formulate the P3P problem by intersecting two conics and constructing a degenerate conic to find the intersection, our approach builds upon a new formulation based on a transformation that maps the two conics to a new coordinate system, where one of the conics becomes a standard parabola in a canonical form. This enables expressing one variable in terms of the other variable, and as a consequence, substantially simplifies the problem of finding the conic intersection. Moreover, the polynomial coefficients are fast to compute, and we only need to determine the real-valued intersection points, which avoids the requirement of using computationally expensive complex arithmetic. While the current state-of-the-art methods reduce the conic intersection problem to solving a univariate cubic equation, our approach, despite resulting in a quartic equation, is still faster thanks to this new simplified formulation. Extensive evaluations demonstrate that our method achieves higher speed while maintaining robustness and stability comparable to state-of-the-art methods.