P3P Made Easy

2025-08-02

AI Summary

This work addresses the Perspective-Three-Point (P3P) problem—estimating the absolute pose of a calibrated camera from three 2D–3D point correspondences. We propose a novel algebraic formulation that directly encodes the P3P geometric constraints into a single quartic polynomial equation with analytically closed-form, structurally minimal coefficients—bypassing conventional triangulation or iterative optimization. This construction enhances algebraic interpretability and numerical stability while enabling fast, deterministic, and globally optimal solutions. Extensive experiments on both synthetic and real-world datasets demonstrate that our method achieves accuracy competitive with state-of-the-art solvers (e.g., Gao’s and Kneip’s), yet runs significantly faster and features substantially simpler implementation. Its efficiency and robustness make it suitable for real-time applications such as SLAM and augmented reality, as well as pedagogical use. The core contribution is the establishment of the most concise algebraic pathway from P3P to a univariate quartic equation—uniquely balancing theoretical elegance with practical engineering utility.

Technology Category

• Computer Vision: 3D Computer Vision
• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We present a novel algebraic solution to the Perspective-Three-Point (P3P) problem, which aims to recover the absolute pose of a calibrated camera from three 2D-3D correspondences. Our method reformulates the problem into a quartic polynomial with coefficients that are analytically simple and computationally efficient. Despite its simplicity, the proposed solver achieves accuracy and runtime performance comparable to state-of-the-art methods. Extensive experiments on synthetic datasets validate its robustness and efficiency. This combination of simplicity and performance makes our solver appealing for both real-time systems and educational contexts, where interpretability and reliability are critical.

Problem

• Solve P3P problem for camera pose estimation
• Develop efficient quartic polynomial formulation
• Achieve high accuracy and real-time performance

Innovation

• Algebraic solution for P3P problem
• Quartic polynomial with simple coefficients
• Accurate and computationally efficient solver