P3P Made Easy
Seong Hun Lee, Patrick Vandewalle, Javier Civera
TL;DR
This work revisits the Perspective-Three-Point ($P3P$) problem and shows that it can be solved by a compact quartic polynomial with coefficients that are easy to derive. Grounded in classical results from Grunert (1841) and Smith (1965), the authors present practical strategies to enhance numerical stability and demonstrate that the approach achieves accuracy and runtime on par with state-of-the-art solvers. The method yields up to four pose hypotheses, refined via Gauss-Newton on the cosine rules, and remains attractive for teaching and edge-device deployments due to its algebraic simplicity. Overall, the paper argues that revisiting classical formulations with modern insights can match or exceed more elaborate modern minimal solvers, and it provides open-source code for replication and deployment.
Abstract
We revisit the classical Perspective-Three-Point (P3P) problem, which aims to recover the absolute pose of a calibrated camera from three 2D-3D correspondences. It has long been known that P3P can be reduced to a quartic polynomial with analytically simple and computationally efficient coefficients. However, this elegant formulation has been largely overlooked in modern literature. Building on the theoretical foundation that traces back to Grunert's work in 1841, we propose a compact algebraic solver that achieves accuracy and runtime comparable to state-of-the-art methods. Our results show that this classical formulation remains highly competitive when implemented with modern insights, offering an excellent balance between simplicity, efficiency, and accuracy.