P3P Made Easy

TL;DR

This paper revisits the classical P3P problem, demonstrating that its simple quartic polynomial formulation remains highly effective and competitive with modern methods in terms of accuracy and efficiency.

Contribution

The authors propose a compact algebraic solver for P3P based on classical formulations, highlighting its competitiveness with modern approaches.

Findings

The classical P3P formulation is still highly effective.

The proposed solver achieves accuracy comparable to state-of-the-art methods.

The solver offers a good balance of simplicity, efficiency, and accuracy.

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.