Affine Perspective-Three-Point Problem

This paper addresses the Perspective-Three-Point (P3P) problem under affine camera models. We derive direct closed-form solvers for weak perspective and para perspective, which are representative affine camera models. The affine P3P solution reduces to a bi-quadratic equation. Unlike exact P3P solvers that require a cubic or quartic equation, it allows for the simple and stable calculation of real solutions using the quadratic formula. Since affine approximations are valid only when scene depth variation is small, we further propose an iterative correction that upgrades the affine solution to the exact P3P solution. Through extensive comparisons using synthetic data and public datasets, we demonstrate that affine P3P solvers with two upgrade iterations achieve performance substantially comparable to that of the state-of-the-art P3P solver.