An Efficient Algebraic Solution to the Perspective-Three-Point Problem
This work addresses a classical computer vision problem for camera localization, offering an incremental improvement in efficiency and stability for applications like robotics and augmented reality.
The paper tackles the perspective-three-point (P3P) problem for camera pose estimation by introducing an algebraic solution that directly determines camera attitude using trigonometric equations, resulting in higher numerical accuracy, robustness, and lower computational cost compared to recent alternatives, as validated through Monte-Carlo simulations.
In this work, we present an algebraic solution to the classical perspective-3-point (P3P) problem for determining the position and attitude of a camera from observations of three known reference points. In contrast to previous approaches, we first directly determine the camera's attitude by employing the corresponding geometric constraints to formulate a system of trigonometric equations. This is then efficiently solved, following an algebraic approach, to determine the unknown rotation matrix and subsequently the camera's position. As compared to recent alternatives, our method avoids computing unnecessary (and potentially numerically unstable) intermediate results, and thus achieves higher numerical accuracy and robustness at a lower computational cost. These benefits are validated through extensive Monte-Carlo simulations for both nominal and close-to-singular geometric configurations.