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.

通过三个已知参考点的观察，我们提出了代数解法来解决经典的P3P问题，从而求得相机的位置和姿态。相比先前的方法，我们首先通过使用对应的几何约束来直接确定相机的姿态，并采用代数方法高效地解决三角函数方程组，从而确定未知的旋转矩阵及相机的位置。通过广泛的 Monte-Carlo模拟验证了该方法相对于最近的替代方法的优势，避免了计算不必要的（可能存在数值不稳定） 中间结果，从而在更低的计算成本下实现了更高的数值精度和鲁棒性。

透视三点问题的高效代数解法