Abstract
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 closeto-singular geometric configurations