Solving the perspective-three-point problem with linear combinations: An accurate and efficient method

In this paper, we present an efficient algebraic solution to the perspective-three-point (P3P) problem that estimates the pose of a fully-calibrated camera from three given 3D-2D point correspondences. Previous P3P approaches typically solve for two sets of parameters: the depths of three 3D points and the pose of the camera. In contrast, our formulation does not involve any depth factor, and therefore can provide a more compact derivation for the P3P problem. By representing the involved rotation matrix and translation vector as a linear combination of known vectors with unknown coefficients and employing the orthogonal nature of the rotation matrix, this formulation finally leads to a univariate quartic equation which can be solved in closed form. The resulting algorithm is easy to understand and implement as it relies substantially on linear algebra. Experimental results demonstrate that the presented method can achieve a comparable accuracy to the state-of-the-art methods, but with significantly reduced computational requirements.