A P3P problem solver representing all parameters as a linear combination

We propose a novel strategy for the Perspective-Three-Point (P3P) problem that determines the position and orientation of a calibrated camera from three known point pairs of 2D-3D correspondences. Starting from three similarity transformation equations that relate the global and the camera-oriented coordinates, our method treats all the extrinsic camera parameters as a linear combination of known vectors with unknown coefficients. By reducing the number of unknowns and using a Gröbner basis, the problem is converted into a fourth-order polynomial equation with a single unknown parameter. Experimental results show that our method is highly practical and precise. Moreover, the performance of our method and its robustness to image noise are similar to those of a state-of-the-art method. In addition, our method exhibits greater computational efficiency than other methods.