Camera pose determination based on 4 coplanar points using tori parameters

Finding the position and orientation of a camera from the coordinates of more than three points is a well-known problem and several solutions have been proposed in the literature. In this work we present a different approach to the problem, in which a geometric interpretation based on tori is used. This approach is robust because it confines. the camera position to a small searching zone, using constraints based on tori information. The result is that the initial guess, requited for the algorithm that iteratively searches for the camera position, is not critical because it is already close to the solution. If more points are used the space constrained become smaller, which make the camera position determination easier. Besides, there is no complexity increment to the algorithm. Geometrical relations between four coplanar points and its respective images are-used to calculate the parameters of six tori. In fact, the camera is located at the intersection point of the six tori, Which is the basis of the algorithm presented here. To evaluate this algorithm, we simulated different positions of the camera, recovered them with the algorithm and quantified the maximum differences between the real and the calculated positions.