We propose a non-iterative solution to the PnP problem—the estimation of the pose of a calibrated camera from n 3D-to-2D point correspondences—whose computational complexity grows linearly with n. This is in contrast to state-of-the-art methods that are O(n 5) or even O(n 8), without being more accurate. Our method is applicable for all n≥4 and handles properly both planar and non-planar configurations. Our central idea is to express then 3D points as a weighted sum of four virtual control points. The problem then reduces to estimating the coordinates of these control points in the camera referential, which can be done inO(n) time by expressing these coordinates as weighted sum of the eigenvectors of a 12×12 matrix and solving a small constantnumber of quadratic equations to pick the right weights. Furthermore, if maximal precision is required, the output of the closed-form solution can be used to initialize a Gauss-Newton scheme, which improves accuracy with negligible amount of additional time. The advantages of our method are demonstrated by thorough testing on both synthetic and real-data.
Reference
Lepetit, Vincent, Francesc Moreno-Noguer, and Pascal Fua."Epnp: An accurate o(n) solution to the pnp problem." International journal of computer vision 81.2(2009): 155-166.
2013-05-01