3D reconstruction from image collections with a single known focal length

In this paper we aim at reconstructing 3D scenes from images with unknown focal lengths downloaded from photosharing websites such as Flickr. First we provide a minimal solution to finding the relative pose between a completely calibrated camera and a camera with an unknown focal length given six point correspondences. We show that this problem has up to nine solutions in general and present two efficient solvers to the problem. They are based on Gröbner basis, resp. on generalized eigenvalues, computation. We demonstrate by experiments with synthetic and real data that both solvers are correct, fast, numerically stable and work well even in some situations when the classical 6-point algorithm fails, e.g. when optical axes of the cameras are parallel or intersecting. Based on this solution we present a new efficient method for large-scale structure from motion from unordered data sets downloaded from the Internet. We show that this method can be effectively used to reconstruct 3D scenes from collection of images with very few (in principle single) images with known focal lengths.