A minimal solution for relative pose with unknown focal length

Assume that we have two perspective images with known intrinsic parameters except for an unknown common focal length. It is a minimally constrained problem to find the relative orientation between the two images given six corresponding points. We present an efficient solution to the problem and show that there are 15 solutions in general (including complex solutions). To the best of our knowledge this was a previously unsolved problem. The solutions are found through eigen-decomposition of a 15×15 matrix. The matrix itself is generated in closed form. We demonstrate through practical experiments that the algorithm is correct and numerically stable.