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. To this problem which to the best of our knowledge was unsolved we present an efficient solver. Through numerical experiments we demonstrate that the algorithm is correct, numerically stable and useful. The solutions are found through eigen-decomposition of a 15×1515×15 matrix. The matrix itself is generated in closed form.