Calibrated and Partially Calibrated Semi-Generalized Homographies

In this paper, we propose the first minimal solutions for estimating the semi-generalized homography given a perspective and a generalized camera. The proposed solvers use five 2D-2D image point correspondences induced by a scene plane. One group of solvers assumes the perspective camera to be fully calibrated, while the other estimates the unknown focal length together with the absolute pose parameters. This setup is particularly important in structure-from-motion and visual localization pipelines, where a new camera is localized in each step with respect to a set of known cameras and 2D-3D correspondences might not be available. Thanks to a clever parametrization and the elimination ideal method, our solvers only need to solve a univariate polynomial of degree five or three, respectively a system of polynomial equations in two variables. All proposed solvers are stable and efficient as demonstrated by a number of synthetic and real-world experiments.