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 of them assumes the perspective camera to be fully calibrated, while the other solver estimates the unknown focal length together with the absolute pose parameters. This setup is particularly important in structure-from-motion and image-based 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. As a consequence of a clever parametrization and the elimination ideal method, our approach only needs to solve a univariate polynomial of degree five or three. The proposed solvers are stable and efficient as demonstrated by a number of synthetic and real-world experiments.