Solving the Plane-Sphere Ambiguity in Top-Down Structure-from-Motion.

Drone-based land surveys and tracking applications with a moving camera require three-dimensional reconstructions from videos recorded using a downward facing camera and are usually generated by Structure-from-Motion (SfM) algorithms. Unfortunately, monocular SfM pipelines can fail in the presence of lens distortion due to a critical configuration resulting in a plane-sphere ambiguity which is characterized by severe curvatures of the reconstructions and erroneous relative camera pose estimations. We propose a 4-point minimal solver for the relative pose estimation for two views sharing the same radial distortion parameters (i.e. from the same camera) with a viewing direction perpendicular to the ground plane. To extract 3D reconstructions from continuous videos, the relative pose of pairwise frames is estimated by using the solver with RANSAC and the Sampson error where globally consistent distortion parameters are determined by taking the medial of all values. Moreover, we propose an additional regularizer for the final bundle adjustment to remove any remaining curvature of the reconstruction if necessary. We tested our methods on synthetic and real-world data and our results demonstrate a significant reduction of curvature and more accurate relative pose estimations. Our algorithm can be easily integrated into existing pipelines and is therefore a practical solution to resolve the plane-sphere ambiguity in a variety of top-down SfM applications.