Horizon Constraint for Unambiguous UAV Navigation in Planar Scenes


When the UAV goes to high altitudes such that the observed surface of the earth becomes planar, the structure and motion recovery of the earth’s moving plane becomes ambiguous. This planar degeneracy has been pointed out very often in the literature; therefore, current navigation methods either completely fail or give many confusing solutions in such scenario. Interestingly, the horizon line in planar scenes is straight and distinctive; hence, easily detected. Therefore, we show in this paper that the horizon line provides two degrees of freedom that control the relative orientation between the camera coordinate system and the local surface of earth. The recovered degrees of freedom help linearize and disambiguate the planar flow, and therefore we obtain a unique solution for the UAV motion estimation. Unlike previous work which used the horizon to provide the roll angle and the pitch percentage and only employed them for flight stability, we extract the exact angles and directly use them to estimate the ego motion. Additionally, we propose a novel horizon detector based on the maximum a posteriori estimation of both motion and appearance features which outperforms the other detectors in planar scenarios. We thoroughly experimented on the proposed method against information from GPS and gyroscopes, and obtained promising results.

Roll and Pitch angles from the Horizon

Equation of the Ground Plane

Ego-Motion Estimation

Given the optical flow between two frames, we first estimate the pseudo-perspective motion parameters. Consequently, we insert the derived equation of the ground plane in the motion equations. By applying several basic operations on the equations (rearranging and taking rations), we obtain a new linear set of equations which can be directly used to obtain the translational and rotational velocities.

Experiments Setup