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.

# Horizon Constraint for Unambiguous UAV Navigation in Planar Scenes

- 1. Introduction
- 2. Roll and Pitch Angles from the Horizon
- 3. Equation of the Ground Plane
- 4. Ego-Motion Estimation
- 5. Experiments Setup
- 6. Results

### Introduction

### 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.