Partial camera calibration from a single circle

The accurate spatial location of a camera, in terms of both position and rotation, is essential in numerous tasks, such as robot navigation, indoor georeferencing for egocentric motion analysis, and estimation of the trajectory for manned and unmanned aerial vehicles. Precise localization requires estimating all six degrees of freedom (DoF) of a rigid body in space, which includes the three spatial coordinates (x, y, and z) and the three rotation angles (yaw, pitch, and roll). Typically, planar targets whose positions are known a priori are used to achieve this task. However, the accurate estimation of all 6 DoF depends on a recognizable target that can be identified from different distances, under different illuminations, and using cameras with different resolutions and focal lengths. In many cases, it is enough to identify the target’s distance and height relative to its lying plane. For instance, a drone that needs to land in a predetermined area delimited by specific horizontal signage needs only to know the distance from the target and the UAV’s altitude to plan a landing trajectory accurately. Therefore, a simple circular target signage can be defined, which is easy to be identified even from far positions and under conditions of poor illumination. In this article, we propose a robust method to identify a circular target and accurately estimate the distance and altitude of the camera relative to the target lying plane. The circular signage is identified using the method of Euclidean invariants of the quadric surfaces. Finally, we present a set of simulations and real-life measurements to evaluate the accuracy and robustness of the proposed method.