Homography estimation from circular motion for use in visual control

This paper presents a new method for estimation of the homography up to similarity from observing a single point that is rotating at constant velocity around a single axis. The benefit of the proposed estimation approach is that it does not require measurement of the points in the world frame. The homography is estimated based on the known shape of the motion and in-image tracking of a single rotating point. The proposed method is compared to the two known methods: the direct approach based on point correspondences and a more recently proposed method based on conic properties. The main advantages of the proposed method are that it also estimates the angular velocity and that it requires only a single circle. The estimation is made directly from the measurements in the image. Because of the advantages of the proposed method over the other methods, the proposed method should be simple to implement for calibration of visually guided robotic systems. All the approaches were compared in the simulation environment in some non-ideal conditions and in the presence of disturbances, and a real experiment was made on a mobile robot. The experimental results confirm that the presented approach gives accurate results, even in some non-ideal conditions.