Spherical objects based motion estimation for catadioptric cameras

In this paper, spherical objects are employed to estimate motion parameters between two central catadioptric cameras. An occluding contour of a sphere is projected to a conic in the central catadioptric image, and such a conic is called a sphere image. The main contribution of this work is that such a sphere image is shown to be able to parameterized by only three parameters rather than five ones as a generic conic requires. Based on such a finding, an efficient motion estimation algorithm is proposed which consists of the following three main steps: firstly, sphere images are efficiently detected by the Hough transform and refined by minimizing the orthogonal distances. Secondly, the centers of these spherical objects are estimated from the above obtained sphere images in the two catadioptric camera coordinate systems respectively. Thirdly, motion parameters are estimated from the corresponding centers. The proposed algorithm is shown workable by experiments and can be applied to camera network calibration and robot localization.