Camera Pose Estimation and Reconstruction from Image Profiles under Circular Motion

This paper addresses the problem of motion estimation and reconstruction of 3D models from profiles of an object rotating on a turntable, obtained from a single camera. Its main contribution is the development of a practical and accurate technique for solving this problem from profiles alone, which is, for the first time, precise enough to allow the reconstruction of the object. No correspondence between points or lines are necessary, although the method proposed can be equally used when these features are available, without any further adaptation. Symmetry properties of the surface of revolution swept out by the rotating object are exploited to obtain the image of the rotation axis and the homography relating epipolar lines, in a robust and elegant way. These, together with geometric constraints for images of rotating objects, are then used to obtain first the image of the horizon, which is the projection of the plane that contains the camera centres, and then the epipoles, thus fully determining the epipolar geometry of the sequence of images. The estimation of the epipolar geometry by this sequential approach (image of rotation axis — homography — image of the horizon — epipoles) avoids many of the problems usually found in other algorithms for motion recovery from profiles. In particular, the search for the epipoles, by far the most critical step, is carried out as a simple one-dimensional optimisation problem. The initialisation of the parameters is trivial and completely automatic for all stages of the algorithm. After the estimation of the epipolar geometry, the Euclidean motion is recovered using the fixed intrinsic parameters of the camera, obtained either from a calibration grid or from self-calibration techniques. Finally, the spinning object is reconstructed from its profiles, using the motion estimated in the previous stage. Results from real data are presented, demonstrating the efficiency and usefulness of the proposed methods.