Recovery of Circular Motion from Profiles of Surfaces

This paper addresses the problem of motion recovery from image profiles, in the important case of turntable sequences. No correspondences between points or lines are used. Symmetry properties of surfaces of revolution are exploited to obtain, in a robust and simple way, the image of the rotation axis of the sequence and the homography relating epipolar lines. These, together with geometric constraints for images of rotating objects, are used to obtain epipoles and, consequently, the full epipolar geometry of the camera system. This sequential approach (image of rotation axis — homography — 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 for the estimation of the epipolar geometry, is carried out as a one-dimensional optimization problem, with a smooth unimodal cost function. The initialization of the parameters is trivial in all three stages of the algorithm. After the estimation of the epipolar geometry, the motion is recovered using the fixed intrinsic parameters of the camera, obtained either from a calibration grid or from self-calibration techniques. Results from real data are presented, demonstrating the efficiency and practicality of the algorithm.