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Epipolar geometry from profiles under circular motion

Addresses the problem of motion estimation from profiles (apparent contours) of an object rotating on a turntable in front of a single camera. A practical and accurate technique for solving this problem from profiles alone is developed. It is precise enough to reconstruct the shape of the object. No correspondences between points or lines are necessary. Symmetry of the surface of revolution swept out by the rotating object is exploited to obtain the image of the rotation axis and the homography relating epipolar lines in two views robustly and elegantly. These, together with geometric constraints for images of rotating objects, are used to obtain first the image of the horizon, which is the projection of the plane that contains the camera centers, and then the epipoles, thus fully determining the epipolar geometry of the image sequence. The estimation of this geometry by this sequential approach avoids many of the problems found in other algorithms. The search for the epipoles, by far the most critical step, is carried out as a simple 1D optimization. Parameter initialization is trivial and completely automatic at all stages. 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.