Self-calibration from turn-table sequences in presence of zoom and focus

This paper proposes a novel method, using constant inter-frame motion, for self-calibration from an image sequence of an object rotating around a single axis with varying camera internal parameters. Our approach makes use of the facts that in many commercial systems rotation angles are often controlled by an electromechanical system, and that the inter-frame essential matrices are invariant if the rotation angles are constant but not necessary known. Therefore, recovering camera internal parameters is possible by making use of the equivalence of essential matrices which relate the unknown calibration matrices to the fundamental matrices computed from the point correspondences. We also describe a linear method that works under restrictive conditions on camera internal parameters, the solution of which can be used as the starting point of the iterative non-linear method with looser constraints. The results are refined by enforcing the global constraints that the projected trajectory of any 3D point should be a conic after compensating for the focusing and zooming effects. Finally, using the bundle adjustment method tailored to the special case, i.e., static camera and constant object rotation, the 3D structure of the object is recovered and the camera parameters are further refined simultaneously. To determine the accuracy and the robustness of the proposed algorithm, we present the results on both synthetic and real sequences.