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We propose a branch-and-bound algorithm to obtain the globally optimal relative rotation between a camera and the rotation sensor attached to it. Compared to previous methods, our approach directly minimizes the image space error related to the measurements which is very natural for camera-based systems. Our algorithm is based on the observation that we may evaluate the residual when the rotation matrix is known. We propose a feasibility test algorithm for the branch-and-bound to efficiently reduce the search volume of the rotation domain. Experimental results are provided using synthetic and real data sets.