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The quality of a mosaic depends on the projective alignment of the images involved. After point-correspondences between the images have been established, bundle adjustment finds an alignment considered optimal under certain hypotheses. This procedure minimizes a nonlinear cost and has to be initialized with care. It is very common to compose inter-frame homographies which have been computed with standard methods in order to get an initial global alignment. This technique is suboptimal if there is noise or missing homographies as it typically uses a small part of the available data.We propose four new closed-form solutions. They all provide non-heuristic initial alignments using all the known inter-frame homographies. Our methods are tested with synthetic and real data and are compared to the standard method. These experiments reveal that our methods are more accurate, taking advantage of the redundant information available in the set of inter-frame homographies.