Structure and motion from lines under affine projections

In this paper we investigate the geometry and algebra of multiple projections of lines with affine cameras. Previously, the case of seven lines in three images has been studied. It was thought that this was the minimal data necessary for recovering affine structure and motion and that there are in general two solutions. It was also thought that these two solutions persist with more than seven lines. In this paper it is shown that the minimal cases are six lines in three images and five lines in four images. These cases are solved and it is shown that there are in general four solutions in both problems. Two almost minimal cases (seven lines in three images and six lines in four images) are solved using linear methods. Furthermore, it is shown that the solution is in general unique in these almost minimal cases. Finally, experiments are conducted on both simulated and real data in order to show the applicability of the theory.

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