Untwisting a Projective Reconstruction

A method for upgrading a projective reconstruction to metric is presented. The method compares favourably to state of the art algorithms and has been found extremely reliable for both large and small reconstructions in a large number of experiments on real data. The notion of a twisted pair is generalized to the uncalibrated case. The reconstruction is first transformed by considering cheirality so that it does not contain any twisted pairs. It is argued that this is essential, since the method then proceeds by local perturbation. As is preferrable, we utilize a cost function that reflects the prior likelihood of calibration matrices well. It is shown that with any such cost function, there is little hope of untwisting a twisted pair by local perturbation. The results show that in practice it is most often sufficient to start with a reconstruction that is free from twisted pairs, provided that the minimized objective function is a geometrically meaningful quantity. When subjected to the common degeneracy of little or no rotation between the views, the proposed method still yields a very reasonable member of the family of possible solutions. Furthermore, the method is very fast and therefore suitable for the purpose of viewing reconstructions.