Multilinear Relationships between Coordinates of Corresponding Image Points and Lines

This paper describes how the fundamental matrix, F , the trifocal tensor T jk i and the quadrilinear relationship existing between corresponding points in four uncalibrated projective images may be derived in a common framework involving matrix determinants. Part of the paper contains a derivation of previous results, and is intended as a summary and reformulation. The derivations are based on the work of Faugeras and Mourrain [4] and Triggs [23, 22]. Tables of all the different relations involving the multi-view tensors are given. New results are obtained concerning the independence of the equations used to compute the trifocal and quadrilinear relationships, and methods of choosing those equations in a robust manner. Note to reviewers. This paper was presented at the International Sophus Lie Symposium in Norway in August 1995, and was intended for inclusion in a Springer Lecture Notes proceedings of the conference. Unfortunately, there were continuing delays in the production of those proceedings, and eventually they were abandoned. In the mean time, Anders Heyden discovered and presented similar results at the European Conference on Computer Vision, 1998. For this reason, some of the results here may be familiar. Nevertheless, having a reaonable claim to priority I am submitting this paper for your consideration.

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