Technical Report CIS9520

TR#:CIS9520
Class:CIS
Title: THE RANK 4 CONSTRAINT IN MULTIPLE $(\geq 3)$ VIEW GEOMETRY.
Authors: A. Shashua and S. Avidan
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Abstract: It has been established that certain trilinear forms of three perspective views give rise to a tensor of 27 intrinsic coefficients [7]. Further investigations have shown the existence of quadlinear forms across four views with the negative result that further views would not add any new constraints. We show in this paper first general results on any number of views. Rather than seeking new constraints (which we know now is not possible) we seek connections across trilinear tensors of triplets of views. Two main results are shown: (i) trilinear tensors across $m > 3$ views are embedded in a low dimensional linear subspace, (ii) given two views, all the induced homography matrices are embedded in a four-dimensional linear subspace. The two results, separately and combined, offer new possibilities of handling the consistency across multiple views in a linear manner (via factorization), some of which are further detailed in this paper.
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