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A minimal parameterization of the trifocal tensor
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
2009 (English)In: IEEE Computer Science Conference on Computer Vision and Pattern Recognition (CVPR), 2009, 1224-1230 p.Conference paper (Refereed)
Abstract [en]

The paper describes a minimal set of 18 parameters that can representany trifocal tensor consistent with the internal constraints.  9parameters describe three orthogonal matrices and 9 parameters describe10 elements of a sparse tensor T' with 17 elements in well-defined positions equal to zero.  Any valid trifocal tensor isthen given as some specific T' transformed by the orthogonalmatrices in the respective image domain.  The paper also describes asimple approach for estimating the three orthogonal matrices in thecase of a general 3 x 3 x 3 tensor, i.e., when the internalconstraints are not satisfied.  This can be used to accomplish a leastsquares approximation of a general tensor to a tensor that satisfies the internal constraints.  This type of constraint enforcement, inturn, can be used to obtain an improved estimate of the trifocal tensorbased on the normalized linear algorithm, with the constraintenforcement as a final step.  This makes the algorithm more similar tothe corresponding algorithm for estimation of the fundamental matrix. An experiment on synthetic data shows that the constraint enforcementof the trifocal tensor produces a significantly better result thanwithout enforcement, expressed by the positions of the epipoles, giventhat the constraint enforcement is made in normalized image coordinates.

Place, publisher, year, edition, pages
2009. 1224-1230 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-50607DOI: 10.1109/CVPRW.2009.5206829ISI: 000279038000157OAI: diva2:271736
Available from: 2009-10-13 Created: 2009-10-13 Last updated: 2010-08-13

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Nordberg, Klas
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