Trilinearity of three perspective views and its associated tensor

Amnon Shashua*, Michael Werman

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

90 Scopus citations


It has been established that certain trilinear forms of three perspective views give rise to a tensor of 27 intrinsic coefficients [11]. We show in this paper that a permutation of the trilinear coefficients produces three homography matrices (projective transformations of planes) of three distinct intrinsic planes, respectively. This, in turn, yields the result that 3D invariants are recovered directly - simply by appropriate arrangement of the tensor's coefficients. On a secondary level, we show new relations between fundamental matrix, epipoles, Euclidean structure and the trilinear tensor. On the practical side, the new results extend the existing envelope of methods of 3D recovery from 2D views - for example, new linear methods that cut through the epipolar geometry, and new methods for computing epipolar geometry using redundancy available across many views.

Original languageAmerican English
Number of pages6
StatePublished - 1995
EventProceedings of the 5th International Conference on Computer Vision - Cambridge, MA, USA
Duration: 20 Jun 199523 Jun 1995


ConferenceProceedings of the 5th International Conference on Computer Vision
CityCambridge, MA, USA


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