The rank 4 constraint in multiple (≥ 3) view geometry

Amnon Shashua, Shai Avidan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

40 Scopus citations


It has been established that certain trilinear froms of three perspective views give rise to a tensor of 27 intrinsic coefficients [8]. 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 [3, 12, 5]. 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.

Original languageAmerican English
Title of host publicationComputer Vision – ECCV 1996 - 4th European Conference on Computer Vision, Proceedings
EditorsBernard Buxton, Roberto Cipolla
PublisherSpringer Verlag
Number of pages11
ISBN (Print)3540611231, 9783540611233
StatePublished - 1996
Externally publishedYes
Event4th European Conference on Computer Vision, ECCV 1996 - Cambridge, United Kingdom
Duration: 15 Apr 199618 Apr 1996

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference4th European Conference on Computer Vision, ECCV 1996
Country/TerritoryUnited Kingdom

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1996.


  • 3D recovery from 2D views
  • Algebraic and projective geometry
  • Matching constraints
  • Projective structure
  • Trilinearity


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