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

  • Amnon Shashua
  • Shai Avidan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1065)

Abstract

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.

Keywords

Trilinearity 3D recovery from 2D views Matching Constraints Projective Structure Algebraic and Projective Geometry 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Amnon Shashua
    • 1
  • Shai Avidan
    • 2
  1. 1.CS departmentTechnion-Israel Institute of TechnologyHaifaIsrael
  2. 2.Institute of Computer ScienceHebrew UniversityJerusalemIsrael

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