Geometric Derivations Of Minimal Sets Of Sufficient Multiview Constraints

Orrin H. Thomas, Edward R. Oshel

Research output: Contribution to journalArticlepeer-review

Abstract

Geometric interpretations of four of the most common determinant formulations of multiview constraints are given, showing that they all enforce the same geometry and that all of the forms commonly in use in the machine vision community are a subset of a more general form. Generalising the work of Yi Ma yields a new general 2×2 determinant trilinear and 3×3 determinant quadlinear. Geometric descriptions of degenerate multiview constraints are given, showing that it is necessary, but insufficient, that the determinant equals zero. Understanding the degeneracies leads naturally into proofs for minimum sufficient sets of bilinear, trilinear and quadlinear constraints for arbitrary numbers of conjugate observations.

Original languageEnglish
Pages (from-to)74-93
Number of pages20
JournalPhotogrammetric Record
Volume27
Issue number137
DOIs
StatePublished - Mar 2012
Externally publishedYes

Keywords

  • Bundle adjustment
  • Constraints
  • Multilinear
  • Multiview
  • Photogrammetry and computer vision
  • Quadlinear
  • Trilinear

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