Structure from motion: A new look from the point of view of invariant theory

Pierre Louis Bazin, Mireille Boutin

Research output: Contribution to journalArticlepeer-review

Abstract

We present a novel simple formulation of the problem of 3D object reconstruction from images. In this formulation, the object is seen as lying at the intersection of the projection of orbits of custom built Lie group actions. The group parameters correspond to unknown irrelevant quantities such as the camera orientation, the depth parameters of the object with respect to the camera, and the focal length. We then use an algorithmic method based on moving frames à la Fels-Olver to obtain a fundamental set of invariants of these group actions. The invariants are used to define a set of equations determining the 3D object, thus providing a mathematical formulation of the problem where the irrelevant parameters do not appear.

Original languageEnglish (US)
Pages (from-to)1156-1174
Number of pages19
JournalSIAM Journal on Applied Mathematics
Volume64
Issue number4
DOIs
StatePublished - Apr 1 2004

Keywords

  • Group action
  • Invariants
  • Moving frame
  • Orthographic camera
  • Pinpoint camera
  • Structure from motion

ASJC Scopus subject areas

  • Applied Mathematics

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