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International Journal of Computer Vision

, Volume 120, Issue 2, pp 134–152 | Cite as

Trinocular Geometry Revisited

  • Matthew Trager
  • Jean Ponce
  • Martial Hebert
Article

Abstract

When do the visual rays associated with triplets of point correspondences converge, that is, intersect in a common point? Classical models of trinocular geometry based on the fundamental matrices and trifocal tensor associated with the corresponding cameras only provide partial answers to this fundamental question, in large part because of underlying, but seldom explicit, general configuration assumptions. This paper uses elementary tools from projective line geometry to provide necessary and sufficient geometric and analytical conditions for convergence in terms of transversals to triplets of visual rays, without any such assumptions. In turn, this yields a novel and simple minimal parameterization of trinocular geometry for cameras with non-collinear or collinear pinholes, which can be used to construct a practical and efficient method for trinocular geometry parameter estimation. We present numerical experiments using synthetic and real data.

Keywords

Trinocular geometry Trilinearities Minimal parameterizations of camera geometry Camera parameter estimation 

Notes

Acknowledgments

This work was supported in part by the ERC grant VideoWorld, the Institut Universitaire de France, the Inria - CMU associate team GAYA, and ONR MURI N000141010934.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Inria, Willow team, ENS/CNRS/Inria UMR 8548ParisFrance
  2. 2.Ecole Normale Supérieure/PSL Research University Willow team, ENS/CNRS/Inria UMR 8548ParisFrance
  3. 3.Robotics InstituteCarnegie-Mellon UniversityPittsburghUSA

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