The Five Points Pose Problem: A New and Accurate Solution Adapted to Any Geometric Configuration

  • Mahzad Kalantari
  • Franck Jung
  • Jean-Pierre Guedon
  • Nicolas Paparoditis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5414)


The goal of this paper is to estimate directly the rotation and translation between two stereoscopic images with the help of five homologous points. The methodology presented does not mix the rotation and translation parameters, which is comparably an important advantage over the methods using the well-known essential matrix. This results in correct behavior and accuracy for situations otherwise known as quite unfavorable, such as planar scenes, or panoramic sets of images (with a null base length), while providing quite comparable results for more “standard” cases. The resolution of the algebraic polynomials resulting from the modeling of the coplanarity constraint is made with the help of powerful algebraic solver tools (the Gröbner bases and the Rational Univariate Representation).


Five points pose problem polynomial direct resolution Gröbner bases relative orientation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mahzad Kalantari
    • 1
    • 2
    • 3
  • Franck Jung
    • 4
  • Jean-Pierre Guedon
    • 2
    • 3
  • Nicolas Paparoditis
    • 1
  1. 1.MATIS LaboratoryInstitut Geographique NationalSaint-Mandé CedexFrance
  2. 2.Institut Recherche Communications Cybernétique de Nantes (IRCCyN) UMR CNRS 6597Nantes Cedex 03France
  3. 3.Institut de Recherche sur les Sciences et Techniques de la Ville CNRS FR 2488France
  4. 4.DDE - Seine MaritimeFrance

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