Journal of Mathematical Imaging and Vision

, Volume 39, Issue 3, pp 259–268

A New Solution to the Relative Orientation Problem Using Only 3 Points and the Vertical Direction

  • Mahzad Kalantari
  • Amir Hashemi
  • Franck Jung
  • Jean-Pierre Guedon

DOI: 10.1007/s10851-010-0234-2

Cite this article as:
Kalantari, M., Hashemi, A., Jung, F. et al. J Math Imaging Vis (2011) 39: 259. doi:10.1007/s10851-010-0234-2


This paper presents a new method to solve the relative pose between two images, using three pairs of homologous points and the knowledge of the vertical direction. The vertical direction can be determined in two ways: The first requires direct physical measurements such as the ones provided by an IMU (inertial measurement unit). The other uses the automatic extraction of the vanishing point corresponding to the vertical direction in an image. This knowledge of the vertical direction solves two unknowns among the three parameters of the relative rotation, so that only three homologous couples of points are requested to position a couple of images. Rewriting the coplanarity equations thus leads to a much simpler solution. The remaining unknowns resolution is performed by “hiding a variable” approach. The elements necessary to build a specific algebraic solver are given in this paper, allowing for a real-time implementation. The results on real and synthetic data show the efficiency of this method.


Relative orientation Vertical direction Minimal solution 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Mahzad Kalantari
    • 1
  • Amir Hashemi
    • 2
  • Franck Jung
    • 3
  • Jean-Pierre Guedon
    • 4
  1. 1.Ecole Nationale des Sciences Géographiques, IGN France, Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), UMR CNRS 6597Polytech’NantesNantesFrance
  2. 2.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran
  3. 3.Commissariat général au développement durable, Direction de la recherche et de l’innovationMinistère de l’écologie, de l’énergie, du développement durable et de la mer, en charge des technologies vertes et des négociations sur le climatLa DéfenseFrance
  4. 4.Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), UMR CNRS 6597Polytech’NantesNantesFrance

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