Finding the Exact Rotation between Two Images Independently of the Translation

  • Laurent Kneip
  • Roland Siegwart
  • Marc Pollefeys
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7577)


In this paper, we present a new epipolar constraint for computing the rotation between two images independently of the translation. Against the common belief in the field of geometric vision that it is not possible to find one independently of the other, we show how this can be achieved by relatively simple two-view constraints. We use the fact that translation and rotation cause fundamentally different flow fields on the unit sphere centered around the camera. This allows to establish independent constraints on translation and rotation, and the latter is solved using the Gröbner basis method. The rotation computation is completed by a solution to the cheiriality problem that depends neither on translation, nor on feature triangulations. Notably, we show for the first time how the constraint on the rotation has the advantage of remaining exact even in the case of translations converging to zero. We use this fact in order to remove the error caused by model selection via a non-linear optimization of rotation hypotheses. We show that our method operates in real-time and compare it to a standard existing approach in terms of both speed and accuracy.


Rotation Matrix Rotation Matrice Visual Odometry Pure Rotation Epipolar Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Laurent Kneip
    • 1
  • Roland Siegwart
    • 1
  • Marc Pollefeys
    • 2
  1. 1.Autonomous Systems LabETH ZurichSwitzerland
  2. 2.Computer Vision and Geometry GroupETH ZurichSwitzerland

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