Analytical results on error sensitivity of motion estimation from two views

  • Konstantinos Daniilidis
  • Hans-Hellmut Nagel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 427)


Fundamental instabilities have been observed in the performance of the majority of the algorithms for three dimensional motion estimation from two views. Many geometric and intuitive interpretations have been offered to explain the error sensitivity of the estimated parameters. In this paper, we address the importance of the form of the error norm to be minimized with respect to the motion parameters. We describe the error norms used by the existing algorithms in a unifying notation and give a geometric interpretation of them. We then explicitly prove that the minimization of the objective function leading to an eigenvector solution suffers from a crucial instability. The analyticity of our results allows us to examine the error sensitivity in terms of the translation direction, the viewing angle and the distance of the moving object from the camera. We propose a norm possessing a reasonable geometric interpretation in the image plane and we show by analytical means that a simplification of this norm leading to a closed form solution has undesirable properties.


Image Plane Error Norm Optical Flow Motion Estimation Displacement Rate 
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 1990

Authors and Affiliations

  • Konstantinos Daniilidis
    • 1
  • Hans-Hellmut Nagel
    • 1
  1. 1.Fraunhofer Institut für Informations- und DatenverarbeitungKarlsruhe 1FRG

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