Discontinuity-Preserving Computation of Variational Optic Flow in Real-Time

  • Andrés Bruhn
  • Joachim Weickert
  • Timo Kohlberger
  • Christoph Schnörr
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3459)


Variational methods are very popular for optic flow computation: They yield dense flow fields and perform well if they are adapted such that they respect discontinuities in the image sequence or the flow field. Unfortunately, this adaptation results in high computational complexity. In our paper we show that it is possible to achieve real-time performance for these methods if bidirectional multigrid strategies are used. To this end, we study two prototypes: i) For the anisotropic image-driven technique of Nagel and Enkelmann that results in a linear system of equations we derive a regular full multigrid scheme. ii) For an isotropic flow-driven approach with total variation (TV) regularisation that requires to solve a nonlinear system of equations we develop a full multigrid strategy based on a full approximation scheme (FAS). Experiments for sequences of size 160 × 120 demonstrate the excellent performance of the proposed numerical schemes. With frame rates of 6 and 12 dense flow fields per second, respectively, both implementations outperform corresponding modified explicit schemes by two to three orders of magnitude. Thus, for the first time ever, real-time performance can be achieved for these high quality methods.


computer vision optical flow differential techniques variational methods multigrid methods partial differential equations 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Andrés Bruhn
    • 1
  • Joachim Weickert
    • 1
  • Timo Kohlberger
    • 2
  • Christoph Schnörr
    • 2
  1. 1.Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Building 27.1Saarland UniversitySaarbrückenGermany
  2. 2.Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer ScienceUniversity of MannheimMannheimGermany

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