A Convex Formulation of Continuous Multi-label Problems

  • Thomas Pock
  • Thomas Schoenemann
  • Gottfried Graber
  • Horst Bischof
  • Daniel Cremers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5304)


We propose a spatially continuous formulation of Ishikawa’s discrete multi-label problem. We show that the resulting non-convex variational problem can be reformulated as a convex variational problem via embedding in a higher dimensional space. This variational problem can be interpreted as a minimal surface problem in an anisotropic Riemannian space. In several stereo experiments we show that the proposed continuous formulation is superior to its discrete counterpart in terms of computing time, memory efficiency and metrication errors.


Variational Problem Continuous Formulation Discrete Approach Metrication Error Proximal Point Method 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Thomas Pock
    • 1
    • 2
  • Thomas Schoenemann
    • 1
  • Gottfried Graber
    • 2
  • Horst Bischof
    • 2
  • Daniel Cremers
    • 1
  1. 1.Department of Computer ScienceUniversity of BonnGermany
  2. 2.Institute for Computer Graphics and VisionGraz University of TechnologyAustria

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