A Continuous Max-Flow Approach to Potts Model

  • Jing Yuan
  • Egil Bae
  • Xue-Cheng Tai
  • Yuri Boykov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6316)


We address the continuous problem of assigning multiple (unordered) labels with the minimum perimeter. The corresponding discrete Potts model is typically addressed with a-expansion which can generate metrication artifacts. Existing convex continuous formulations of the Potts model use TV-based functionals directly encoding perimeter costs. Such formulations are analogous to ’min-cut’ problems on graphs. We propose a novel convex formulation with a continous ’max-flow’ functional. This approach is dual to the standard TV-based formulations of the Potts model. Our continous max-flow approach has significant numerical advantages; it avoids extra computational load in enforcing the simplex constraints and naturally allows parallel computations over different labels. Numerical experiments show competitive performance in terms of quality and significantly reduced number of iterations compared to the previous state of the art convex methods for the continuous Potts model.


Potts Model Dual Model Label Function Variational Perspective Simplex 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 2010

Authors and Affiliations

  • Jing Yuan
    • 1
  • Egil Bae
    • 2
  • Xue-Cheng Tai
    • 2
    • 3
  • Yuri Boykov
    • 1
  1. 1.Computer Science DepartmentUniversity of Western OntarioLondon OntarioCanada
  2. 2.Department of MathematicsUniversity of BergenNorway
  3. 3.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore

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