Optimal Levels for the Two-phase, Piecewise Constant Mumford-Shah Functional

Petter Strandmark, Fredrik Kahl, Niels Christian Overgaard

Research output: Contribution to conferencePaper, not in proceeding


Recent results have shown that denoising an image with the Rudin, Osher and Fatemi (ROF) total variation model can be accomplished by solving a series of binary optimization problems. We observe that this fact can be used in the other direction. The procedure is applied to the two-phase, piecewise constant Mumford-Shah functional, where an image is approximated with a function taking only two values. When the difference between the two levels is kept constant, a global optimum can be found efficiently. This allows us to solve the full problem with branch and bound in only one dimension.
Original languageEnglish
Publication statusPublished - 2009
EventSwedish Symposium on Image Analysis (SSBA) 2009 - Halmstad, Sweden
Duration: 2009 Mar 192009 Mar 20


ConferenceSwedish Symposium on Image Analysis (SSBA) 2009

Subject classification (UKÄ)

  • Computer Vision and Robotics (Autonomous Systems)
  • Mathematics


  • total variation
  • segmentation
  • image processing


Dive into the research topics of 'Optimal Levels for the Two-phase, Piecewise Constant Mumford-Shah Functional'. Together they form a unique fingerprint.
  • Optimizing Parametric Total Variation Models

    Strandmark, P., Kahl, F. & Overgaard, N. C., 2009, [Host publication title missing]. p. 2240-2247

    Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review

    6 Citations (SciVal)
    107 Downloads (Pure)

Cite this