Optimal Levels for the Two-phase, Piecewise Constant Mumford-Shah Functional
Petter Strandmark, Fredrik Kahl, Niels Christian Overgaard · Lund University Publications (Lund University) · 2009
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.