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The Mumford Shah method is to find the minimal function of the following functional $$F(u,K)=\int_{\Omega\setminus K}(u-u_0)^2+\alpha\int_{\Omega\setminus K}|\nabla u|^2+\beta Length(K),$$ where $\Omega$ is a bounded domain in $\mathbb R^2$, $K$ is the set of discontinuities, $u_0$ is the initial image($0\leq u_0\leq1$) and $\alpha,\beta$ are two non-negative constants.

Q :

  • How to determine the constants $\alpha,\beta$?

  • What is the relation to the Level-Set-Method?

PS: If you could give reference of the MATLAB code, it will be more grateful.

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    Mumford Shah is a functional. There do exist methods to try and optimize on it, but the name refers to the functional. – 2017-01-13

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