A Survey on Multiple Level Set Methods with Applications for Identifying Piecewise Constant Functions

We try to give a brief survey about using multiple level set methods for identifying piecewise constant or piecewise smooth functions. A general framework is presented. Application using this general framework for different practical problems are shown. We try to show some details in applying the general approach for applications to: image segmentation, optimal shape design, elliptic inverse coefficient identification, electricall impedance tomography and positron emission tomography. Numerical experiments are also presented for some of the problems.