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A survey on multiple level set methods with applications for identifying piecewise constant functions. (English) Zbl 1076.49020

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

MSC:

49Q10 Optimization of shapes other than minimal surfaces
49L99 Hamilton-Jacobi theories
35R30 Inverse problems for PDEs
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
92C55 Biomedical imaging and signal processing
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
49N90 Applications of optimal control and differential games
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