Tai, Xue-Cheng; Chan, Tony F. A survey on multiple level set methods with applications for identifying piecewise constant functions. (English) Zbl 1076.49020 Int. J. Numer. Anal. Model. 1, No. 1, 25-47 (2004). 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. Cited in 24 Documents 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 Keywords:level set methods; image segmentations; inverse problems; optimal shape design; electrical impedance tomography; positron emission tomography PDFBibTeX XMLCite \textit{X.-C. Tai} and \textit{T. F. Chan}, Int. J. Numer. Anal. Model. 1, No. 1, 25--47 (2004; Zbl 1076.49020)