Volume 1, Issue 1
A Survey on Multiple Set Methods with Applications for Identifying Piecewise Constant Function

X.-C. Tai & T. F. Chan

Int. J. Numer. Anal. Mod., 1 (2004), pp. 25-48

Published online: 2004-01

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  • Abstract
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.
  • Keywords

survey level set methods image segmentation inverse problems optimal shape design electrical impedance tomography positron emission tomography

  • AMS Subject Headings

49Q10 49L99 35C44 35R30 65J20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-1-25, author = {X.-C. Tai and T. F. Chan}, title = {A Survey on Multiple Set Methods with Applications for Identifying Piecewise Constant Function}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2004}, volume = {1}, number = {1}, pages = {25--48}, abstract = {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.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/964.html} }
TY - JOUR T1 - A Survey on Multiple Set Methods with Applications for Identifying Piecewise Constant Function AU - X.-C. Tai & T. F. Chan JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 25 EP - 48 PY - 2004 DA - 2004/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/964.html KW - survey KW - level set methods KW - image segmentation KW - inverse problems KW - optimal shape design KW - electrical impedance tomography KW - positron emission tomography AB - 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.
X.-C. Tai & T. F. Chan. (1970). A Survey on Multiple Set Methods with Applications for Identifying Piecewise Constant Function. International Journal of Numerical Analysis and Modeling. 1 (1). 25-48. doi:
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