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Volume 2, Issue 4
A Piecewise Constant Level Set Framework

J. Lie, M. Lysaker & X.-C. Tai

Int. J. Numer. Anal. Mod., 2 (2005), pp. 422-438.

Published online: 2005-02

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  • Abstract

In this work we discuss variants of a PDE based level set method. Traditionally interfaces are represented by the zero level set of continuous level set functions. We instead use piecewise constant level set functions, and let interfaces be represented by discontinuities. Some of the properties of the standard level set function are preserved in the proposed method. Using the methods for interface problems, we need to minimize a smooth convex functional under a constraint. The level set functions are discontinuous at convergence, but the minimization functional is smooth and locally convex. We show numerical results using the methods for segmentation of digital images.

  • Keywords

image segmentation, image processing, PDE, variational, level set, piecewise constant level set.

  • AMS Subject Headings

49Q10, 35R30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-2-422, author = {J. Lie, M. Lysaker and X.-C. Tai}, title = {A Piecewise Constant Level Set Framework}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {4}, pages = {422--438}, abstract = {

In this work we discuss variants of a PDE based level set method. Traditionally interfaces are represented by the zero level set of continuous level set functions. We instead use piecewise constant level set functions, and let interfaces be represented by discontinuities. Some of the properties of the standard level set function are preserved in the proposed method. Using the methods for interface problems, we need to minimize a smooth convex functional under a constraint. The level set functions are discontinuous at convergence, but the minimization functional is smooth and locally convex. We show numerical results using the methods for segmentation of digital images.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/939.html} }
TY - JOUR T1 - A Piecewise Constant Level Set Framework AU - J. Lie, M. Lysaker & X.-C. Tai JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 422 EP - 438 PY - 2005 DA - 2005/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/939.html KW - image segmentation, image processing, PDE, variational, level set, piecewise constant level set. AB -

In this work we discuss variants of a PDE based level set method. Traditionally interfaces are represented by the zero level set of continuous level set functions. We instead use piecewise constant level set functions, and let interfaces be represented by discontinuities. Some of the properties of the standard level set function are preserved in the proposed method. Using the methods for interface problems, we need to minimize a smooth convex functional under a constraint. The level set functions are discontinuous at convergence, but the minimization functional is smooth and locally convex. We show numerical results using the methods for segmentation of digital images.

J. Lie, M. Lysaker and X.-C. Tai. (2005). A Piecewise Constant Level Set Framework. International Journal of Numerical Analysis and Modeling. 2 (4). 422-438. doi:
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