Volume 2, Issue 4
A Piecewise Constant Level Set Framework

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

DOI:

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 dicontinuities. 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 convergenve, 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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