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Related Experiment Videos

A binary level set model and some applications to Mumford-Shah image segmentation.

Johan Lie1, Marius Lysaker, Xue-Cheng Tai

  • 1Department of Mathematics, University of Bergen, Johannes Brunsgate 12, N-5008 Norway. johanl@mi.uib.no

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|May 5, 2006
PubMed
Summary

This paper introduces a novel level set method using piecewise constant functions to represent interfaces, offering a new approach for image segmentation and interface problems.

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Area of Science:

  • Computational Mathematics
  • Computer Vision

Background:

  • Traditional level set methods represent interfaces using continuous functions.
  • Existing methods face challenges in accurately capturing sharp interfaces.

Purpose of the Study:

  • To propose a novel PDE-based level set method for interface representation.
  • To explore the application of this method in digital image segmentation.

Main Methods:

  • Representing interfaces by discontinuities of piecewise constant level set functions (values 1 or -1).
  • Minimizing a smooth convex functional under a quadratic constraint.
  • Relating the method to phase-field approaches.

Main Results:

  • The proposed method allows for discontinuous level set functions at convergence.

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  • Numerical results demonstrate the method's effectiveness in segmenting digital images.
  • Preserves some properties of standard level set methods while introducing new characteristics.

    • Conclusions:

    • The novel level set method provides an effective alternative for interface problems.
    • The approach shows promise for advanced digital image segmentation tasks.