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A multiresolution stochastic level set method for Mumford-Shah image segmentation.

Yan Nei Law1, Hwee Kuan Lee, Andy M Yip

  • 1Department of Mathematics, National University of Singapore, Singapore. andyyip@nus.edu.sg

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|November 14, 2008
PubMed
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This study introduces a hybrid optimization algorithm for the Mumford-Shah image segmentation model, overcoming sensitivity to initial guesses. The novel basin hopping scheme efficiently finds global solutions, outperforming traditional methods.

Area of Science:

  • Computer Vision
  • Image Processing
  • Computational Mathematics

Background:

  • The Mumford-Shah model is a cornerstone of image segmentation.
  • Existing algorithms often suffer from sensitivity to initial parameter choices, hindering effective application.
  • Efficient computation of global or near-global optimal solutions is crucial for practical use.

Purpose of the Study:

  • To develop an efficient algorithm for computing global minimum solutions for the multiphase piecewise constant Mumford-Shah model.
  • To address the critical issue of sensitivity to initial guesses in Mumford-Shah model optimization.
  • To enhance the practical applicability of the Mumford-Shah model in image segmentation tasks.

Main Methods:

  • A hybrid optimization approach combining gradient-based and stochastic methods.

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  • A novel basin hopping scheme with global updates to escape local minima effectively.
  • A multiresolution strategy to reduce computational cost and improve global minimum search.

    • Main Results:

    • The proposed hybrid algorithm achieves high-quality solutions rapidly, significantly outperforming simulated annealing.
    • The basin hopping scheme demonstrates superior efficiency in escaping local traps compared to standard stochastic methods.
    • A theoretical result was derived, connecting solutions across different spatial resolutions.

    Conclusions:

    • The developed hybrid algorithm offers an effective solution for the global optimization of the Mumford-Shah model.
    • The novel basin hopping and multiresolution approaches enhance efficiency and solution quality.
    • This work advances the practical application of the Mumford-Shah model in image segmentation.