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A Multistage Image Segmentation and Denoising Method – Based on the Mumford and Shah Variational Approach

  • Song Gao
  • Tien D. Bui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3211)

Abstract

A new multistage segmentation and smoothing method based on the active contour model and the level set numerical techniques is presented in this paper. Instead of simultaneous segmentation and smoothing as in [10], [11], the proposed method separates the segmentation and smoothing processes. We use the piecewise constant approximation for segmentation and the diffusion equation for denoising, therefore the new method speeds up the segmentation process significantly, and it can remove noise and protect edges for images with very large amount of noise. The effects of the model parameter ( are also systematically studied in this paper.

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References

  1. 1.
    Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial differential equations and the Calculus of Variations. In: Applied Mathematical Sciences, vol. 147, Springer, Heidelberg (2002)Google Scholar
  2. 2.
    Chambolle, A.: Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations. SIAM Jour. on Appl. Math. 55, 827–863 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chan, T.F., Vese, L.V.: Active Contours without edges. IEEE Tran. Image Proces. 10, 266–277 (2001)zbMATHCrossRefGoogle Scholar
  4. 4.
    Gao, S., Bui, T.D.: A New Image Segmentation And Smoothing Model. In: IEEE International Symposium on Biomedical Imaging, April 2004, pp. 137–140 (2004)Google Scholar
  5. 5.
    Geman, S., Geman, D.: Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images. IEEE Trans. on PAMI 6, 721–741 (1984)zbMATHGoogle Scholar
  6. 6.
    Koepfler, G., Lopez, C., Morel, J.M.: A Multiscale Algorithm for Image Segmentation by Variational Method. SIAM J. Numer. Anal. 33, 282–299 (1994)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Mumford, D., Shah, J.: Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577–685 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  9. 9.
    Snyder, W., Logenthiran, A., Santago, P., Link, K., Bilbro, G., Rajala, S.: Segmentation of Magnetic Resonance Images using Mean Field Annealing. Image and Vision Comput. 10, 361–368 (1992)CrossRefGoogle Scholar
  10. 10.
    Tsai, A., Yezzi, A., Willsky, A.S.: Curve Evolution Implementation of the Mumford–Shah Functional for Image Segmentation, Denoising, Interpolation, and Magnification. IEEE Tran. on Image Proces 10, 1169–1186 (2001)zbMATHCrossRefGoogle Scholar
  11. 11.
    Vese, L.V., Chan, T.F.: A multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model. International Journal of Computer Vision 50, 271–293 (2002)zbMATHCrossRefGoogle Scholar
  12. 12.
    Weickert, J.: Anisotropic diffusion in Image Processing. Teubner, Stuttgart (1998)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Song Gao
    • 1
  • Tien D. Bui
    • 1
  1. 1.Department of Computer ScienceConcordia UniversityMontrealCanada

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