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

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Image Analysis and Recognition (ICIAR 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3211))

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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. 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. Chambolle, A.: Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations. SIAM Jour. on Appl. Math. 55, 827–863 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chan, T.F., Vese, L.V.: Active Contours without edges. IEEE Tran. Image Proces. 10, 266–277 (2001)

    Article  MATH  Google Scholar 

  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. Geman, S., Geman, D.: Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images. IEEE Trans. on PAMI 6, 721–741 (1984)

    MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  7. Mumford, D., Shah, J.: Optimal approximation by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577–685 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  8. Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  12. Weickert, J.: Anisotropic diffusion in Image Processing. Teubner, Stuttgart (1998)

    MATH  Google Scholar 

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© 2004 Springer-Verlag Berlin Heidelberg

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Gao, S., Bui, T.D. (2004). A Multistage Image Segmentation and Denoising Method – Based on the Mumford and Shah Variational Approach. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2004. Lecture Notes in Computer Science, vol 3211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30125-7_11

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  • DOI: https://doi.org/10.1007/978-3-540-30125-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23223-0

  • Online ISBN: 978-3-540-30125-7

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