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Noisy Image Segmentation by a Robust Clustering Algorithm Based on DC Programming and DCA

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Advances in Data Mining. Medical Applications, E-Commerce, Marketing, and Theoretical Aspects (ICDM 2008)

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Abstract

We present a fast and robust algorithm for image segmentation problems via Fuzzy C-Means (FCM) clustering model. Our approach is based on DC (Difference of Convex functions) programming and DCA (DC Algorithms) that have been successfully applied in a lot of various fields of Applied Sciences, including Machine Learning. In an elegant way, the FCM model is reformulated as a DC program for which a very simple DCA scheme is investigated. For accelerating the DCA, an alternative FCM-DCA procedure is developed. Moreover, in the case of noisy images, we propose a new model that incorporates spatial information into the membership function for clustering. Experimental results on noisy images have illustrated the effectiveness of the proposed algorithm and its superiority with respect to the standard FCM algorithm in both running-time and quality of solutions.

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References

  1. Ahmed, M.N., Yamany, S.M., Mohamed, N., Farag, A.A., Moriarty, T.: A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data. IEEE Trans. on Medical Imaging 21, 193–199 (2002)

    Article  Google Scholar 

  2. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithm. Plenum Press, New York (1981)

    Google Scholar 

  3. Bezdek, J.C., Hall, L.O., Clake, L.P.: Review of MR image segmentation techniques using pattern recognition. Medical Physics 20, 1033–1048 (1993)

    Article  Google Scholar 

  4. Chuang, K.S., Tzeng, H.L., Chen, S., Wu, J., Chen, T.J.: Fuzzy c-means clustering with spatial information for image segmentation. Computerized Medical Imaging and Graphics 30, 9–15 (2006)

    Article  Google Scholar 

  5. Dunn, J.C.: A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters. Journal of Cybernetics 3, 32–57 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hung, W.L., Yang, M.S., Chen, D.H.: Parameter selection for suppressed fuzzy c-means with an application to MRI segmentation. Pattern Recognition Letters 27, 424–438 (2006)

    Article  Google Scholar 

  7. Krause, N., Singer, Y.: Leveraging the margin more carefully. In: International Conference on Machine Learning ICML (2004)

    Google Scholar 

  8. Le Thi, H.A.: Contribution á l’optimisation non convexe et l’optimisation globale: Théorie, Algorithmes et Applications. Habilitation á Diriger des Recherches, Université de Rouen (1997)

    Google Scholar 

  9. Le Thi, H.A., Pham Dinh, T.: Large scale molecular optimization from distance matrices by a D.C. optimization approach. SIAM Journal on Optimization 14, 77–116 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) Programming and DCA revisited with DC models of real world nonconvex optimization problems. Annals of Operations Research 133, 23–46 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. Le Thi, H.A., Belghiti, T., Pham Dinh, T.: A new efficient algorithm based on DC programming and DCA for Clustering. Journal of Global Optimization (July 2006) (in press)

    Google Scholar 

  12. Le Thi, H.A., Le Hoai, M., Pham Dinh, T.: Optimization based DC programming and DCA for Hierarchical Clustering. European Journal of Operational Research (June 2006) (in press)

    Google Scholar 

  13. Liu, Y., Shen, X., Doss, H.: Multicategory ψ-Learning and Support Vector Machine: Computational Tools. Journal of Computational and Graphical Statistics 14, 219–236 (2005)

    Article  MathSciNet  Google Scholar 

  14. Liu, Y., Shen, X.: Multicategory ψ-Learning. Journal of the American Statistical Association 101, 500–509 (2006)

    Article  MathSciNet  Google Scholar 

  15. Neumann, J., Schnörr, C., Steidl, G.: SVM-based Feature Selection by Direct Objective Minimisation. In: Pattern Recognition, Proc. of 26th DAGM Symposium, pp. 212–219 (2004)

    Google Scholar 

  16. Pham, D.L.: Image segmentation using probabilistic fuzzy c-means clustering. Image Processing 1, 722–725 (2001)

    Google Scholar 

  17. Pham, D.L.: Fuzzy Clustering with spatial constraints. In: Proc.IEEE Intern. Conf. on Image Processing, New Yord, USA (August 2002)

    Google Scholar 

  18. Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to DC programming: Theory, Algorithms and Applications. Acta Mathematica Vietnamica 22, 289–355 (1997)

    MATH  MathSciNet  Google Scholar 

  19. Pham Dinh, T., Le Thi, H.A.: DC optimization algorithms for solving the trust region subproblem. SIAM J. Optimization 8, 476–505 (1998)

    Article  MATH  Google Scholar 

  20. Rajapakse, J.C., Giedd, J.N., Rapoport, J.L.: Statistical Approach to Segmentation of Singke-Chanel Cerebral MR Images. IEEE Trans. On Medical Imaging 16 (April 2004)

    Google Scholar 

  21. Ronan, C., Fabian, S., Jason, W., Léon, B.: Trading Convexity for Scalability. In: International Conference on Machine Learning ICML (2006)

    Google Scholar 

  22. Shen, X., Tseng, G.C., Zhang, X., Wong, W.H.: On ψ-Learning. Journal of American Statistical Association 98, 724–734 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  23. Yuille, A.L., Rangarajan, A.: The Convex Concave Procedure (CCCP). In: Advances in Neural Information Processing System, vol. 14, MIT Press, Cambridge (2002)

    Google Scholar 

  24. Weber, S., Schüle, T., Schnörr, C.: Prior Learning and Convex-Concave Regularization of Binary Tomography. Electr. Notes in Discr. Math. 20, 313–327 (2005)

    Article  Google Scholar 

  25. Zhang, D.Q., Chen, S.C.: A novel kernelized fuzzy C-means algorithm with application in medical image segmentation. Artificial Intelligence in Medicine 32, 37–50 (2004)

    Article  Google Scholar 

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Petra Perner

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© 2008 Springer-Verlag Berlin Heidelberg

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Hoai An, L.T., Minh, L.H., Phuc, N.T., Dinh Tao, P. (2008). Noisy Image Segmentation by a Robust Clustering Algorithm Based on DC Programming and DCA. In: Perner, P. (eds) Advances in Data Mining. Medical Applications, E-Commerce, Marketing, and Theoretical Aspects. ICDM 2008. Lecture Notes in Computer Science(), vol 5077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70720-2_6

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  • DOI: https://doi.org/10.1007/978-3-540-70720-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70717-2

  • Online ISBN: 978-3-540-70720-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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