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A Modified Deterministic Annealing Algorithm for Robust Image Segmentation

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Abstract

In this paper, we present a modified deterministic annealing algorithm, which is called DA-RS, for robust image segmentation. The presented algorithm is implemented by incorporating the local spatial information and a robust non-Euclidean distance measure into the formulation of the standard deterministic annealing (DA) algorithm. This implementation offers several improved features compared to existing image segmentation methods. First, it has less sensitivity to noise and other image artifacts due to the incorporation of spatial information. Second, it is independent of data initialization and has the ability to avoid many poor local optima due to the deterministic annealing process. Lastly, it possesses enhancing robustness and segmentation ability due to the injection of a robust non-Euclidean distance measure, which is obtained through a nonlinear mapping by using Gaussian radial basis function (GRBF). Experimental results on synthetic and real images are given to demonstrate the effectiveness and efficiency of the presented algorithm.

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References

  1. Pal, N.R., Pal, S.K.: A review on image segmentation techniques. Pattern Recognit. 26(9), 1277–1294 (1993)

    Article  Google Scholar 

  2. Bezdek, J.C., Hall, L.O., Clarke, L.P.: Review of MR image segmentation techniques using pattern recognition. Med. Phys. 20, 1033–1048 (1993)

    Article  Google Scholar 

  3. Pham, D.L., Xu, C., Prince, J.L.: Current methods in medical image segmentation. Annu. Rev. Biomed. Eng. 2, 315–337 (2000) Palo Alto, CA

    Article  Google Scholar 

  4. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)

    MATH  Google Scholar 

  5. Pham, D.L.: Spatial Models for Fuzzy Clustering. Comput. Vis. Image Underst. 84, 285–297 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Liew, A.W.C., Yan, H.: An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation. IEEE Trans. Med. Imaging 22(9), 1063–1075 (2003)

    Article  Google Scholar 

  7. Tolias, Y.A., Panas, S.M.: On applying spatial constraints in fuzzy image clustering using a fuzzy rule-based system. IEEE Signal Process. Lett. 5(10), 245–247 (1998)

    Article  Google Scholar 

  8. Tolias, Y.A., Panas, S.M.: Image segmentation by a fuzzy clustering algorithm using adaptive spatially constrained membership functions. IEEE Trans. Syst. Man Cybern. 28(3), 359–369 (1998)

    Article  Google Scholar 

  9. 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. Med. Imaging 21(3), 193–199 (2002)

    Article  Google Scholar 

  10. Liew, A.W.C., Leung, S.H., Lau, W.H.: Fuzzy image clustering incorporating spatial continuity. Inst. Elec. Eng. Proc. Vis. Image Signal Process. 147(2), 185–192 (2000)

    Article  Google Scholar 

  11. Liew, A.W.C., Leung, S.H., Lau, W.H.: Segmentation of color lip images by spatial fuzzy clustering. IEEE Trans. Fuzzy Syst. 11(4), 542–549 (2003)

    Article  Google Scholar 

  12. Zhang, D.Q., Chen, S.C.: A novel kernelized fuzzy C-means algorithm with application in medical image segmentation. Artif. Intell. Med. 32, 37–50 (2004)

    Article  Google Scholar 

  13. Zhang, D.Q., Chen, S.C.: Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure. IEEE Trans. Syst. Man Cybern. 34(4), 1907–1916 (2004)

    Article  Google Scholar 

  14. Vovk, U., Pernus, F., Likar, B.: MRI intensity inhomogeneity correction by combining intensity and spatial information. Phys. Med. Biol. 49, 4119–4133 (2004)

    Article  Google Scholar 

  15. Rose, K., Gurewitz, E., Fox, G.C.: Statistical mechanics and phase transitions in clustering. Phys. Rev. Lett. 65(8), 945–948 (1990)

    Article  Google Scholar 

  16. Rose, K.: Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proc. IEEE 86(11), 2210–2239 (1998)

    Article  Google Scholar 

  17. Rajagopalan, A.N., Jain, A., Desai, U.B.: Data clustering using hierarchical deterministic annealing and higher order statistics. IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process. 46(8), 1100–1104 (1999)

    Article  MATH  Google Scholar 

  18. Rose, K., Gurewitz, E., Fox, G.C.: Constrained clustering as an optimization method. IEEE Trans. Pattern Anal. Mach. Intell. 15(8), 785–794 (1993)

    Article  Google Scholar 

  19. Dave, R.N., Krishnapuram, R.: Robust clustering methods: a unified view. IEEE Trans. Fuzzy Syst. 5(2), 270–293 (1997)

    Article  Google Scholar 

  20. Yang, X.L., Song, Q., Wu, Y.L.: A robust deterministic annealing algorithm for data clustering. Data Knowl. Eng. 62(1), 84–100 (2007)

    Article  Google Scholar 

  21. Cristianin, N., Shawe-Taylar, J.: An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  22. Müller, K.R., Mike, S., Rätsch, G., Tsuda, K., Schölkopf, B.: An introduction to kernel based learning algorithms. IEEE Trans. Neural Netw. 12(2), 181–201 (2001)

    Article  Google Scholar 

  23. Schölkopf, B., Smola, A.J.: Learning with Kernels. MIT Press, Cambridge (2002)

    Google Scholar 

  24. Schölkopf, B., Burges, C.J.C., Vapnik, V.: Extracting support data for a given task. In: Fayyad, U.M., Uthurusamy, R. (eds.) Ist Int. Conf. on Knowledge Discovery and Data Mining, pp. 252–257. AAAI Press, Menlo Park (1995)

    Google Scholar 

  25. McGill University, Canada [Online]. Available: http://www.bic.mni.mcgill.ca/brainweb

  26. Cocosco, C.A., Kollokian, V., Kwan, R.K.S., Evans, A.C.: BrainWeb: online interface to a 3D MRI simulated brain database. NeuroImage 5(4), S245 (1997)

    Google Scholar 

  27. Pham, D.L., Prince, J.L.: Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans. Med. Imaging 18(9), 737–752 (1999)

    Article  Google Scholar 

  28. Yang, X.L., Song, Q., Cao, A.Z.: A new cluster validity index for data clustering. Neural Process. Lett. 23(3), 325–344 (2006)

    Article  Google Scholar 

  29. Graepel, T., Obermayer, K.: Fuzzy topographic kernel clustering. In: Brauer, W. (ed.) Proceedings of the 5th GI Workshop Fuzzy Neuro Systems, pp. 90–97 (1998)

  30. Wells, W.M., Grimson, W.E.L., Kikinis, R., Jolesz, F.A.: Adaptive segmentation of MRI data. IEEE Trans. Med. Imaging 15(4), 429–442 (1996)

    Article  Google Scholar 

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Yang, XL., Song, Q., Wang, Y. et al. A Modified Deterministic Annealing Algorithm for Robust Image Segmentation. J Math Imaging Vis 30, 308–324 (2008). https://doi.org/10.1007/s10851-007-0058-x

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  • DOI: https://doi.org/10.1007/s10851-007-0058-x

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