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Two Fast and Robust Modified Gaussian Mixture Models Incorporating Local Spatial Information for Image Segmentation

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Abstract

The Gaussian Mixture Model (GMM) with the spatial constraint, e.g. Hidden Markov Random Field (HMRF), has been proven effective for image segmentation. The parameter β in the HMRF model is used to balance between robustness to noise and effectiveness of preserving the detail of the image. In other words, the determination of parameter β is, in fact, noise dependent to some degree. In this paper, we propose a simple and effective algorithm to make the traditional Gaussian Mixture Model more robust to noise, with consideration of the relationship between the local spatial information and the pixel intensity value information. The conditional probability of an image pixel is influenced by the probabilities of pixels in its immediate neighborhood to incorporate the spatial and the intensity information. In this case, the parameter β can be assigned to a small value to preserve image sharpness and detail in non-noise images. Meanwhile, the neighborhood window is used to tolerate the noise for heavy-noised images. Thus, the parameter β is independent of image noise degree in our model. Furthermore, we propose another algorithm for our modified GMM (MGMM) with the simplification of conditional probability computation (MGMM_S). Finally, our algorithm is not limited to GMM – it is general enough so that it can be applied to other distributions based on the construction of the Finite Mixture Model (FMM) technique. Experimental results of synthetic and real images demonstrate the improved robustness and effectiveness of our approach.

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References

  1. McLachlan, G., & Peel, D. (2000). Finite mixture models. New York: Wiley.

    Book  Google Scholar 

  2. C.M. Bishop, Pattern Recognition and Machine Learning. Springer, 2006.

  3. Krinidis, S., & Chatzis, V. (2010). A robust fuzzy local information C-means clustering algorithm. IEEE Trans Image Process, 5(19), 1328–1337.

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Chen, S., & Zhang, D. (2004). Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure. IEEE Transactions on Systems, Man and Cybernetics, 34(4), 1907–1916.

    Article  Google Scholar 

  6. Cai, W., Chen, S., & Zhang, D. (March 2007). Fast and robust fuzzy C-means clustering algorithms incorporating local information for image segmentation. Pattern Recogn, 40(3), 825–838.

  7. Carson, C., Belongie, S., Greenspan, H., & Malik, J. (Aug. 2002). Blobworld: image segmentation using expectation-maximization and its application to image querying. IEEE Trans Pattern Anal Mach Intell, 24(8), 1026–1038.

  8. Thanh, M. N., Wu, Q. M. J., & Ahuja, S. (2010). An extension of the standard mixture model for image segmentation. IEEE Trans Neural Netw, 21(8), 1326–1338.

    Article  Google Scholar 

  9. M.N. Thanh and Q.M. J. Wu, “Gaussian-Mixture-Model-Based Spatial Neighborhood Relationships for Pixel Labeling Problem,” IEEE Trans. Syst. Man Cybern. B, vol. PP, no. 99, pp. 1–10, 2011.

  10. Chatzis, S. P., & Varvarigou, T. A. (Oct. 2008). A fuzzy clustering approach toward hidden Markov random field models for enhanced spatially constrained image segmentation. IEEE Trans Fuzzy Syst, 16(5), 1351–1361.

  11. 11 P. Clifford, “Markov Random Fields in Statistics,” in Disorder in Physical Systems. A Volume in Honour of John M. Hammersley on the Occasion of His 70th Birthday, G. Grimmett and D. Welsh, Eds. Oxford, U.K.: Clarendon Press, Oxford Science Publication, 1990.

  12. Rabiner, L. R. (1989). A tutorial on hidden markov models and selected applications in speech recognition. Proc IEEE, 77(2), 257–286.

    Article  Google Scholar 

  13. Zhang, Y., Brady, M., & Smith, S. (Jan. 2001). Segmentation of brain mr images through a hidden markov random field model and the expectation maximization algorithm. IEEE Trans Med Imag, 20(1), 45–57.

  14. Dempster, P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via EM algorithm. J Roy Stat Soc B, 39(1), 1–38.

    Google Scholar 

  15. G.E.B. Archer and D.M. Titterington, “Parameter Estimation for Hidden Markov Chains,” J. Statistical Planning Inference, 2002.

  16. 16 J. Besag, “Statistical Analysis of Non-Lattice Data,” The Statistician, vol. 24, pp. 179–195, 1975.

  17. Zhang, J., Modestino, J. W., & Langan, D. (July 1994). Maximum-likelihood parameter estimation for unsupervised stochastic model-based image segmentation. IEEE Trans Image Process, 3, 404–420.

  18. McLachlan, G. J., & Krishnan, T. (1997). “The EM Algorithm and Extensions”, in Series in Probability and Statistics. New York: Wiley.

    Google Scholar 

  19. Zhou, Z., Leahy, R., & Qi, J. (1997). Approximate maximum likelihood hyperparameter estimation for Gibbs priors. IEEE Trans Image Process, 6(6), 844–861.

    Article  Google Scholar 

  20. Besag, J. (1986). On the statistical analysis of dirty pictures. J Roy Stat Soc B, 48, 259–302.

    Google Scholar 

  21. Qian, W., & Titterington, D. (1991). Estimation of parameters in hidden Markov models. Philos Trans Roy Soc London A, 337, 407–428.

    Article  Google Scholar 

  22. Zhang, J. (Jan. 1993). The mean field theory in em procedures for blind Markov random field image restoration. IEEE Trans Image Process, 2(1), 27–40.

  23. Forbes, F., & Peyrard, N. (2003). Hidden Markov random field model selection criteria based on mean field-like approximations. IEEE Trans Pattern Anal Mach Intell, 25(9), 1089–1101.

    Article  Google Scholar 

  24. Sanjay, G. S., & Hebert, T. J. (1998). Bayesian pixel classification using spatially variant finite mixtures and the generalized EM algorithm. IEEE Trans Image Process, 7(7), 1014–1028.

    Article  Google Scholar 

  25. Diplaros, A., Vlassis, N., & Gevers, T. (2007). A spatially constrained generative model and an em algorithm for image segmentation. IEEE Trans Neural Netw, 18(3), 798–808.

    Article  Google Scholar 

  26. Blekas, K., Likas, A., Galatsanos, N. P., & Lagaris, I. E. (2005). A spatially constrained mixture model for image segmentation. IEEE Trans Neural Netw, 16(2), 494–498.

    Article  Google Scholar 

  27. Nikou, C., Galatsanos, N. P., & Likas, A. (2007). A class-adaptive spatially variant mixture model for image segmentation. IEEE Trans Image Process, 16(4), 1121–1130.

    Article  Google Scholar 

  28. Nikou, C., Likas, A., & Galatsanos, N. P. (2010). A bayesian framework for image segmentation with spatially varying mixtures. IEEE Trans Image Process, 19(9), 2278–2289.

    Article  Google Scholar 

  29. Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. J Roy Stat Soc B, 36(2), 192–326.

    Google Scholar 

  30. M.N.M. van Lieshout, “Markovianity in Space and Time,” Dynamics and Stochastics: Festschrift in Honor of Michael Keane, pp. 154–167, 2006.

  31. http://infoman.teikav.edu.gr/~stkrini/pages/develop/FLICM/FLICM.html

  32. http://www.cs.uoi.gr/~kblekas/sw/MAPsegmentation.html

  33. http://web.mac.com/soteri0s/Sotirios_Chatzis/Software.html

  34. Martin, D., Fowlkes, C., Tal, D., & Malik, J. (2001). A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. roc 8th IEEE Int Conf Comput Vis, Vancouver, BC, Canada, 2, 416–423.

    Google Scholar 

  35. Unnikrishnan, R., Pantofaru, C., & Hebert, M. (2005). A Measure for Objective Evaluation of Image Segmentation Algorithms. IEEE Conf Comput Vis Pattern Recognit, 3, 34–41.

    Google Scholar 

  36. R. Unnikrishnan and M. Hebert, “Measures of Similarity,” in Proc. IEEE Workshop Comput. Vis. Appl., pp. 394–400, 2005.

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Acknowledgments

This work was supported in part by the Canada Chair Research Program and the Natural Sciences and Engineering Research Council of Canada. This work was supported in part by the National Natural Science Foundation of China under Grant 61105007 and 61103141. This work was supported in part by PAPD (A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions). This work was supported in part by the Natural Science Foundation of Jiangsu Province NO. BK2012858. This work was supported in part by the Innovation Fund of China Academy of Space Technology: CAST201302.

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Authors and Affiliations

  1. School of Computer & Software, Nanjing University of Information Science & Technology, Nanjing, China

    Hui Zhang, Yuhui Zheng, Danhua Xu, Dingcheng Wang & Q. M. Jonathan Wu

  2. JiangSu Provincial Center for Disease Prevention and Control, Nanjing, China

    Tian Wen

  3. Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science & Technology, Nanjing, China

    Hui Zhang, Yuhui Zheng, Danhua Xu & Dingcheng Wang

  4. Department of Electrical and Computer Engineering, University of Windsor, Windsor, Canada

    Hui Zhang, Thanh Minh Nguyen & Q. M. Jonathan Wu

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  1. Hui Zhang
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  2. Tian Wen
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  3. Yuhui Zheng
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  4. Danhua Xu
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  5. Dingcheng Wang
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  6. Thanh Minh Nguyen
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  7. Q. M. Jonathan Wu
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Correspondence to Q. M. Jonathan Wu.

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Hui Zhang and Tian Wen contributed equally to this work.

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Zhang, H., Wen, T., Zheng, Y. et al. Two Fast and Robust Modified Gaussian Mixture Models Incorporating Local Spatial Information for Image Segmentation. J Sign Process Syst 81, 45–58 (2015). https://doi.org/10.1007/s11265-014-0898-8

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  • DOI: https://doi.org/10.1007/s11265-014-0898-8

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