Abstract
Fuzzy C-Means (FCM) clustering and Gaussian Mixture Model (GMM) are two popular tools for data processing. In this study the unsupervised algorithm combining FCM clustering in the Kernel Space (KFCM) and GMM is presented. First, a ”kernel trick” is applied to the FCM algorithm. Then, the number of clusters is chosen automatically in the kernel space. On the basis of obtained starting parameters, i.e. number of mixture components, mean vector, covariance matrices and mixing proportion coefficients, the final GMM parameters are estimated. For this estimation the Expectation Maximization (EM) algorithm is used. The presented methodology - combination of KFCM and GMM methods named unsupervised cascade clustering - constitutes the basic step in Ewing’s sarcoma segmentation. On this basis the voxels intensity values describing segmented tumour and surrounded healthy tissue are defined and fuzzy connectedness analysis is performed. The obtained mixture parameters estimation results are compared with the results obtained using two different methods described in literature.
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References
Buraczewski, J.: Radiodiagnostyka zmian nowotworowych. Państwowy Zakład Wydawnictw Lekarskich, Warszawa (1987)
Davies, A.M., Sundaram, M., James, S.L.J.: Imaging of Bone Tumors and Tumor-Like Lesions, Techniques and Applications, Medical Radiology, Diagnostic Imaging. Springer, Heidelberg (2009)
Pruszynski, B.: Radiologia, Diagnostyka obrazowa, Rtg, TK, USG, MR i medycyna nuklearna. Wydawnictwo Lekarskie PZWL, Warszawa (2005)
Stoba, C., Czauderna, P.: Guzy kości u dzieci. Diagnostyka i leczenie. Wydawnictwo Folium, Lublin (1997)
Czajkowska, J.: Parametryzacja i trójwymiarowa segmentacja guzow kości w seriach rezonansu magnetycznego. Politechnika Ślźska, Gliwice (2011)
Helimed Diagnostic Imaging, Katowice (2004-2010)
Kawa, J., Pietka, E.: Kernelized Fuzzy C-Means Method in Fast Segmentation of Demyelination Plaques in Multiple Sclerosis. In: Proceedings of the 29th Annual International Conference of the IEEE EMBS (August 2007)
Heo, G., Gader, P.: An Extension of Global Fuzzy C-Means Using Kernel Methods. In: IEEE International Conference on Fuzzy Systems (July 2010)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers (1981)
Chuang, K.S., Tzeng, H.L., Chen, S., Wu, J., Chen, T.J.: Fuzzy C-Means Clustering with Spatial Information for Image Segmentation. In: Computerized Medical Imaging and Graphics, vol. 30, pp. 9–15. Elsevier (2006)
Wieclawek, W., Rudzki, M., Czajkowska, J.: Live-Wire Approach with FCM Clustering and Adaptive Filtering for Edge Detection in Medical Images. In: XIăInternational PhD Workshop, OWD 2009, Conference Archives PTETiS, Wisşa, vol. 26, pp. 475–478 (2009)
Gustafson, D.E., Kessel, W.C.: Fuzzy Clustering with a Fuzzy Covariance Matrix. In: Proceedings of Conference on Decision Control, pp. 761–766. IEEE (1979)
Hathaway, R.J., Huband, J.M., Bezdek, J.C.: Kernelized Fuzzy C-Means Method in Fast Segmentation of Demyelination Plaques in Multiple Sclerosis. In: Proceedings of International Conference on Fuzzy Systems. IEEE (August 2005)
Chou, C.H., Su, M.C., Lai, E.: A New Cluster Validity Measure and Its Application to Image Compression. Pattern Analysis and Applications 7(2), 205–220 (2004)
Milligan, G.W., Cooper, M.C.: An Examination of Procedures for Determining the Number of Clusters in Data Set. Psychometrika 50(2), 159–179 (1985)
Pal, N.R., Bezdek, J.C.: On Cluster Validity for the Fuzzy C-Means Model. IEEE Transactions on Fuzzy Systems 3(3), 370–379 (1995)
Figueiredo, M., Jain, A.K.: Unsupervised Learning of Finite Mixture Models. IEEE Transaction on Pattern Analysis and Machine Intelligence 24(3), 381–396 (2002)
McLachlan, G., Peel, D.: Finite Mixture Model. Wiley Series in Probability and Statistics (2000)
Honda, K., Ichihashi, H.: Regularized Linear Fuzzy Clustering and Probabilistic PCA Mixture Models. IEEE Transaction on Fuzzy Systems 13(4), 508–516 (2005)
Mekhalfa, F., Nacereddine, N., Goumeidane, A.B.: Unsupervised Algorithm for Radiographic Image Segmentation Based on the Gaussian Mixture Model. In: The International Conference on Computer as a Tool, EUROCON (September 2007)
Chandramouli, R., Srikantam, V.K.: Optimum Probability Model Selection Using Akaike’s Information Criterion for Low Power Applications. In: IEEE International Symposium on Circuits and Systems (May 2000)
Wagenaar, D.A.: FSMEM for MoG, Term Project for CS/CNS/EE 156b: Learning Systems, Class by P. Perona and M. Welling, Caltech (June 2000)
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Czajkowska, J., Bugdol, M., Pietka, E. (2012). Kernelized Fuzzy C-Means Method and Gaussian Mixture Model in Unsupervised Cascade Clustering. In: Piętka, E., Kawa, J. (eds) Information Technologies in Biomedicine. Lecture Notes in Computer Science(), vol 7339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31196-3_6
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DOI: https://doi.org/10.1007/978-3-642-31196-3_6
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