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By Xu B.G.

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V. Cappellini, and A. Mecocci. 1996. Comments on A Possibilistic Approach to Clustering. IEEE Transactions on Fuzzy Systems 4(3):393–396. Bezdek, J. C. 1981. Pattern Recognition with Fuzzy Objective Function Algorithm. New York: Plenum. Bezdek, J. , and N. R. Pal. 1988. Some New Indexes for Cluster Validity. IEEE Transactions on System, Man, and Cybernetics, Part B 28:301–315. Brandt, M. , T. P. Bohan, L. A. Kramer, and J. M. Fletcher. 1994. Estimation of CSF, White and Gray Matter Volumes in Hydrocephalic Children Using Fuzzy Clustering of MR Images.

5 Properties of the Proposed Classes of Entropy Measures In the previous two subsections we have proposed two classes of entropy measures and we have shown that the expressions for the proposed entropy measures do not have any unnecessary terms. 8)) of the two classes of entropy measures incur certain restrictions, so that the proposed entropies satisfy some important properties. In this subsection, we shall discuss the restrictions regarding the base parameters and then provide few properties of the proposed entropies.

From Fig. 652). 2 compares the performance of different c-means algorithms on some brain MR images with respect to DB, Dunn, and β index considering c = 4 (back-ground, gray matter, white matter, and CSF). 2 confirm that the RFCM algorithm produces pixel clusters more promising than do the conventional methods. Some of the existing algorithms like PCM and FPCM have failed to produce multiple clusters as they generate coincident clusters even when they have been initialized with the final prototypes of FCM.

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