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Detection and Separation of Ring-Shaped Clusters Using Fuzzy Clustering
August 1994 (vol. 16 no. 8)
pp. 855-861

A new fuzzy clustering algorithm, designed to detect and characterize ring-shaped clusters and combinations of ring-shaped and compact spherical clusters, has been developed. This FKR algorithm includes automatic search for proper initial conditions in the two cases of concentric and excentric (intersected) combinations of clusters. Validity criteria based on total fuzzy area and fuzzy density are used to estimate the optimal number of substructures in the data set. The FKR algorithm has been tested on a variety of simulated combinations of ring-shaped and compact spherical clusters, and its performance proved to be very good, both in identifying the input shapes and in recovering the input parameters. Application of the FKR algorithm to an MRI image of the heart's left ventricle was used to investigate the possibility of using this algorithm as an aid in image processing.

[1] J. C. Bezdek, "Fuzzy mathematics in pattern classification," Ph.D. dissertation, Cornell Univ., Ithaca, NY, USA, 1973.
[2] J. C. Bezdek,Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum, New York, 1981.
[3] J.C. Bezdek, C. Coray, R. Gunderson, and J. Watson, "Detection and characterization of cluster substructure. I. Linear structure: Fuzzy clines,"SIAM J. Appl. Math., vol. 40, pp. 339-357, 1981.
[4] J.C. Bezdek, C. Coray, R. Gunderson, and J. Watson, "Detection and characterization of cluster substructure. II. Fuzzy c-varieties and convex combinations thereof,"SIAM J. Appl. Math., vol. 40, pp. 358-372, 1981.
[5] D. E. Gustafson and W. Kessel, "Fuzzy clustering with a fuzzy covariance matrix," inProc. IEEE CDC, 1979, pp. 761-766.
[6] I. Gath, and A. Geva, "Unsupervised optimal fuzzy clustering,"IEEE Trans. Patt. Anal. Mach. Intell.vol. 11, pp. 773-781, 1989.
[7] P.V.C. Hough, "Method and means for recognizing complex patterns," U.S. Patent 3069654, 1962.
[8] J. Illingworth and J. Kittler, "The Adaptive Hough Transform,"IEEE Trans. PAMI, Vol. 9, No. 5, Sept. 1987, pp. 690- 698.
[9] R. N. Dave, "Fuzzy shell-clustering and applications to circle detection in digital images,"J. Gen. Sys., vol. 16, pp. 343-355, 1990.
[10] W.A. Morgan, "A test for the significance of the difference between the two variances in a sample from a normal bivariate population,"Biometrikavol. 31, pp. 13-19, 1939.
[11] E.J.C. Pitman, "A note on normal correlation,"Biometrika, vol. 31, pp. 9-12, 1939.
[12] R. Dubes and A. K. Jain, "Validity studies in clustering methodologies,"Patt. Recognitionvol. 11, pp. 235-254, 1979.
[13] A. K. Jain and R. C. Dubes,Algorithms for Clustering Data. Englewood Cliffs, NJ: Prentice-Hall, 1988.
[14] I. Gath and A. Geva, "Fuzzy clustering for the estimation of the parameters of the components of mixtures of normal distributions,"Patt. Recognition Lett.vol. 9, pp. 77-86, 1989.
[15] R.N. Dave and K. Bhaswan, "New measures for evaluating fuzzy partitions induced through c-shells clustering,"Proc. SPIE Conf. on Intelligent Robots and Computer Vision, vol. 1607, pp. 406-414, 1991.

Index Terms:
pattern recognition; fuzzy set theory; ring-shaped clusters; fuzzy clustering; compact spherical clusters; FKR algorithm; automatic search; proper initial conditions; concentric; excentric; validity criteria; total fuzzy area; fuzzy density; MRI image; heart left ventricle; image processing
Citation:
Y. Man, I. Gath, "Detection and Separation of Ring-Shaped Clusters Using Fuzzy Clustering," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 8, pp. 855-861, Aug. 1994, doi:10.1109/34.308484
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