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<p>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.</p>
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

I. Gath and Y. Man, "Detection and Separation of Ring-Shaped Clusters Using Fuzzy Clustering," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 16, no. , pp. 855-861, 1994.
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