Fuzzy Shell-Clustering and Applications to Circle Detection in Digital Images

A new type of Fuzzy Clustering algorithm called Fuzzy-Shell Clustering (FSC) is introduced, The FSC algorithm seeks cluster prototypes that are p-dimensional hyper-spherical-shells. In two-dimensional data, this amounts to finding cluster prototypes that are circles. Thus the FSC algorithm can be applied for detection of circles in digital images. The algorithm does not require the data-points to be in any particular order, therefore its performance can be compared with the global transformation techniques such as Hough transforms. Several numerical examples are considered and the performance of the FSC algorithm is compared to the performance of the methods based on generalized Hough transform (HT). The FSC is shown to be superior to the HT method with regards to memory requirement and computation time. Like the HT method, the FSC is successful even if only a part of a circular shape is present in the image. Other potential applications of FSC are also considered.