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The paper deals with the multiple closed curve detection problem, i.e. the multiple circle and the multiple ellipse detection problem are especially considered. Based on data coming from a number of closed curves not known in advance, it is necessary to recognize these curves. The approach we propose is based on center-based clustering, which means that the problem is reduced to searching for an optimal partition whose cluster-centers are the closed curves we searched for. By using a modified well-known k-means algorithm with carefully chosen initial approximation we shall look for these curves. For detecting the most appropriate number of clusters (closed curves), we have also proposed a new, specialized index that was significantly better than other well-known indexes.

A Fast and Efficient Method for Solving the Multiple Closed Curve Detection Problem