A Fast and Efficient Method for Solving the Multiple Generalized Circle Detection Problem

In this paper, we consider the multiple generalized circle detection problem. We propose a method for solving this problem that is based on center-based clustering, where clustercenters are generalized circles. An efficient algorithm is proposed, which is based on a modification of the well-known k-means algorithm for generalized circles as cluster-centers. In doing so, it is extremely important to have a good initial approximation. In the case of well-separated generalized circles, we search for an initial partition as an initial approximation by using the DBSCANalgorithm, and in the case of intersected generalized circles, initial approximation is searched for in the form of initial generalized circles by using the Incremental algorithm and the DIRECT global optimization algorithm. For the purpose of recognizing detected generalized circles, a new DBC-index is proposed, which is specialized for such situations.