engleski

Multiple circle detection based on center-based clustering

The multiple circle detection problem has been considered in the paper on the basis of given data point set $mathcal{; ; A}; ; subset  Rn$. It is supposed that all data points from the set $mathcal{; ; A}; ; $ come from $k$ circles that should be reconstructed or detected. The problem has been solved by the application of center-based clustering of the set $mathcal{; ; A}; ; $, i.e. an optimal $k$-partition is searched for, whose clusters are determined by corresponding circle-centers. Thereby, the algebraic distance from a point to the circle is used. First, an adaptation of the well-known $k$-means algorithm is given in the paper. Also, the incremental algorithm for searching for an approximate globally optimal $k$-partition is proposed. The algorithm locates either a globally optimal $k$-partition or a locally optimal k-partition close to the global one. Since optimal partitions with 2, 3, ... clusters are determined successively in the algorithm, several well-known indexes for determining an appropriate number of clusters in a partition are adopted for this case. Thereby, the Hausdorff distance between two circles is used and adopted. The proposed method and algorithm are illustrated and tested on several numerical examples.

multiple circle detection; center-based clustering; globally optimal partition; approximate optimization; DIRECT

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