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Abstract. This paper deals with the multiple ellipse fitting problem based on a given set of data points in a plane. The presumption is that all data points are derived from k ellipses that should be fitted. The problem is solved by means of center-based clustering, where cluster centers are ellipses. If the Mahalanobis distance-like function is introduced in each cluster, then the cluster center is represented by the corresponding Mahalanobis circle-center. The distance from a point a ∈ R 2 to the Mahalanobis circle is based on the algebraic criterion. The well-known k-means algorithm has been adapted to search for a locally optimal partition of the Mahalanobis circle-centers. Several numerical examples are used to illustrate the proposed algorithm.

Abstract. This paper considers a multiple-circle detection problem on the basis of given data. The problem is solved by application of the center-based clustering method. For the purpose of searching for a locally optimal partition modeled on the well-known k-means algorithm, the k-closest circles algorithm has been constructed. The method has been illustrated by several numerical examples.

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