Original scientific paper
https://doi.org/10.17535/crorr.2015.0004
Multiple ellipse fitting by center-based clustering
Tomislav Marošević
; Department of Mathematics, Josip Juraj Strossmayer University of Osijek, Osijek, Croatia
Rudolf Scitovski
; Department of Mathematics, Josip Juraj Strossmayer University of Osijek, Osijek, Croatia
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.
Keywords
multiple ellipse fitting; center-based clustering; algebraic criterion; Mahalanobis distance
Hrčak ID:
138572
URI
Publication date:
30.3.2015.
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