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A combination of k-means and DBSCAN algorithm for solving the multiple generalized circle detection problem

Advances in Data Analysis and Classification volume 15, pages 83–98 (2021)Cite this article

Abstract

Motivated by the problem of identifying rod-shaped particles (e.g. bacilliform bacterium), 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 cluster-centers 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. For the purpose of recognizing detected generalized circles, a QAD-indicator is proposed. Also a new DBC-index is proposed, which is specialized for such situations. The recognition process is intitiated by searching for a good initial partition using the DBSCAN-algorithm. If QAD-indicator shows that generalized circle-cluster-center does not recognize searched generalized circle for some cluster, the procedure continues searching for corresponding initial generalized circles for these clusters using the Incremental algorithm. After that, corresponding generalized circle-cluster-centers are calculated for obtained clusters. This will happen if a data point set stems from intersected or touching generalized circles. The method is illustrated and tested on different artificial data sets coming from a number of generalized circles and real images.

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Notes

  1. All evaluations were done on the basis of our own Mathematica-modules, and were performed on the computer with a 2.90 GHz Intel(R) Core(TM)i7-75000 CPU with 16GB of RAM.

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Acknowledgements

The author would like to thank Mrs. Katarina Moržan for significantly improving the use of English in the paper. This work was supported by the Croatian Science Foundation through research grants IP-2016-06-6545 and IP-2016-06-8350.

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Author notes

  1. Rudolf Scitovski

    Present address: Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31000, Osijek, Croatia

Authors and Affiliations

  1. Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31000, Osijek, Croatia

    Kristian Sabo

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  1. Rudolf Scitovski
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  2. Kristian Sabo
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Correspondence to Kristian Sabo.

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Scitovski, R., Sabo, K. A combination of k-means and DBSCAN algorithm for solving the multiple generalized circle detection problem. Adv Data Anal Classif 15, 83–98 (2021). https://doi.org/10.1007/s11634-020-00385-9

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  • DOI: https://doi.org/10.1007/s11634-020-00385-9

Keywords

  • Multiple generalized circles
  • The detection problem
  • Modified k-means
  • DBSCAN
  • Incremental algorithm

Mathematics Subject Classification

  • 6207
  • 62H30
  • 68T10
  • 90C26
  • 90C27
  • 90C56
  • 91C20