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Incremental method for multiple line detection problem — iterative reweighted approach

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  • Sabo, Kristian
  • Grahovac, Danijel
  • Scitovski, Rudolf

Abstract

In this paper we consider the multiple line detection problem by using the center-based clustering approach, and propose a new incremental method based on iterative reweighted approach. We prove the convergence theorem and construct an appropriate algorithm which we test on numerous artificial data sets. A stopping criterion in the algorithm is defined by using the parameters from the DBSCAN algorithm. We give necessary conditions for the most appropriate partition, which have been used during elimination of unacceptable center-lines that appear in the output of the algorithm. The algorithm is also illustrated on a real-world image coming from Precision Agriculture.

Suggested Citation

  • Sabo, Kristian & Grahovac, Danijel & Scitovski, Rudolf, 2020. "Incremental method for multiple line detection problem — iterative reweighted approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 588-602.
  • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:588-602
    DOI: 10.1016/j.matcom.2020.07.013
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    References listed on IDEAS

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    1. Bagirov, Adil M. & Ugon, Julien & Mirzayeva, Hijran, 2013. "Nonsmooth nonconvex optimization approach to clusterwise linear regression problems," European Journal of Operational Research, Elsevier, vol. 229(1), pages 132-142.
    2. Rudolf Scitovski, 2017. "A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set," Journal of Global Optimization, Springer, vol. 68(4), pages 713-727, August.
    3. Ratko Grbić & Emmanuel Nyarko & Rudolf Scitovski, 2013. "A modification of the DIRECT method for Lipschitz global optimization for a symmetric function," Journal of Global Optimization, Springer, vol. 57(4), pages 1193-1212, December.
    4. Markovsky, Ivan & Luisa Rastello, Maria & Premoli, Amedeo & Kukush, Alexander & Van Huffel, Sabine, 2006. "The element-wise weighted total least-squares problem," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 181-209, January.
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