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Assessing Similarity of Random sets via Skeletons

Author

Listed:
  • Johan Debayle

    (MINES Saint-Etienne, CNRS, UMR 5307 LGF, Centre SPIN)

  • Vesna Gotovac Ðogaš

    (University of Split)

  • Kateřina Helisová

    (Czech Technical University in Prague)

  • Jakub Staněk

    (Charles University)

  • Markéta Zikmundová

    (University of Chemistry and Technology Prague)

Abstract

The paper concerns a method for assessing similarity of realisations of random sets based on a construction of their morphological skeletons and a consequent covering of the realisations by unions of the so-called maximal discs. Since the realisations are considered to be binary images, the skeletons together with the corresponding discs can be viewed as realisations of marked point processes with specific properties. A special function for such marked point processes is defined. This function is analogous to the mark-weighted K-function. The function is then used for comparison of given realisations. More precisely, a random sample of the functions is taken from the realisations and the equality in distribution of the functions is tested by an envelope test and by a kernel test. The described procedure is illustrated on a simulation study with the aim to distinguish between realisations coming from different processes and to determine similarity of realisations coming from the same processes.

Suggested Citation

  • Johan Debayle & Vesna Gotovac Ðogaš & Kateřina Helisová & Jakub Staněk & Markéta Zikmundová, 2021. "Assessing Similarity of Random sets via Skeletons," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 471-490, June.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:2:d:10.1007_s11009-020-09785-y
    DOI: 10.1007/s11009-020-09785-y
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    References listed on IDEAS

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    1. Mari Myllymäki & Tomáš Mrkvička & Pavel Grabarnik & Henri Seijo & Ute Hahn, 2017. "Global envelope tests for spatial processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 381-404, March.
    2. Jesper Møller & Kateřina Helisová, 2010. "Likelihood Inference for Unions of Interacting Discs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 365-381, September.
    3. López-Pintado, Sara & Romo, Juan, 2009. "On the Concept of Depth for Functional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 718-734.
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