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Stochastic Reconstruction for Inhomogeneous Point Patterns

  • Kateřina Koňasová
  • Jiří DvořákEmail author
Article
  • 11 Downloads

Abstract

The stochastic reconstruction approach for point processes aims at producing independent patterns with the same properties as the observed pattern, without specifying any particular model. Instead a so-called energy functional is defined, based on a set of point process summary characteristics. It measures the dissimilarity between the observed pattern (input) and another pattern. The reconstructed pattern (output) is sought iteratively by minimising the energy functional. Hence, the output has approximately the same values of the prescribed summary characteristics as the input pattern. In this paper, we focus on inhomogeneous point patterns and apply formal hypotheses tests to check the quality of reconstructions in terms of the intensity function and morphological properties of the underlying point patterns. We argue that the current version of the algorithm available in the literature for inhomogeneous point processes does not produce outputs with appropriate intensity function. We propose modifications to the algorithm which can remedy this issue.

Keywords

Stochastic reconstruction Point process Summary characteristics Inhomogeneous process Intensity function 

Mathematics Subject Classification (2010)

60G55 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Probability and Mathematical Statistics, Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic

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