On the Local Connectivity Number of Stationary Random Closed Sets

  • Evgueni Spodarev
  • Volker Schmidt
Conference paper
Part of the Computational Imaging and Vision book series (CIVI, volume 30)


Random closed sets (RACS) in the d—dimensional Euclidean space are considered, whose realizations belong to the extended convex ring. A family of nonparametric estimators is investigated for the simultaneous estimation of the vector of all specific Minkowski functionals (or, equivalently, the specific intrinsic volumes) of stationary RACS. The construction of these estimators is based on a representation formula for the expected local connectivity number of stationary RACS intersected with spheres, whose radii are small in comparison with the size of the whole sampling window. Asymptotic properties of the estimators are given for unboundedly increasing sampling windows. Numerical results are provided as well.


Mathematical morphology random closed sets stationarity Minkowski functionals intrinsic volumes nonparametric estimation local Euler—Poincaré characteristic principal kinematic formula Boolean model 


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Copyright information

© Springer 2005

Authors and Affiliations

  • Evgueni Spodarev
    • 1
  • Volker Schmidt
    • 1
  1. 1.Abteilung StochastikUniversität UlmUlmGermany

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