Euler characteristic and related measures for random geometric sets

DOI10.1007/BF01048319zbMath0943.82541WikidataQ105583342 ScholiaQ105583342MaRDI QIDQ1279382

Herbert Wagner, Klaus R. Mecke

Publication date: 4 September 2000

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

Euler characteristicintegral geometryMinkowski functionalsrandom setscontinuum percolation

Mathematics Subject Classification ID

Percolation (82B43) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

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Second Order Analysis of Geometric Functionals of Boolean Models ⋮ Minkowski tensor density formulas for Boolean models ⋮ Mean geometry for 2D random fields: level perimeter and level total curvature integrals ⋮ Dimensionality and morphology of particle and bubble clusters in turbulent flow ⋮ Critical probability of percolation over bounded region in N-dimensional Euclidean space ⋮ Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals ⋮ Simulating stochastic geometries: Morphology of overlapping grains ⋮ Integral-geometry morphological image analysis ⋮ Integral Geometry in Statistical Physics ⋮ Topological estimation of percolation thresholds ⋮ Geometric functionals of fractal percolation ⋮ Euler-Poincaré characteristic and phase transition in the Potts model on \(\mathbb{Z}^2\) ⋮ The shape of parallel surfaces: porous media, fluctuating interfaces and complex fluids

Cites Work

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• Euler characteristic in percolation theory.
• Minkowski functionals of Poisson processes
• Projected thick sections through multi-dimensional particle aggregates
• Local Properties of Binary Images in Two Dimensions

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