Mean geometry for 2D random fields: level perimeter and level total curvature integrals

DOI10.1214/19-AAP1508zbMath1464.60049OpenAlexW2612870928MaRDI QIDQ2192734

Agnès Desolneux, Hermine Biermé

Publication date: 17 August 2020

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aoap/1591603216

zbMATH Keywords

Euler characteristicGauss-Bonnet theoremperimeterGaussian random fieldexcursion setspersistent homologytotal curvaturestationary random fieldshot noise random field

Mathematics Subject Classification ID

Random fields (60G60) Geometric probability and stochastic geometry (60D05) Stationary stochastic processes (60G10) Sample path properties (60G17)

Related Items (6)

Percolation of the excursion sets of planar symmetric shot noise fields ⋮ Asymptotics for the critical level and a strong invariance principle for high intensity shot noise fields ⋮ Statistical inference on stationary shot noise random fields ⋮ Normal convergence of nonlocalised geometric functionals and shot-noise excursions ⋮ Testing marginal symmetry of digital noise images through the perimeter of excursion sets ⋮ The effect of discretization on the mean geometry of a 2D random field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the perimeter of excursion sets of shot noise random fields
• A central limit theorem for the Euler characteristic of a Gaussian excursion set
• A test of Gaussianity based on the Euler characteristic of excursion sets
• Rotation and scale space random fields and the Gaussian kinematic formula
• Operations on constructible functions
• Chern classes for singular algebraic varieties
• Euler characteristic and related measures for random geometric sets
• On excursion sets, tube formulas and maxima of random fields.
• Crossings of smooth shot noise processes
• High level excursion set geometry for non-Gaussian infinitely divisible random fields
• On the total curvature of knots
• EULER INTEGRATION OF GAUSSIAN RANDOM FIELDS AND PERSISTENT HOMOLOGY
• Euler integration over definable functions
• Stochastic and Integral Geometry
• Excursion sets of three classes of stable random fields
• Normal convergence of multidimensional shot noise and rates of this convergence
• Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ ², F and t Fields
• Bicovariograms and Euler characteristic of regular sets
• Simplicial Homology of Random Configurations
• Stochastic Geometry and Wireless Networks: Volume I Theory
• Random Fields and Geometry
• Theory of Random Sets
• Exact moments of curvature measures in the Boolean model

This page was built for publication: Mean geometry for 2D random fields: level perimeter and level total curvature integrals