Asymptotic variance of grey-scale surface area estimators

Publikation: Working paperForskning

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Abstrakt

Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude.
OriginalsprogEngelsk
UdgiverCentre for Stochastic Geometry and Advanced Bioimaging, Aarhus University
Antal sider30
StatusUdgivet - 2014
Udgivet eksterntJa
NavnCSGB Research Reports
Nummer05

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