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Local Digital Estimators of Intrinsic Volumes for Boolean Models and in the Design-Based Setting

Part of: Geometric probability and stochastic geometry Communication, information

Published online by Cambridge University Press:  22 February 2016

Anne Marie Svane
Anne Marie Svane*
Affiliation:
Aarhus University
*
∗ Postal address: Department of Mathematics, Aarhus University, 8000 Aarhus C, Denmark. Email address: anne.marie.svane@gmail.com
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Abstract

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In order to estimate the specific intrinsic volumes of a planar Boolean model from a binary image, we consider local digital algorithms based on weighted sums of 2×2 configuration counts. For Boolean models with balls as grains, explicit formulas for the bias of such algorithms are derived, resulting in a set of linear equations that the weights must satisfy in order to minimize the bias in high resolution. These results generalize to larger classes of random sets, as well as to the design-based situation, where a fixed set is observed on a stationary isotropic lattice. Finally, the formulas for the bias obtained for Boolean models are applied to existing algorithms in order to compare their accuracy.

Keywords

Digitization in 2Dintrinsic volumelocal estimatorconfigurationBoolean modeldesign-based digitization

MSC classification

Primary: 94A08: Image processing (compression, reconstruction, etc.)
Secondary: 60D05: Geometric probability and stochastic geometry
Type
Research Article
Information
Advances in Applied Probability , Volume 46 , Issue 1 , March 2014 , pp. 35 - 58
Copyright
© Applied Probability Trust 

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