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March 2014 Local digital estimators of intrinsic volumes for Boolean models and in the design-based setting
Anne Marie Svane
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Adv. in Appl. Probab. 46(1): 35-58 (March 2014). DOI: 10.1239/aap/1396360102

Abstract

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 2x2 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.

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Anne Marie Svane. "Local digital estimators of intrinsic volumes for Boolean models and in the design-based setting." Adv. in Appl. Probab. 46 (1) 35 - 58, March 2014. https://doi.org/10.1239/aap/1396360102

Information

Published: March 2014
First available in Project Euclid: 1 April 2014

zbMATH: 1350.94014
MathSciNet: MR3189047
Digital Object Identifier: 10.1239/aap/1396360102

Subjects:
Primary: 94A08
Secondary: 60D05

Keywords: Boolean model , configuration , design-based digitization , Digitization in 2D , intrinsic volume , local estimator

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 1 • March 2014
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