UNBIASED ESTIMATORS OF SPECIFIC CONNECTIVITY

Jean-Paul Jernot, Patricia Jouannot, Christian Lantuéjoul

Abstract

This paper deals with the estimation of the specific connectivity of a stationary random set in IRd. It turns out that the "natural" estimator is only asymptotically unbiased. The example of a boolean model of hypercubes illustrates the amplitude of the bias produced when the measurement field is relatively small with respect to the range of the random set. For that reason unbiased estimators are desired. Such an estimator can be found in the literature in the case where the measurement field is a right parallelotope. In this paper, this estimator is extended to apply to measurement fields of various shapes, and to possess a smaller variance. Finally an example from quantitative metallography (specific connectivity of a population of sintered bronze particles) is given.

Keywords
Boolean model; edge effects; Euler-Poincaré characteristic; specific connectivity; unbiased estimation

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DOI: 10.5566/ias.v26.p129-136

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)