Unbiased estimation of the specific Euler-Poincaré characteristic

Patricia Jouannot; Jean-Paul Jernot; Christian Lantuejoul

Acta Stereologica

0351-580X

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Patricia Jouannot, Jean-Paul Jernot & Christian Lantuejoul

Unbiased estimation of the specific Euler-Poincaré characteristic

(Volume 15 (1996) — Number 1 - Mathematical foundations of stereology - Feb. 1996)

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Abstract

The structures considered in the present paper are the realisation of a stationary ergodic random set and the problem is to estimate their specific Euler-Poincaré characteristic. The estimator proposed here leads to unbiased results whatever the space dimension. It has been tested on a 3D face centred cubic Bernoulli grid with densities ranging from 0 to 1. Moreover, the variance of this estimator has been calculated experimentally for every dimension and for all possible densities. With a large number of fields (~l0000), these experimental results fit the theoretical curves calculated for 0, 1 and 2D spaces.

Keywords : stereology, variance, Euler-Poincaré characteristic

Om dit artikel te citeren:

Patricia Jouannot, Jean-Paul Jernot & Christian Lantuejoul, «Unbiased estimation of the specific Euler-Poincaré characteristic», Acta Stereologica [En ligne], Volume 15 (1996), Number 1 - Mathematical foundations of stereology - Feb. 1996, 45-51 URL : https://popups.uliege.be/0351-580x/index.php?id=421.