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- Volume 15 (1996)
- Number 1 - Mathematical foundations of stereology ...
- Unbiased estimation of the specific Euler-Poincaré characteristic
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Unbiased estimation of the specific Euler-Poincaré characteristic
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.
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A propos de : Patricia Jouannot
Centre de Géostatistique, 35 rue Saint Honoré, 77305 Fontainebleau, France
A propos de : Jean-Paul Jernot
LERMAT, ISMRA, Boulevard du Maréchal Juin, 14050 Caen Cedex, France
A propos de : Christian Lantuejoul
Centre de Géostatistique, 35 rue Saint Honoré, 77305 Fontainebleau, France