Unbiased estimation of the specific Euler-Poincaré characteristic
Centre de Géostatistique, 35 rue Saint Honoré, 77305 Fontainebleau, France
LERMAT, ISMRA, Boulevard du Maréchal Juin, 14050 Caen Cedex, France
Centre de Géostatistique, 35 rue Saint Honoré, 77305 Fontainebleau, France
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.