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This paper deals with the estimation of the specific connectivity of a stationary random set in IRd. It turns out that the ĆnaturalĆ 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 re ...

In a random stacking of particles, the coordination number is defined as the mean number of particles touching a given one. A classical measurement by image analysis is directly based on this definition. It can be applied in the theoretical case of a global analysis but some problems occur for pract ...

A new formula is established to evaluate the Euler-Poincare characteristic of a polyconvex subset X in Rd starting only from measurements of X in the cells of a tessellation. Simplifications occur when X is a union of cells of the tessellation, leading to another formula that unifies and extends sev ...

The problem addressed in this paper is the detection of defects on atomic structures. The procedure proposed is in two steps. At first a tessellation isbuilt starting from the atoms. It consists of a partition of the space into cells, and is used to define the neighbourhood relationships between the ...