Weighted Voronoi tessellation with a poisson field of centroids

One considers a weighted Voronoi tessellation generated by a system of n Poisson fields of centroids. One investigates the composition and the boundary field of this structure. It is proved that the boundary field intensity between grains of types i and j (1ijn) is equal to where p_i is the volume part, _i>0 is the weight (for the comparison of distances) of the i-th component, c is a scaling factor. One obtains formulas for the boundary field intensities in plane and linear sections of the structure: . Estimators for the parameters p_i and _i from the observation of the linear section are proposed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 160–172, 1986.