Counting Figures in Planar Random Configurations

Random configurations are considered that are generated by a
Poisson process of figures in the plane, and a recent result is
used to derive formulae for the estimation of the number of
figures, and their mean area and perimeter. The formulae require
merely the determination of the area, the perimeter, and the
Euler-Poincaré characteristic of the random configurations in a
fixed field of view. There are no similar formulae for the standard
deviations of the estimates; their magnitudes in typical cases are
therefore assessed by Monte Carlo simulations.