Counting figures in planar random configurations

A. M. Kellerer
1985 Journal of Applied Probability  
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
more » ... gnitudes in typical cases are therefore assessed by Monte Carlo simulations.
doi:10.1017/s0021900200029028 fatcat:cuzta7hcmra67bbhcetrz2bvo4