THE ESTIMATION OF THE EULER-POINCARE CHARACTERISTIC FROM OBSERVATIONSON PARALLEL SECTIONS

An unbiased estimator of the Euler-Poincare characteristic (Euler numb er) of an arbitrary object or a random structure, respectively, is giv en. The estimator is based on joint observations of pairs of parallel section profiles. Thus the present paper extends the use of Sterio's d isector from counting particles to determining the Euler number for a wide class of probes. The correctness of the given formulae is proved with mathematical strictness. Furthermore, the feasibility of the meth od is illustrated by an example from materials sciences.