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The estimation of the Euler‐Poincare characteristic from observations on parallel sections
Author(s) -
OHSER J.,
NAGEL W.
Publication year - 1996
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1996.tb00006.x
Subject(s) - euler's formula , poincaré conjecture , estimation , mathematics , mathematical analysis , physics , statistical physics , engineering , systems engineering
Summary An unbiased estimator of the Euler‐Poincaré characteristic (Euler number) of an arbitrary object or a random structure, respectively, is given. The estimator is based on joint observations of pairs of parallel section profiles. Thus the present paper extends the use of Sterio's disector 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 method is illustrated by an example from materials sciences.