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An integral‐geometric approach for the Euler–Poincaré characteristic of spatial images
Author(s) -
Werner Nagel,
Joachim Ohser,
K. Pischang
Publication year - 2000
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 - 10.1046/j.1365-2818.2000.00668.x
Subject(s) - correctness , euler's formula , image (mathematics) , euler number (physics) , mathematics , set (abstract data type) , graph , poincaré conjecture , euler characteristic , computer science , algorithm , artificial intelligence , mathematical analysis , discrete mathematics , backward euler method , euler equations , semi implicit euler method , programming language
The determination of the Euler–Poincaré characteristic of a set can be based on observations of a digitized image of that set. In the present paper the correctness of the method is proved due to a strict integral‐geometric approach. Our result also provides a link to the methods which are used in image analysis and are based on graph theory.