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Local contributions to the Euler–Poincaré characteristic of a set
Author(s) -
JERNOT J. P.,
JOUANNOTCHESNEY P.,
LANTUEJOUL C.
Publication year - 2004
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.0022-2720.2004.01336.x
Subject(s) - euler's formula , tessellation (computer graphics) , discretization , set (abstract data type) , poincaré conjecture , euler characteristic , duality (order theory) , euler angles , mathematics , pure mathematics , mathematical analysis , computer science , geometry , programming language
Summary The Euler–Poincaré characteristic (EPC) of a polyconvex subset X of R d can be evaluated by covering the subset with an auxiliary tessellation, measuring its contribution within each cell of the tessellation and adding all contributions. Two different ways are proposed to define the contribution of a cell to the EPC of X. These contributions turn out to be related by duality formulae. Finally, three applications are given: the measurement of the EPC on adjacent fields, the measurement of the EPC on discretized images and the detection of defects in atomic structures.