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Symmetrized Bingham distribution for representing texture: parameter estimation with respect to crystal and sample symmetries
Author(s) -
Niezgoda Stephen R.,
Magnuson Eric A.,
Glover Jared
Publication year - 2016
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s160057671600649x
Subject(s) - homogeneous space , quaternion , distribution (mathematics) , texture (cosmology) , cauchy distribution , symmetry (geometry) , mathematics , sample (material) , orientation (vector space) , statistical physics , materials science , mathematical analysis , geometry , physics , computer science , artificial intelligence , thermodynamics , image (mathematics)
The quaternion Bingham distribution has been used to model preferred crystallographic orientation, or crystallographic texture, in polycrystalline materials in the materials science and geological communities. A primary difficulty in applying the Bingham distribution has been the lack of an efficient method for fitting the distribution parameters with respect to the material's underlying crystallographic symmetry or any statistical sample symmetry due to processing. This paper presents a symmetrized distribution, based on the quaternion Bingham, which can account for any general combination of crystallographic or sample symmetries. A numerical scheme is also introduced for estimating the parameters of the symmetrized distribution based on the well known expectation maximization algorithm.