Symmetrized Bingham Distribution for Representing Texture: Parameter estimation with respect to crystal and sample symmetries

TL;DR

This paper introduces a symmetrized quaternion Bingham distribution that models crystallographic textures considering symmetries, along with an EM-based parameter estimation method for improved fitting in materials science.

Contribution

The paper presents a novel symmetrized Bingham distribution and an EM algorithm for efficient parameter estimation accounting for crystal and sample symmetries.

Findings

Effective modeling of texture with symmetry considerations

Accurate parameter estimation using EM algorithm

Applicable to diverse crystallographic symmetries

Abstract

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 materials underlying crystallographic symmetry or any statistical sample symmetry due to processing. In this paper we present a symmetrized distribution, based on the quaternion Bingham, which can account for any general combination of crystallographic or sample symmetries. We also introduce a numerical scheme for estimating the parameters of the symmetrized distribution based on the well known expectation maximization algorithm.