Statistics of ambiguous rotations

  title={Statistics of ambiguous rotations},
  author={Richard Arnold and Peter E. Jupp and Helmut Schaeben},
  journal={J. Multivar. Anal.},

Reduced Statistical Representation of Crystallographic Textures Based on Symmetry-Invariant Clustering of Lattice Orientations

As proven in numerous experimental and theoretical studies, physical and mechanical properties of materials are determined by their internal structure. In the particular case of polycrystalline

Locally isometric embeddings of quotients of the rotation group modulo finite symmetries

Reproducing Kernels and New Approaches in Compositional Data Analysis

The compositional domain is re-interpreted as the quotient topology of a sphere modded out by a group action to understand the function space on compositional domains in terms of that on spheres and to use spherical harmonics theory along with reflection group actions for constructing a compositional Reproducing Kernel Hilbert Space (RKHS).

Density-based clustering of crystal (mis)orientations and the orix Python library

Data clustering incorporating symmetry is applied to crystal orientations and misorientations and the orix Python library for crystal orientation analysis is introduced.

Inference for spherical location under high concentration

It is shown that the spherical mean is, at any $f, a parametrically super-efficient estimator of $\pmb\theta$ and that the Watson and Wald tests for $\mathcal{H}_0:{\pmb \theta}={\pmb(\theta)_0$ enjoy similar, non-standard, optimality properties.

Fitting the grain orientation distribution of a polycrystalline material conditioned on a Laguerre tessellation

The description of distributions related to grain microstructure helps physicists to understand the processes in materials and their properties. This paper presents a general statistical methodology

Crystallographic Preferred Orientation

  • H. Schaeben
  • Encyclopedia of Mathematical Geosciences
  • 2021



Spherical Regression on Matched Pairs of Orientation Statistics

The matched pairs section of the analysis of 3 x 3 orientation statistics in Prentice (1986) may be improved on by constructing a rotational regression model, an analogue of spherical regression. The

A statistical model for random rotations

Parameter Estimation in Spherical Symmetry Groups

Simulations and experiments establish the advantages of the extended VMF EM-ML estimator for data acquired by Electron Backscatter Diffraction (EBSD) microscopy of a polycrystalline Nickel alloy sample.

Distributions of Misorientation Angles and Misorientation Axes for Crystallites with Different Symmetries

The misorientation angle is the simplest characteristic of the difference between orientations of two crystallites in a polycrystalline material. Another is the corresponding rotation axis. These

Modeling and Inference for Measured Crystal Orientations and a Tractable Class of Symmetric Distributions for Rotations in Three Dimensions

Electron backscatter diffraction (EBSD) is a technique used in materials science to study the microtexture of metals, producing data that measure the orientations of crystals in a specimen. We

Regression and correlation for 3 × 3 rotation matrices

This paper investigates a regression model for orthogonal matrices introduced by Prentice (1989). It focuses on the special case of 3 × 3 rotation matrices. The model under study expresses the

Bayesian Inference for a New Class of Distributions on Equivalence Classes of Three-Dimensional Orientations With Applications to Materials Science

A flexible existing model class for random rotations (called uniform-axis-random-spin models) is used to induce probability distributions on the equivalence classes of rotations to form parametric probability models for unlabeled orientation data.

Angle between principal axis triples

SUMMARY The principal axis angle ξ0, or Kagan angle, is a measure of the difference between the orientations of two seismic moment tensors. It is the smallest angle needed to rotate the principal

A Bayesian approach to determining and parametrizing earthquake focal mechanisms

SUMMARY We develop a new probabilistic (Bayesian) method for estimating the distribution of focal mechanism parameters, based on seismic-wave polarity data. We investigate the use of generalized

The Bingham Distribution of Quaternions and Its Spherical Radon Transform in Texture Analysis

AbstractSpherical geometry of quaternions is employed to characterize the Bingham distribution on the 3-dimensional sphere $${\mathbb{S}}^3 \subset {\mathbb{R}}^4 $$ as being uniquely composed of a