## 8 Citations

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

- Materials ScienceCrystals
- 2021

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…

### Using directional statistics to test hypotheses regarding rigid body attitude: Comparison to univariate and multivariate Cardan angle tests.

- MathematicsJournal of biomechanics
- 2020

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

- Mathematics, Computer ScienceJ. Multivar. Anal.
- 2021

### Reproducing Kernels and New Approaches in Compositional Data Analysis

- Computer ScienceArXiv
- 2022

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

- PhysicsJournal of applied crystallography
- 2020

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

- Mathematics, Computer ScienceThe Annals of Statistics
- 2020

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

- Materials Science
- 2022

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…

## References

SHOWING 1-10 OF 49 REFERENCES

### Spherical Regression on Matched Pairs of Orientation Statistics

- Mathematics
- 1989

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…

### Parameter Estimation in Spherical Symmetry Groups

- MathematicsIEEE Signal Processing Letters
- 2015

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

- Chemistry
- 1997

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

- Mathematics
- 2009

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

- Mathematics
- 2006

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

- MathematicsTechnometrics
- 2016

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

- Mathematics
- 2012

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

- Geology
- 2009

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

- Mathematics
- 2004

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…