Statistical Estimation and Clustering of Group-invariant Orientation Parameters
Abstract
We treat the problem of estimation of orientation parameters whose values are invariant to transformations from a spherical symmetry group. Previous work has shown that any such group-invariant distribution must satisfy a restricted finite mixture representation, which allows the orientation parameter to be estimated using an Expectation Maximization (EM) maximum likelihood (ML) estimation algorithm. In this paper, we introduce two parametric models for this spherical symmetry group estimation problem: 1) the hyperbolic Von Mises Fisher (VMF) mixture distribution and 2) the Watson mixture distribution. We also introduce a new EM-ML algorithm for clustering samples that come from mixtures of group-invariant distributions with different parameters. We apply the models to the problem of mean crystal orientation estimation under the spherically symmetric group associated with the crystal form, e.g., cubic or octahedral or hexahedral. Simulations and experiments establish the advantages of the extended EM-VMF and EM-Watson estimators for data acquired by Electron Backscatter Diffraction (EBSD) microscopy of a polycrystalline Nickel alloy sample.
Cite
@article{arxiv.1503.04474,
title = {Statistical Estimation and Clustering of Group-invariant Orientation Parameters},
author = {Yu-Hui Chen and Dennis Wei and Gregory Newstadt and Marc DeGraef and Jeffrey Simmons and Alfred Hero},
journal= {arXiv preprint arXiv:1503.04474},
year = {2015}
}
Comments
arXiv admin note: text overlap with arXiv:1411.2540