A Dictionary Approach to Electron Backscatter Diffraction Indexing.

We propose a framework for indexing of grain and subgrain structures in electron backscatter diffraction patterns of polycrystalline materials. We discretize the domain of a dynamical forward model onto a dense grid of orientations, producing a dictionary of patterns. For each measured pattern, we identify the most similar patterns in the dictionary, and identify boundaries, detect anomalies, and index crystal orientations. The statistical distribution of these closest matches is used in an unsupervised binary decision tree (DT) classifier to identify grain boundaries and anomalous regions. The DT classifies a pattern as an anomaly if it has an abnormally low similarity to any pattern in the dictionary. It classifies a pixel as being near a grain boundary if the highly ranked patterns in the dictionary differ significantly over the pixel's neighborhood. Indexing is accomplished by computing the mean orientation of the closest matches to each pattern. The mean orientation is estimated using a maximum likelihood approach that models the orientation distribution as a mixture of Von Mises-Fisher distributions over the quaternionic three sphere. The proposed dictionary matching approach permits segmentation, anomaly detection, and indexing to be performed in a unified manner with the additional benefit of uncertainty quantification.

Methodology for estimation of intrinsic dimensions and state variables of microstructures.

According to the manifold hypothesis, real data can be compressed to lie on a low-dimensional manifold. This paper explores the estimation of the dimensionality of this manifold with an interest in identifying independent degrees of freedom and possibly identifying state variables that would govern materials systems. The challenges identified that are specific to materials science are (i) accurate estimation of the number of dimensions of the data, (ii) coping with the intrinsic random and low-bit-depth nature of microstructure samples, and (iii) linking noncompressed domains such as processing to microstructure. Dimensionality estimates are made with the maximum-likelihood-estimation method with the Minkowski p-norms being used as a measure of the distance between microstructural images. It is found that, where dimensionality estimates are required to be accurate, it is necessary to use the Minkowski 1-norm (also known as the L_{1}-norm or Manhattan distance). This effect is found to be due to image quantification and proofs are given regarding the distortion produced by quantization. It is also found that homogenization is an effective way of estimating the dimension of random microstructure image sets. An estimate of 40 dimensions for the fibers of a SiC/SiC fiber composite is obtained. It is also found that, with images generated from a sparse domain (surrogate to the process domain), it is possible to infer the nature of the process manifold from images alone.