Boundary identification in EBSD data with a generalization of fast multiscale clustering

Electron backscatter diffraction (EBSD) studies of cellular or subgrain microstructures present problems beyond those in the study of coarse-grained polycrystalline aggregates. In particular, identification of boundaries delineating some subgrain structures, such as microbands, cannot be accomplished simply with pixel-to-pixel misorientation thresholding because many of the boundaries are gradual transitions in crystallographic orientation. Fast multiscale clustering (FMC) is an established data segmentation technique that is combined here with quaternion representation of orientation to segment EBSD data with gradual transitions. This implementation of FMC addresses a common problem with segmentation algorithms, handling data sets with both high and low magnitude boundaries, by using a novel distance function that is a modification of Mahalanobis distance. It accommodates data representations, such as quaternions, whose features are not necessarily linearly correlated but have known distance functions. To maintain the linear run time of FMC with such data, the method requires a novel variance update rule. Although FMC was originally an algorithm for two-dimensional data segmentation, it can be generalized to analyze three-dimensional data sets. As examples, several segmentations of quaternion EBSD data sets are presented.