Grain detection from 2d and 3d EBSD data--specification of the MTEX algorithm

We present a fast and versatile algorithm for the reconstruction of the grain structure from 2d and 3d Electron Back Scatter Diffraction (EBSD) data. The algorithm is rigorously derived from the modeling assumption that grain boundaries are located at the bisectors of adjacent measurement locations. This modeling assumption immediately implies that grains are composed of Voronoi cells corresponding to the measurement locations. Thus our algorithm is based on the Voronoi decomposition of the 2d or 3d measurement domain. It applies to any geometrical configuration of measurement locations and allows for missing data due to measurement errors. The definition of grains as compositions of Voronoi cells implies another fundamental feature of the proposed algorithm--its invariance with respect to spatial displacements, i.e., rotations or shifts of the specimen. This paper also serves as a reference paper for the texture analysis software MTEX, which is a comprehensive and versatile, freely available MATLAB toolbox that covers a wide range of problems in quantitative texture analysis, including the analysis of EBSD data.