Efficient computation of the angularly resolved chord length distributions and lineal path functions in large microstructure datasets

Chord length distributions (CLDs) and lineal path functions (LPFs) have been successfully utilized in prior literature as measures of the size and shape distributions of the important microscale constituents in the material system. Typically, these functions are parameterized only by line lengths, and thus calculated and derived independent of the angular orientation of the chord or line segment. We describe in this paper computationally efficient methods for estimating chord length distributions and lineal path functions for 2D (two dimensional) and 3D microstructure images defined on any number of arbitrary chord orientations. These so called fully angularly resolved distributions can be computed for over 1000 orientations on large microstructure images (5003 voxels) in minutes on modest hardware. We present these methods as new tools for characterizing microstructures in a statistically meaningful way.