Fig. 6 : Voxel-wise scattering signal sampling and ellipsoid modelling of the scattering distribution.
From: X-ray scattering tensor tomography based finite element modelling of heterogeneous materials
a Schematic image acquisition for one voxel. b For this voxel, the scattering signals are sampled along multiple direction vector \({\hat{{{{\bf{s}}}}}}_{k}\) (here k = 1, …, 7). Then the three principal axes of an ellipsoid that fit the scattering distribution can be computed using principal component analysis (PCA). c Possible shapes of ellipsoids that voxel-wise model the scattering distribution depending on the micro-structures. For example, a voxel that mostly contains isotropic (spherical) structures has a sphere-shaped scattering distribution whereas a voxel with fibre-like structures has a flat-ellipsoid-shaped distribution as in the left-bottom part in (c). (a, b) are reprinted with permission from23. (Copyright 2024 by the American Physical Society).
