Figure 2
From: Dynamic X-ray radiography reveals particle size and shape orientation fields during granular flow
Determination method of fabric properties (particle size and orientation). From left to right: (a) patches of 64 × 64 pixels are extracted from a radiograph, (b) multiplied by a circular Hamming window, and (c) processed by a two-dimensional Fourier transform, leading to the power spectrum of the patch, from which two different processes are applied. Top line: (d) the spectrum is summed on circular shells, leading to (e) the energy distribution function of the radius. Bottom line: (f) the spectrum is multiplied by the orientation matrix Q(K) (cf. equation (4)), and summed over all wavevectors k, leading to the symmetric matrix T (cf. equation (5)), that (g) can also be represented by an ellipse based on its eigenvalues (ellipse shape) and eigenvectors (ellipse orientation).
