Fig. 2.

The empirically observed covariance versus angle between diffusion weighting directions (b-vectors) for the HCP b = 3000 (left) and b = 7000 data sets described in Table 1. Each point represents one pair of b-vectors and the covariance is calculated across all intra-cerebral voxels. The points with zero angle corresponds to the variance (pooled across all voxels) for each direction. The solid grey line corresponds to the exponential (Eq. (9)) and the dashed black line to the spherical (Eq. (10)) covariance function. These are “Chi-by-eye” lines and are there to demonstrate their respective general appearance in relation to the empirically observed covariance. The same “length scale” parameters were used for both plots (a = 1.23 and a = 0.5 for the spherical and the exponential functions respectively).