Local Parameter Estimation: Results

Example distributions from a single voxel. Figure 1 (a) and (b) show samples from the marginal posterior distributions on $\theta$ and $\phi$ from the diffusion tensor model. The voxel was chosen from the splenium of the Corpus Callosum. (c) shows (a) and (b), plotted as a joint histogram around the surface of a sphere. This is then the joint marginal posterior distribution of $\theta$ and $\phi$ or the marginal posterior distribution of principal diffusion direction (PDD). Note how narrow this distribution is. This represents a high confidence in our calculated PDD, which is as predicted in an area of dense white matter such as the corpus callosum. Figure 2 (a) and (b) show samples from the marginal posterior distributions on $\theta$ and $\phi$ from the simple partial volume model. The same voxel was chosen as in Figure 1. Again (c) shows (a) and (b), plotted as a joint histogram around the surface of a sphere.

Figure 1: Samples from marginal posterior distributions of the diffusion tensor model in a white matter voxel. (a) shows samples from the marginal posterior distribution on $\theta$. (b) shows samples from the marginal posterior distribution on $\phi$. (c) shows (a) and (b) plotted around a sphere, representing the marginal posterior distribution on principal diffusion direction.

Figure 2: Samples from marginal posterior distributions of the partial volume model in a white matter voxel. (a) shows samples from the marginal posterior distribution on $\theta$. (b) shows samples from the marginal posterior distribution on $\phi$. (c) shows (a) and (b) plotted around a sphere, representing the marginal posterior distribution on principal diffusion direction.