Diagonalization

The tensor expressed in the scanner frame of reference is diagonalized to give eigenvalues and eigenvectors:

Diagonalization is done using the Jacobi routine from Numerical Recipes in C, The art of Scientific Computing. Press, WH, Teukolsky, SA, Vetterling, WT, Flannery, BP. 2nd edition, Cambridge University Press.

Here is shown an example of three eigenvalue maps, l₁, l₂, and l₃ (scaled individually):

The X, Y and Z components of the maximum eigenvector are shown here (absolute values):

The X, Y and Z components can be used to generate a RGB map, where the color shows the primary direction, such that red = (anatomical) left-right, blue = (anatomical) front-back, and green = head-toe (threshold for FA < 0.2).