Next: Fiber Tracing Algorithm Up: Method Previous: Streamline Integration

The ``Mountain'' function

 
Figure 6: Height plot for anisotropy measure (``mountain'' function) described in Section 2.6 for an axial slice of the data. The higher portions, red, corresponds to stronger anisotropy. See Eq. $(30)$.

 

For the continuous tensor field, we use a anisotropy measure height function $c_\ell(x,y,z)$, defined using a continues version of Eq. 4:

\begin{displaymath}
c_\ell(x,y,z) = \frac{\lambda_1 - \lambda_2}{\lambda_1 + \lambda_2 +\lambda_3}\\
\end{displaymath} (30)

where $\lambda_i$ are eigenvalues of $T(x,y,z)$. Metaphorically, we call this a ``mountain function'' because we initiate the fibers at the high points and peaks of the mountain (the most highly directional portions of a region) and grow them following the major eigenvector directions. The metaphor continues as the anisotropy measure decreases; we let the fibers grow until they go ``under water'' into the lakes (corresponding to a chosen lower value for the anisotropy measure); the low anisotropy values indicate an absence of fibers. We can also incorporate the mountain function within the filter function $g()$ itself, so that the higher regions will be given more weight in the scheme.

Next: Fiber Tracing Algorithm Up: Method Previous: Streamline Integration
Leonid Zhukov 2003-01-05