Biomedical Engineering Reference
In-Depth Information
of the rest of the level set method. However, if that is not the case, the reader
should see [2] for a detailed description of the narrow band method.
4.2.7 Assembling the Basic Algorithm
To summarize this section, we conclude with an algorithmic description of the
full level set method. The strategies of using reinitialization or velocity exten-
sions are similar, so the algorithms will be presented together.
1. Initialize
φ
to be the signed distance function to the initial interface
.If
necessary, reinitialization can be used to enforce this condition.
2. Compute the speed function
F
. This is, obviously, application dependent.
3. Determine
F
ext
from
F
(if using velocity extensions).
4. Advance
φ
in time using Eq. 4.5, with speed
F
(or
F
ext
if using velocity
extensions).
5. Reinitialize (if using reinitialization).
6. Return to step 2.
Note that reinitialization does not have to be done every time step, but can
be done as needed, so step 5 can be skipped most of the time. The frequency of
reinitialization is application dependent. Automated detectors for determining
when reinitialization is required have been proposed, but the computational cost
of these detectors is of the same order of magnitude as doing reinitialization in
the first place. Consequently, it is preferable to simply choose an appropriate
number of time steps between each reinitialization.
On the other hand, velocity extensions must be done every time step. The
common belief that the velocity extension method is more accurate was certainly
true when it was first introduced. However, improvements in the reinitialization
process have closed the gap. Nonetheless, for the majority of applications, the
speed function
F
is defined only on the front, so velocity extensions will be
required every step anyway, just to be able to use Eq. 4.5. In that case, it makes
more sense to use velocity extensions and never do reinitialization. For the
remainder of the applications where stability is a concern, it is essentially a
toss-up between the two.
