Biomedical Engineering Reference
In-Depth Information
26
25
24
23
22
Exact solution
20 reinits w/ old method
20 reinits w/ new method
21
20
20
21
22
23
24
25
26
Figure 4.8:
Comparison of modern and original reinitialization results for a
coarsely meshed circle. The exact solution and the modern reinitialization
method are nearly overlapping. This figure reprinted from [22].
continually sorting the nodes, it is sufficient to simply take points out of the set
T
in the same order in which they entered. The only exception is that the initial
set of grid points in the set
T
should still start out sorted. This observation is of
interest because it reduces the computational complexity of the fast marching
method from
O
(
N
log
N
) to simply
O
(
N
) where
N
is the total number of grid
points.
4.2.5 Velocity Extensions
As noted in the previous section, reinitialization fixes the level set function when
the velocity field does not preserve the level set function as a signed distance
function. An alternative way to preserve the signed distance function is to adjust
