Biomedical Engineering Reference
In-Depth Information
Accepted
Tentative
Distant
−1
(t)
φ
−
1
φ
(0)
Figure 4.3: Illustration of the sets
A
,
T
, and
D
associated with the fast marching
method. This figure reprinted from [22].
for
φ
ij
is computed using Eq. 4.21. The algorithm terminates when all points
have migrated into the set
A
. See Fig. 4.3 for an illustration of the sets
A
,
T
,
and
D
.
The full algorithm for the fast marching method becomes:
1. Initialize all the points adjacent to the initial interface with an initial
value, put those points in
A
. A discussion about initialization follows in
Section 4.2.3. All points
x
i
,
j
∈
A
, adjacent to a point in
A
, are given initial
estimates for
φ
i
,
j
by solving Eq. 4.21. These points are tentative points and
put in the set
T
. All remaining points unaccounted for are placed in
D
and
given initial value of
φ
i
,
j
=+∞
.
2. Choose the point
x
i
,
j
∈
T
which has the smallest value of
φ
i
,
j
and move it
into
A
.
3. Any point which is adjacent to
x
i
,
j
(i.e. the points
x
i
−
1
,
j
,
x
i
,
j
−
1
,
x
i
+
1
,
j
, and
x
i
,
j
+
1
) which is in
T
has its value
φ
i
,
j
recalculated using Eq. 4.21. Any point
adjacent to
x
i
,
j
and in
D
has its value
φ
i
,
j
computed using Eq. 4.21 and is
moved into the set
T
.
4. If
T
=∅
, go to step 2.
