Image Processing Reference
In-Depth Information
(
FPV
) only when the 1-voxel reached the state that the voxel is regarded as
the end point of a 3D line figure. For example, voxels existing on a plane
figure of the unit thickness cannot be deleted unless they are on a border of
a figure because the topology is not preserved if they are deleted, even if the
distance value is
1
on those voxels. However, even those voxels will become
deletable at some point when they are shaved from a border according to the
predetermined order until a centerline is obtained. Thus, some of voxels are in
the state that they are kept in without deletion during only the same cycle as is
currently executed. We call those voxels that should be preserved during only
a specific one cycle currently being executed
temporary preservation state
.We
give a specific mark showing the
temporary preservation state
to those voxels.
The following algorithm (Algorithm 5.6) was derived based on almost the
same basic policy as Algorithm 5.4.
Algorithm 5.6 (Axis thinning accompanied by Euclidean distance
transformation using list manipulation).
Explanation of input images, etc., is the same as Algorithm 5.5.
[STEP 1]
(Squared Euclidean distance transformation) (Same as Algo-
rithm 5.4 [STEP 1])
[STEP 2]
(Detection of initial border voxels and write their coordinates into
the list) (Same as Algorithm 5.5 [STEP 2])
(Main cycle processing)
[STEP 3]
(Detection of FPV and classification of border voxels;
l
n
←
0
means
FPV
.)
for
n
=
1
to
N
do
if
(
l
n
≤
mind)
then
if
C
2(=(
i
n
,j
n
,k
n
) is not deletable )
then
l
n
←
16
(
temporal preservation voxel
(
TPV
))
else
if
((
i
n
,j
n
,k
n
) is an edge voxel) (See Note)
then
exclude an element
e
n
from the list (
FPV
)
else
m
←
the number of nonzero-voxels in the 26-neighborhood of (
i
n
,j
n
,k
n
)
l
n
←
int(
m/
3
)+
7
(classification of border voxels)
endif
endif
enddo
(Subcycle processing)
[STEP 4]
(Deletion of a voxel)
Note: An edge voxel here means a voxel that has only one nonzero voxel in the
26-neighborhood.
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