Image Processing Reference
In-Depth Information
[STEP 1]
(Detection of positive border voxels and their grouping)
Extract all positive border voxels and group them according to the position of
0-voxels in their 6-neighborhood. Here a positive border voxel means a positive
voxel that has at least one 0-voxel in the 6-neighborhood. For example, a pos-
itive voxel that has a 0-voxel in the direction of
T
in Fig. 6.2 in the neighbor-
hood is classified into the group
BT
. If more than one 0-voxels exists in the 6-
neighborhood, the priority is given in the order (
T,B,W,E,N,S
). Each group
of positive border voxels is represented as
B
=
{
BT, BB, BW, BE, BN, BS
}
.
This process is written as follows.
for
all (
i, j, k
)s
do
if
(
f
ijk
>
0
)
∩
((
i, j, k
)
=endvoxel)
then
if
f
i,j,k−
1
=
0
then
w
ijk
←
2
else if
f
i,j,k
+1
=
0
then
wijk
←
3
else if
f
i−
1
,j,k
=
0
then
wijk
←
4
else if
f
i
+1
,j,k
=
0
then
wijk
←
5
else if
f
i,j−
1
,k
=
0
then
wijk
←
6
else if
f
i,j
+1
,k
=
0
then
wijk
←
7
endif
endif
enddo
[STEP 2]
(Extraction of a voxel that is of the minimum density value among
deletable voxels and that is not an end voxel) (See Note also)
Find a voxel in the set
B
that is deletable, not an edge voxel, and has the
minimum density value in
B
. Denote the density value of a detected voxel by
min.
min
Suciently large integer;
for
all (
i, j, k
)s
do
if
2
←
7
if
f
ijk
<
min
≤
w
ijk
≤
∩
((
i, j, k
) = deletable and not an edge voxel)
then
min
←
f
ijk
;
endif
endif
enddo
[STEP 3]
(Deletion)
(i)Searcheachgroupin
B
in the order of
BT, BB, BW, BE, BN, BS
.
Note: Deletability and a border voxel are defined in the same way as for a binary
image obtained by regarding all positive voxels as 1-voxels.
Note: If there is more than one deletable border voxel in some group, all of those
voxels are processed before moving to the processing of the next group. Deletion
of a voxel from an image is executed at the moment when it is found to be
deletable. That is, the corresponding voxel is replaced by a 0-voxel (sequential
algorithm). Once a voxel is given a mark of an edge voxel, it is regarded as a
finally preserved voxel and will never be deleted in the subsequent procedure.
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