Image Processing Reference
In-Depth Information
speaking, it will be enough to prepare a 1D memory of the size of a few times
of the number of border voxels in an input image. An example of this type of
algorithms is given below.
(a) Surface thinning
Algorithm 5.5 (Surface thinning accompanied by Euclidean dis-
tance transformation using list manipulation).
Input:
= input binary image is stored when the algorithm starts.
f
ijk
=densityvalueofavoxel(
i, j, k
)thattakes
0
or
1
when the algorithm
starts. A set of 1-voxels is considered to be a figure.
m
= type of the connectivity (
m
=
6
,
18
,
18
,
26
).
Output:
F
=
{
f
ijk
}
F
{
f
ijk
}
=
= result of surface thinning is stored when the algorithm
finishes.
Border voxel list: list =
: Each element in the list consists
of 3D coordinate values of a voxel and its label.
Function int(
x
). Convert the value of an argument into an integer (omit the
fractional part).
{
e
n
:(
i
n
,j
n
,k
n
,l
n
)
}
[STEP 1]
(Squared Euclidean distance transformation (same as Algo-
rithm 5.4))
for
all (
i, j, k
)s
do
f
ijk
←
de
((
i, j, k
)
,
(
p, q, r
))
2
;
(
p,q,r
)
{
min
f
pqr
=
0
,
1
≤
p
≤
L,
1
≤
q
≤
M,
1
≤
r
≤
N
}
enddo
(For details of algorithm of the Euclidean distance transformation, see Sec-
tion 5.5)
(Shift distance values by
20
for using integers
1
∼
19
as labels)
for
all (
i, j, k
)s
do
if
(
f
ijk
=
0
),
then
f
ijk
←
f
ijk
+
20
enddo
maxd
←
(Maximum of the Euclidean distance transformation values in the
image
F
)
mind
←
(Minimum of the nonzero values of the Euclidean distance
transformation in the image
F
)
[STEP 2]
(Detection of initial border voxels and write them into the list)
for
all (
i, j, k
)s
do
if
f
ijk
>
20
and a 0-voxel exists in the 6-neighborhood of
f
ijk
then
add(
i, j, k, f
ijk
) to the list
(At this moment, the distance value of a voxel (
i
n
,j
n
,k
n
)isgivento
l
n
of
the list)
f
ijk
←
1
endif
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