Image Processing Reference
In-Depth Information
z
pqr
←
k
r
pqr
←
f
ijk
endif
enddo
enddo
for
all (
i, j, k
) such that
r
ijk
>
0
do
h
(
x
ijk
)(
y
ijk
)(
z
ijk
)
←
1
enddo
Algorithm 5.16 (Extraction of Skeleton 2 of Def. 5.9).
Input image
F
=
{
f
ijk
}
: Squared Euclidean DT image.
Output image:
: Skeleton image. Initial value is
0
for all voxels.
In the output, the value
1
is given to skeleton voxels, and
0
is given to
other voxels.
Work arrays
H
=
{
h
ijk
}
G
=
V
=
g
ijk
}
v
ijk
}
G
=
{
g
ijk
}
,
U
=
{
u
ijk
}
,
V
=
{
v
ijk
}
,
{
,
{
,
:Initialvalueis
0
for all voxels in all arrays.
During executing the program, all voxel values outside of an input image are
regarded as
0
. Arrays
and
T
=
{
t
n
}
G
,and
V
are assigned to the same
G
V
and
and
memory space, respectively.
[STEP 1]
(Generation of a label image)
Input image:
F
=
{
f
ijk
}
squared Euclidean DT image
Output image:
(label image)
Scan an input image, and give labels represented by sequential positive num-
bers starting by
1
to a voxel of
U
=
{
u
ijk
}
F
having a positive value, that is,
f
ijk
>
0
.
Labels are written into a corresponding voxel of a work array
U
.
[STEP 2]
(Reverse distance transformation with labels)
(1) Processing in the row direction (forward scan)
Input image:
F
=
{
f
ijk
}
Squared Euclidean distance transformation image,
U
(label image).
Output image:
=
{
u
ijk
}
G
=
{
g
ijk
}
(Reverse Euclidean distance transformation im-
age),
(label image).
Perform the following procedure in each row with increasing suxes
i
from
1
until
M
.
(a) If
f
ijk
<f
(
i−
1)
jk
,
perform the following procedure for
n
such that
0
V
=
{
v
ijk
}
≤
n
≤
(
f
(
i−
1)
jk
−
f
ijk
−
1
)
/
2
,
(a-1) if
f
(
i
+
n
)
jk
≥
(
n
+
1
)
2
, go to the next
i
,
f
(
i−
1)
jk
−
(a-2) unless (a-1),
(a-2-1) if
g
(
i
+
n
)
jk
<f
(
i−
1)
jk
−
(
n
+
1
)
2
,
(
n
+
1
)
2
,
g
(
i
+
n
)
jk
←
f
(
i−
1)
jk
−
u
(
i−
1)
jk
,
go to the next
n
.
(a-2-2) otherwise, go to the next
n
.
(b) If
f
ijk
≥
v
(
i
+
n
)
jk
←
f
(
i−
1)
jk
,
(b-1) if
g
ijk
<f
ijk
,
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