Image Processing Reference
In-Depth Information
Input image:
F
=
{
f
ijk
}
; 3D positive image with the background.
Output image :
G
=
{
g
ijk
}
; result of thinning (binary image)
.
[STEP 1]
(3D GWDT)
(Initialization)
for
all (
i, j, k
)s
do
if
f
ijk
>
0
then
g
ijk
←
M
endif
M
is an integer that is suciently larger than the maximum distance value.
if
f
ijk
=
0
then
g
ijk
←
0
endif
enddo
(Iteration)
for
all (
i, j, k
)s
do
g
ijk
←
∈N
[26
(
i, j, k
)
min
{
g
ijk
,f
ijk
+
π
pqrijk
×
g
pqr
;(
p, q, r
)
}
:
π
pqrijk
is a coe
cient, assuming either value of
1
,
√
2
,or
√
3
according to the
location of (
p, q, r
)relativeto(
i, j, k
).
N
[26]
(
i, j, k
) is the 26-neighborhood of
(
i, j, k
).
enddo
(Test of the terminating rule)
Stop the procedure and go to
[STEP 2]
if no change in a voxel value occurs
in the whole of an input image. Otherwise, go to (iteration).
[STEP 2]
(Thinning)
Perform Algorithm 6.2, regarding the distance image
G
as an input positive
image. After finishing the procedure, the result of thinning of the image
F
is
stored in
.
This algorithm will be implemented easily by combining Algorithm 6.1
and 6.2.
G
6.3.2 Experimental results
An artificial 3D binary image including a geometrical figure was generated.
This figure (Object 1 and Object 2) consists of two or three cylinders in 3D
space (Figs. 6.3, 6.4). Density values inside these cylinders at the distance
r
from the axis of a cylinder are determined by [
a
r
)],where[]
represents a ceiling function,
R
= the radius of the cylinder, and
a
=the
gradient of density distribution. In real experiments,
R
=
10
and
a
=
10
.
Effects of the rotation of a figure, noise in density values, and noise in figure
shape were studied systematically. Parts of results are shown in Fig. 6.3.
The same algorithms were also tested by a real CT image. A chest CT
image taken by helical CT was processed using thresholding operations to
obtain a positive image with the background. In this image figures roughly
×
(
R
+
1
−
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