Image Processing Reference
In-Depth Information
(ii) Find and remove from
B
an element satisfying all of the following condi-
tions.
(a) A density value is equal to min.
(b) A voxel is deletable.
(c) A voxel is not an edge voxel.
(iii) Delete a voxel of an image
corresponding to the element removed
above. If the voxel is found to be not deletable in the above procedure, give a
corresponding voxel the mark showing an edge voxel.
for
bordertype =
2
to
7
do
for
all (
i, j, k
)s
do
if
(
w
ijk
F
=bordertype)
∩
(
f
ijk
=min)
then
if
(
i, j, k
)
=edgevoxel
then
if
(
i, j, k
) = deletable
then
f
ijk
←
0
endif
else
(
i, j, k
)=edgevoxel
endif
endif
enddo
enddo
[STEP 4]
(Test of the terminating rule)
if
no voxel was deleted in
[STEP 3]
then stop
else go to [STEP 1]
endif
The result of thinning is stored in an image
F
when the program finishes.
This algorithm is a sequential type and repeatedly scans the whole of a
input image (the procedure of [STEP 1]
[STEP 3] is executed repeatedly).
The number of times of iteration depends on the size (width) of an input
figure (connected component).
Next, let us present another algorithm, which is obtained by adding to the
above Algorithm 6.2 a preprocessing consisting of 3D GWDT [Naruse77a].
As was stated in the previous section, GWDT is a processing that gives each
voxel the minimum value of the sum of density values along a path (= the
weight of a path) to that voxel from a background voxel. In this algorithm,
we use the sum of density values weighted by the Euclidean distance between
adjacent voxels instead of the simple sum of density values. Weight coecients
∼
assume either of
1
,
√
2
,and
√
3
according to relative locations of an adjacent
voxel. The outline of the algorithm is as follows [Yasue96].
Algorithm 6.3 (Thinning of a gray-tone image with GWDT - out-
line).
Search WWH ::
Custom Search