Image Processing Reference
In-Depth Information
(2) Denote a current voxel by (
i, j, k
).
If
f
ijk
=
1
,thengoto(3).If
f
ijk
=
0
,then
l
ijk
←
0
, and go to (4).
(3) Let us use the scanning method given in the left figure of Fig. 5.1 (b) and
denote a current voxel by
x
0
=(
i, j, k
). Denote voxels that were already
scanned in its neighborhood as in the right figure of Fig. 5.1 (b) and
assume that the label of
x
p
(= the value of an image
L
)is
l
p
(= positive
integer) (
p
=
0
,
1
,
2
,...,
13
).
(3-1) If there are
n
kinds of different positive values in
{
T
(
l
p
)
,p
=
, let us express those integers by
L
1
,L
2
,...,L
n
in the
increasing order.
If
n
=
0
(no positive value exists), then go to (3-2); go to (3-3) if
n
=
1
. Otherwise go to (3-4).
(3-2)
λ
0
,
1
,
2
,...,
13
}
←
λ
+
1
,
T
(
λ
)
←
λ
,
l
ijk
←
λ
.Goto(4).
(3-3)
l
ijk
←
L
1
.Goto(4).
(3-4)
l
ijk
←
L
1
. For all
T
(
γ
) such that
T
(
γ
)=
L
p
(
2
≤
p
≤
P,
1
≤
γ
≤
λ
),
L
1
.Goto(4).
(4) If all voxels have been processed, go to (5). Otherwise proceed to the next
voxel. Then go to (2).
(5) Rewrite all integers (labels) in the table
T
(
λ
) to the serial number integers.
Denote the maximum value (of the label) by
b
0
.Goto(6).
(6) Rewriting labels: For all (
i, j, k
)'s, if
l
ijk
>
0
,
l
ijk
←
T
(
γ
)
←
T
(
l
ijk
).
In step (3) of the above procedure,
p
≤
3
for both the 6-connectivity
case and the 18
-connectivity case,
p
≤
9
for the 18-connectivity case, and
p
13
for the 26-connectivity case. It is obvious from the definition of the
connectivity that
n
≤
3
.
This algorithm is a straightforward extension of a method that has been
widely used in 2D image processing. Although it may seem complicated, the
performance will be good if only a conventional sequential computer with a
single processor is employed, because scanning the whole of an input image is
required only twice.
In an output label image, serial numbers of integers starting by unit are
given to each connected component as its label. Therefore, the maximum label
means the number of connected components included in an input image. By
extracting voxels storing a specified integer value, we can extract individual
connected components separately. Due to these properties, labeling is fre-
quently utilized as a preprocessing in object counting or feature measurement
of images including many objects.
≤
4
for the 26-connectivity case, and otherwise
n
≤
5.3 Shrinking
Shrinking is a processing that replaces a deletable 1-voxel by a 0-voxel while
preserving topology. When shrinking is complete, a simply connected compo-
nent becomes a single isolated voxel (= only one 1-voxel). Results cannot be
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